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工程力学
Engineering Mechanics
Since 1984 Monthly
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Chief Editor: Xinzheng LU
Editor & Publisher: 《工程力学》杂志社
ISSN 1000-4750 CN 11-2595/O3
Articles online first have been peer-reviewed and accepted, which are not yet assigned to volumes /issues, but are citable by Digital Object Identifier (DOI).
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2023 No. 4, Publish Date: 2023-04-25
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2023, 40(4): 1-11.
doi: 10.6052/j.issn.1000-4750.2022.08.ST06
Abstract:
The hub station structure is generally composed of a large-span roof structure and a lower concrete frame structure, and it also contains non-structural components such as piping system. It is of great significance to study the seismic response characteristics of the complex hub station structure under the influence of multiple factors to ensure its seismic safety. 4 typical hub station structures are selected and the finite element method is used to analyze their seismic response characteristics. The results show that the hub station structures are characterized by 'upper flexibility and lower rigidity'. The seismic responses of the hub station structure are amplified twice from the bases to the tops of the roof structures. The roof structures are vertical earthquake sensitive, and the distribution pattern of inter-story displacement of the lower frame structures is different from that of the common frames. After considering the soil-structure interaction, the self-oscillation frequency of the hub structure is reduced, the deformation of the hub roof structure is increased, and the stress distribution of the bars tends to be uniform. For different hub station structures, the focal mechanisms of the most unfavorable ground motions are different. The adverse effect of seismic traveling wave effect shall be considered for lower frame structures, and the traveling wave effect may not be considered for the roof structures. The seismic response of the pipeline system has undergone three amplifications from the base of the hub station structure to the pipeline system. The seismic performance analysis of the pipeline system in the hub station must consider the amplification of the seismic response of the pipeline system by the main structure.
The hub station structure is generally composed of a large-span roof structure and a lower concrete frame structure, and it also contains non-structural components such as piping system. It is of great significance to study the seismic response characteristics of the complex hub station structure under the influence of multiple factors to ensure its seismic safety. 4 typical hub station structures are selected and the finite element method is used to analyze their seismic response characteristics. The results show that the hub station structures are characterized by 'upper flexibility and lower rigidity'. The seismic responses of the hub station structure are amplified twice from the bases to the tops of the roof structures. The roof structures are vertical earthquake sensitive, and the distribution pattern of inter-story displacement of the lower frame structures is different from that of the common frames. After considering the soil-structure interaction, the self-oscillation frequency of the hub structure is reduced, the deformation of the hub roof structure is increased, and the stress distribution of the bars tends to be uniform. For different hub station structures, the focal mechanisms of the most unfavorable ground motions are different. The adverse effect of seismic traveling wave effect shall be considered for lower frame structures, and the traveling wave effect may not be considered for the roof structures. The seismic response of the pipeline system has undergone three amplifications from the base of the hub station structure to the pipeline system. The seismic performance analysis of the pipeline system in the hub station must consider the amplification of the seismic response of the pipeline system by the main structure.
2023, 40(4): 12-20.
doi: 10.6052/j.issn.1000-4750.2021.09.0753
Abstract:
Based on three kinds of conventional Monte Carlo simulation methods for multidirectional irregular waves, the corresponding original spectral representations of a spatio-temporal random field are proposed. Then three dimension-reduction methods for simulating multidirectional irregular waves are derived by introducing the dimension-reduction idea of a random function. As a result, the random field of multidirectional irregular waves is accurately represented by employing merely 2-4 elementary random variables. Numerical examples show that the effective wave heights of the representative samples simulated by the three dimension-reduction methods can satisfy the normative requirements. Meanwhile, the second-order statistics (simulated values) of the representative sample set fit well with the target values. In general, the accuracy of the proposed method is higher than that of the conventional Monte Carlo scheme, which verifies the validity of the former. In addition, by analyzing the simulation accuracy and efficiency of the three dimension-reduction methods, the most suitable scheme of multidirectional irregular waves for engineering application is proposed. This provides an effective way, combining the probability density evolution theory, for the refined dynamic analysis of offshore engineering structures subjected to random waves.
Based on three kinds of conventional Monte Carlo simulation methods for multidirectional irregular waves, the corresponding original spectral representations of a spatio-temporal random field are proposed. Then three dimension-reduction methods for simulating multidirectional irregular waves are derived by introducing the dimension-reduction idea of a random function. As a result, the random field of multidirectional irregular waves is accurately represented by employing merely 2-4 elementary random variables. Numerical examples show that the effective wave heights of the representative samples simulated by the three dimension-reduction methods can satisfy the normative requirements. Meanwhile, the second-order statistics (simulated values) of the representative sample set fit well with the target values. In general, the accuracy of the proposed method is higher than that of the conventional Monte Carlo scheme, which verifies the validity of the former. In addition, by analyzing the simulation accuracy and efficiency of the three dimension-reduction methods, the most suitable scheme of multidirectional irregular waves for engineering application is proposed. This provides an effective way, combining the probability density evolution theory, for the refined dynamic analysis of offshore engineering structures subjected to random waves.
2023, 40(4): 21-34.
doi: 10.6052/j.issn.1000-4750.2021.10.0763
Abstract:
The two-dimensional thermoelectric coupling problem of an infinite thermoelectric plate with elliptical hole subjected to the action of uniform electric current and uniform total energy flux is studied. The analytical solutions of the electric current density and total energy flux are derived by the complex variable function method and the conformal mapping technique. The theoretical results of the degradation of elliptical hole to circular hole are compared with the results of uniform material with circular hole, and the theoretical derivation is verified. The thermal stress caused by the interference of elliptical hole in insulation with uniform heat flow is analyzed numerically by the method of complex function. The results show that the electric current density and energy flux concentration appear at the axial end of the elliptical hole. When the loaded current direction is parallel to the long axis direction, the electric current density and energy flux decrease with the increase of the axis ratio of the elliptical hole. When they are not parallel, the electric current density and energy flux increase with the increase of the axial ratio of the elliptical hole, and increase with the increase of the angle between the direction of the loaded electric current and the long axis direction of the elliptical hole. The thermal stress caused by uniform heat flow is concentrated at the axial end of the elliptical hole. The thermal stress increases with the increase of the axial ratio of the elliptical hole and the angle between the direction of the loaded electric current and the long axis direction of the elliptical hole.
The two-dimensional thermoelectric coupling problem of an infinite thermoelectric plate with elliptical hole subjected to the action of uniform electric current and uniform total energy flux is studied. The analytical solutions of the electric current density and total energy flux are derived by the complex variable function method and the conformal mapping technique. The theoretical results of the degradation of elliptical hole to circular hole are compared with the results of uniform material with circular hole, and the theoretical derivation is verified. The thermal stress caused by the interference of elliptical hole in insulation with uniform heat flow is analyzed numerically by the method of complex function. The results show that the electric current density and energy flux concentration appear at the axial end of the elliptical hole. When the loaded current direction is parallel to the long axis direction, the electric current density and energy flux decrease with the increase of the axis ratio of the elliptical hole. When they are not parallel, the electric current density and energy flux increase with the increase of the axial ratio of the elliptical hole, and increase with the increase of the angle between the direction of the loaded electric current and the long axis direction of the elliptical hole. The thermal stress caused by uniform heat flow is concentrated at the axial end of the elliptical hole. The thermal stress increases with the increase of the axial ratio of the elliptical hole and the angle between the direction of the loaded electric current and the long axis direction of the elliptical hole.
2023, 40(4): 35-45.
doi: 10.6052/j.issn.1000-4750.2021.10.0760
Abstract:
In order to study the seismic performance of square concrete filled steel tubular (CFST) short columns, a total of 6 specimens with different cross-sectional sizes were tested under combined constant axial loading and cyclic lateral loading. The failure mode, hysteretic curves, skeleton curves and seismic performance indexes (e. g. stiffness degradation, energy dissipation, ductility, et al.) with different cross-section sizes were analyzed. Meanwhile, the nominal shear strength of specimens with different cross-section sizes was studied. The results indicate that the final failure modes, i.e., the bulge formed a complete ring on each side and the core concrete crushed at the same location, are similar for all columns with different cross-sectional sizes. The decline of nominal shear strength can be observed obviously as the structural size increases, i.e. the nominal shear strength decreases by 63.1% and 59.8% as the cross-section size varies from 200 mm to 600 mm under two opposite loading directions, indicating an obvious size effect; the relative nominal stiffness and the average energy dissipation coefficient decrease with the increase of structural size. The predicted values of shear strength formula that considers the size effect agree well with the tested values, implying this formula can be used to evaluate the shear capacity of square CFST short columns.
In order to study the seismic performance of square concrete filled steel tubular (CFST) short columns, a total of 6 specimens with different cross-sectional sizes were tested under combined constant axial loading and cyclic lateral loading. The failure mode, hysteretic curves, skeleton curves and seismic performance indexes (e. g. stiffness degradation, energy dissipation, ductility, et al.) with different cross-section sizes were analyzed. Meanwhile, the nominal shear strength of specimens with different cross-section sizes was studied. The results indicate that the final failure modes, i.e., the bulge formed a complete ring on each side and the core concrete crushed at the same location, are similar for all columns with different cross-sectional sizes. The decline of nominal shear strength can be observed obviously as the structural size increases, i.e. the nominal shear strength decreases by 63.1% and 59.8% as the cross-section size varies from 200 mm to 600 mm under two opposite loading directions, indicating an obvious size effect; the relative nominal stiffness and the average energy dissipation coefficient decrease with the increase of structural size. The predicted values of shear strength formula that considers the size effect agree well with the tested values, implying this formula can be used to evaluate the shear capacity of square CFST short columns.
2023, 40(4): 46-57.
doi: 10.6052/j.issn.1000-4750.2021.09.0723
Abstract:
This research intends to reduce the post-earthquake residual inter-story drift, enhance the seismic collapse-resistant capacity and avoid the soft-story failure due to inter-story drift concentration of moment-resisting frame (MRF) through the implementation of self-centering energy-absorbing rocking core (SCENARIO). Based on the continuum distributed parameter model, the influences of moment-resisting stiffness and lateral force-resisting stiffness of SCENARIO on the inter-story drift distribution and capacity of SCENARIO and MRF are studied. This research proposes the displacement-based design method of MRF retrofitted with SCENARIO, and the detailed design procedures are also provided. A three-story MRF is retrofitted with SCENARIO following the proposed design procedure. The results from the static pushover and dynamic analyses indicate that the SCENARIO can efficiently reduce the post-earthquake residual inter-story drift of MRF, and produce a uniform inter-story drift distribution. Moreover, the retrofitted building can achieve the performance objective.
This research intends to reduce the post-earthquake residual inter-story drift, enhance the seismic collapse-resistant capacity and avoid the soft-story failure due to inter-story drift concentration of moment-resisting frame (MRF) through the implementation of self-centering energy-absorbing rocking core (SCENARIO). Based on the continuum distributed parameter model, the influences of moment-resisting stiffness and lateral force-resisting stiffness of SCENARIO on the inter-story drift distribution and capacity of SCENARIO and MRF are studied. This research proposes the displacement-based design method of MRF retrofitted with SCENARIO, and the detailed design procedures are also provided. A three-story MRF is retrofitted with SCENARIO following the proposed design procedure. The results from the static pushover and dynamic analyses indicate that the SCENARIO can efficiently reduce the post-earthquake residual inter-story drift of MRF, and produce a uniform inter-story drift distribution. Moreover, the retrofitted building can achieve the performance objective.
2023, 40(4): 58-70.
doi: 10.6052/j.issn.1000-4750.2021.09.0693
Abstract:
An experimental study on two two-story-two-span CFST frames with or without internal stirrups subjected to horizontal cyclic loading was conducted. The frame specimens were scaled down to 2∶5. The objective of this study is to investigate the influence of stirrups welded inside the CFST columns on the aseismic performance of the frames. Numerical analysis was carried out using ABAQUS, and the finite element model was verified by comparing the test results. Based on the FE models, the influence of the equivalent stirrup ratio was investigated. The experimental and numerical analysis results indicate that the stirrups reduce the slippage between steel tube and infilled concrete and, strengthen the confinement effect of steel tube on infilled concrete at same time. Moreover, the flexural bearing capacity and energy dissipation capacity of the frames were improved. The stirrups also change the ratio of line stiffness and flexural bearing capacity between beam and column indirectly. Compared with the conventional frames, the frames designed using ‘strong columns’ can improve the stiffness, bearing capacity and energy dissipation capacity of the frames by more than 70%, 20% and 50%, respectively.
An experimental study on two two-story-two-span CFST frames with or without internal stirrups subjected to horizontal cyclic loading was conducted. The frame specimens were scaled down to 2∶5. The objective of this study is to investigate the influence of stirrups welded inside the CFST columns on the aseismic performance of the frames. Numerical analysis was carried out using ABAQUS, and the finite element model was verified by comparing the test results. Based on the FE models, the influence of the equivalent stirrup ratio was investigated. The experimental and numerical analysis results indicate that the stirrups reduce the slippage between steel tube and infilled concrete and, strengthen the confinement effect of steel tube on infilled concrete at same time. Moreover, the flexural bearing capacity and energy dissipation capacity of the frames were improved. The stirrups also change the ratio of line stiffness and flexural bearing capacity between beam and column indirectly. Compared with the conventional frames, the frames designed using ‘strong columns’ can improve the stiffness, bearing capacity and energy dissipation capacity of the frames by more than 70%, 20% and 50%, respectively.
2023, 40(4): 71-79.
doi: 10.6052/j.issn.1000-4750.2021.09.0734
Abstract:
In order to overcome the difficulty of elastic modulus adjustment procedures applied in reinforced concrete (RC) structures, a homogeneous generalized yield function is developed for RC eccentric compression member with rectangular section. The piecewise-smooth interaction equation of bearing capacity is developed for RC eccentric compression members with rectangular section using the quadratic function and their failure mechanism is considered. The partition expressions of sectional characteristic function are proposed through regression analysis to consider the influence of the sectional geometry and material property on the bearing capacity, hence the homogeneous generalized yield function is developed for these members by adopting the first order polynomials with fractional exponential power. Furthermore, an adaptive criterion for identification of highly stressed element is defined by using the element bearing ratio. The elastic modulus of the highly-stressed element is reduced strategically so that the ultimate bearing capacity of RC arches is evaluated by linear elastic iteration. Compared with the model test and the incremental non-linear finite element method, the proposed method proves to have high computational accuracy and efficiency.
In order to overcome the difficulty of elastic modulus adjustment procedures applied in reinforced concrete (RC) structures, a homogeneous generalized yield function is developed for RC eccentric compression member with rectangular section. The piecewise-smooth interaction equation of bearing capacity is developed for RC eccentric compression members with rectangular section using the quadratic function and their failure mechanism is considered. The partition expressions of sectional characteristic function are proposed through regression analysis to consider the influence of the sectional geometry and material property on the bearing capacity, hence the homogeneous generalized yield function is developed for these members by adopting the first order polynomials with fractional exponential power. Furthermore, an adaptive criterion for identification of highly stressed element is defined by using the element bearing ratio. The elastic modulus of the highly-stressed element is reduced strategically so that the ultimate bearing capacity of RC arches is evaluated by linear elastic iteration. Compared with the model test and the incremental non-linear finite element method, the proposed method proves to have high computational accuracy and efficiency.
2023, 40(4): 80-90.
doi: 10.6052/j.issn.1000-4750.2021.09.0745
Abstract:
To investigate the global buckling behaviour of welded I-section overhanging beams of Q460 high strength steel and to develop the global buckling design method for such beams in the code, six overhanging beams were totally tested under concentrated loads. The initial geometric imperfections and the residual stresses were all measured. The test results show that when the dominative stability segment of specimens is located in the simply supported span, the global buckling capacity of the specimens decreases with the increase of the overhanging’s length-to-span ratio and the height-to-width ratio of the cross section has a greater effect on the global buckling capacity of the overhanging beam than that of overhanging’s length-to-span ratio. By the grounds of the test, the finite element model considering initial geometric imperfections and residual stresses was developed. The model was validated against test results, and a good agreement was obtained. According to the validated finite element model, parametric studies were carried out to analyze the effects of the loading form, of the loading ratio, of the simply supported span length, of the overhanging length and, of the height-to-width ratio on the global buckling capacity of welded I-section overhanging beams of Q460 high strength steel. Based on the results of eigenvalue buckling analysis, the calculated formulas of elastic critical moment for the overhanging beam were obtained by regression. Furthermore, the calculated formulas of ultimate moment for the Q460 high strength steel welded I-section overhanging beam was proposed through the regression results of test and finite element parametric analysis.
To investigate the global buckling behaviour of welded I-section overhanging beams of Q460 high strength steel and to develop the global buckling design method for such beams in the code, six overhanging beams were totally tested under concentrated loads. The initial geometric imperfections and the residual stresses were all measured. The test results show that when the dominative stability segment of specimens is located in the simply supported span, the global buckling capacity of the specimens decreases with the increase of the overhanging’s length-to-span ratio and the height-to-width ratio of the cross section has a greater effect on the global buckling capacity of the overhanging beam than that of overhanging’s length-to-span ratio. By the grounds of the test, the finite element model considering initial geometric imperfections and residual stresses was developed. The model was validated against test results, and a good agreement was obtained. According to the validated finite element model, parametric studies were carried out to analyze the effects of the loading form, of the loading ratio, of the simply supported span length, of the overhanging length and, of the height-to-width ratio on the global buckling capacity of welded I-section overhanging beams of Q460 high strength steel. Based on the results of eigenvalue buckling analysis, the calculated formulas of elastic critical moment for the overhanging beam were obtained by regression. Furthermore, the calculated formulas of ultimate moment for the Q460 high strength steel welded I-section overhanging beam was proposed through the regression results of test and finite element parametric analysis.
2023, 40(4): 91-101.
doi: 10.6052/j.issn.1000-4750.2021.10.0754
Abstract:
An inerter system can absorb vibration energy efficiently and amplify the deformation of its internal energy dissipating device (EDD), thereby improving the EDD’s efficiency of energy dissipation and response mitigation. This is called the characteristic of damping enhancement, which is the key mechanism of the inerter system and can be used as a concise design principle for the inerter system. However, the existing damping-enhancement formulae for the design of inerter systems are complicated and inconvenient to apply. To give full play to the damping enhancement characteristic of the inerter system, the “maximum damping enhancement” is adopted as the design principle, and the satisfaction of the performance demands is taken as the direct goal. And then the closed-form design formulae are obtained. Based on the theory of random vibration, the closed-form formulae of the mean-square responses for a single-degree-of-freedom (SDOF) structure with an inerter system are obtained under the white noise excitation, and the expressions of optimal parameters of the inerter system are derived according to the extremum conditions and the non-inherent-damping assumption. The design process of the inerter damping system is provided based on the principle of damping enhancement and the closed-form formulae. The corresponding computer program is developed for the design and performance verification of SDOF structures with inerter systems. The analysis results of the design cases confirm the correctness and validity of the design principles and the simple closed-form formulae in this paper.
An inerter system can absorb vibration energy efficiently and amplify the deformation of its internal energy dissipating device (EDD), thereby improving the EDD’s efficiency of energy dissipation and response mitigation. This is called the characteristic of damping enhancement, which is the key mechanism of the inerter system and can be used as a concise design principle for the inerter system. However, the existing damping-enhancement formulae for the design of inerter systems are complicated and inconvenient to apply. To give full play to the damping enhancement characteristic of the inerter system, the “maximum damping enhancement” is adopted as the design principle, and the satisfaction of the performance demands is taken as the direct goal. And then the closed-form design formulae are obtained. Based on the theory of random vibration, the closed-form formulae of the mean-square responses for a single-degree-of-freedom (SDOF) structure with an inerter system are obtained under the white noise excitation, and the expressions of optimal parameters of the inerter system are derived according to the extremum conditions and the non-inherent-damping assumption. The design process of the inerter damping system is provided based on the principle of damping enhancement and the closed-form formulae. The corresponding computer program is developed for the design and performance verification of SDOF structures with inerter systems. The analysis results of the design cases confirm the correctness and validity of the design principles and the simple closed-form formulae in this paper.
2023, 40(4): 102-115.
doi: 10.6052/j.issn.1000-4750.2021.10.0765
Abstract:
In order to study the flexural performance of high-strength steel reinforced ultra-high performance concrete (UHPC) beams, six specimens were designed and tested under static loads, with the variation parameters being the steel ratio, position of steel and volume fraction of steel fiber. The failure patterns and curves between load and mid-span deflection of specimens were obtained. The bearing capacity, deformation capacity and strain variation laws of steel, longitudinal reinforcements and UHPC were analyzed. Based on experimental study, the finite element analysis model of flexural performance of high-strength steel reinforced UHPC beams was established, and the calculated results were in consistence with experimental results. Then parametric analysis was carried out. The results showed that the appropriate reinforcement failure occurred for all specimens, and longitudinal tensile reinforcements and bottom flange of steel yielded first and then UHPC of compression zone was crushed. At the failure stage, the load experienced four stages, including sudden drop, fluctuation, slow rise and slow decline. The deformation capacity coefficients of specimens were larger than 5, showing strong deformation capacity. The strain of UHPC conformed to plane section assumption before cracking of specimen; but only the strain of UHPC at the compression zone and a small part of the tensile zone near the neutral axis distributed linearly after cracking. Higher steel ratio and steel strength lead to larger bearing capacity and deformation capacity of specimens. When the compression strength of UHPC increased and the position of steel moved down, the bearing capacity of specimens increased but the deformation capacity decreased. When the volume fraction of steel fiber increased, the crack resistance and deformation capacity increased, but the bearing capacity changed insignificantly.
In order to study the flexural performance of high-strength steel reinforced ultra-high performance concrete (UHPC) beams, six specimens were designed and tested under static loads, with the variation parameters being the steel ratio, position of steel and volume fraction of steel fiber. The failure patterns and curves between load and mid-span deflection of specimens were obtained. The bearing capacity, deformation capacity and strain variation laws of steel, longitudinal reinforcements and UHPC were analyzed. Based on experimental study, the finite element analysis model of flexural performance of high-strength steel reinforced UHPC beams was established, and the calculated results were in consistence with experimental results. Then parametric analysis was carried out. The results showed that the appropriate reinforcement failure occurred for all specimens, and longitudinal tensile reinforcements and bottom flange of steel yielded first and then UHPC of compression zone was crushed. At the failure stage, the load experienced four stages, including sudden drop, fluctuation, slow rise and slow decline. The deformation capacity coefficients of specimens were larger than 5, showing strong deformation capacity. The strain of UHPC conformed to plane section assumption before cracking of specimen; but only the strain of UHPC at the compression zone and a small part of the tensile zone near the neutral axis distributed linearly after cracking. Higher steel ratio and steel strength lead to larger bearing capacity and deformation capacity of specimens. When the compression strength of UHPC increased and the position of steel moved down, the bearing capacity of specimens increased but the deformation capacity decreased. When the volume fraction of steel fiber increased, the crack resistance and deformation capacity increased, but the bearing capacity changed insignificantly.
2023, 40(4): 116-128, 192.
doi: 10.6052/j.issn.1000-4750.2021.10.0769
Abstract:
The evaluation of modal identification accuracy runs through the whole process of modal recognition research, but the evaluation method of modal identification accuracy based on a single or a few examples is accidental. Therefore, a method for evaluating modal identification accuracy based on structural response database is proposed. The key step of database construction is to calculate the structural response based on modal parameters. A database construction method is proposed to construct the physical model of structures (mass, stiffness and damping matrix) based on modal parameters, and then calculate the structural response, and the feasibility is verified with an example. Random subspace legal order is difficult, and false mode elimination is difficult; An optimized random subspace method based on singular entropy incremental order determination and two-stage spurious mode elimination in steady state diagram is proposed, and the identification accuracy of the optimized random subspace method is evaluated by database method. The results show that the method based on database is feasible. The optimized random subspace method has high identification accuracy of frequency and mode shape, but low identification accuracy of damping ratio.
The evaluation of modal identification accuracy runs through the whole process of modal recognition research, but the evaluation method of modal identification accuracy based on a single or a few examples is accidental. Therefore, a method for evaluating modal identification accuracy based on structural response database is proposed. The key step of database construction is to calculate the structural response based on modal parameters. A database construction method is proposed to construct the physical model of structures (mass, stiffness and damping matrix) based on modal parameters, and then calculate the structural response, and the feasibility is verified with an example. Random subspace legal order is difficult, and false mode elimination is difficult; An optimized random subspace method based on singular entropy incremental order determination and two-stage spurious mode elimination in steady state diagram is proposed, and the identification accuracy of the optimized random subspace method is evaluated by database method. The results show that the method based on database is feasible. The optimized random subspace method has high identification accuracy of frequency and mode shape, but low identification accuracy of damping ratio.
2023, 40(4): 129-143.
doi: 10.6052/j.issn.1000-4750.2021.10.0771
Abstract:
Accurate finite element analysis (FEA) depends on the accurate definition of materials. The definition of material properties of large-rupture-strain fiber reinforced polymer (LRS FRP) in the fiber direction is realized by writing the user subroutine UMAT. Based on the theoretical framework of the concrete damaged plasticity model in Abaqus, a modified concrete damaged plasticity model is proposed to define the material properties of LRS FRP-confined concrete. These modifications include: the parameter K related to the yield criterion is calibrated by the test data of LRS FRP-confined concrete; the hardening/softening criterion is related to the confinement stiffness; the flow rule is related to axial plastic strain. The modified material model is used for FEA. The results show that the stress-strain curve predicted by FEA is consistent with the test results. Based on the FEA results, the non-uniform of stress distribution on the rectangular column section is discussed, which can be divided into effective confinement area and weak confinement area according to the confinement effect, and the non-uniform stress distribution in the effective confinement area increases with the increase of section ratio (the ratio of long side to short side).
Accurate finite element analysis (FEA) depends on the accurate definition of materials. The definition of material properties of large-rupture-strain fiber reinforced polymer (LRS FRP) in the fiber direction is realized by writing the user subroutine UMAT. Based on the theoretical framework of the concrete damaged plasticity model in Abaqus, a modified concrete damaged plasticity model is proposed to define the material properties of LRS FRP-confined concrete. These modifications include: the parameter K related to the yield criterion is calibrated by the test data of LRS FRP-confined concrete; the hardening/softening criterion is related to the confinement stiffness; the flow rule is related to axial plastic strain. The modified material model is used for FEA. The results show that the stress-strain curve predicted by FEA is consistent with the test results. Based on the FEA results, the non-uniform of stress distribution on the rectangular column section is discussed, which can be divided into effective confinement area and weak confinement area according to the confinement effect, and the non-uniform stress distribution in the effective confinement area increases with the increase of section ratio (the ratio of long side to short side).
2023, 40(4): 144-151.
doi: 10.6052/j.issn.1000-4750.2021.10.0783
Abstract:
In order to study the mechanical behavior and damage model of steel fiber reinforced concrete (SFRC) under compression-shear loading (C-S), 60 SFRC specimens were tested with different steel fiber volume ratio (\begin{document}$ \gamma $\end{document} ![]()
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In order to study the mechanical behavior and damage model of steel fiber reinforced concrete (SFRC) under compression-shear loading (C-S), 60 SFRC specimens were tested with different steel fiber volume ratio (
2023, 40(4): 152-161.
doi: 10.6052/j.issn.1000-4750.2021.10.0786
Abstract:
An elastic-plastic damage model describing the complex mechanical behavior of concrete under cyclic loading is established. The model uses the four-parameter equivalent strain to convert the complex multi-axis problem into the uniaxial equivalent strain space, and considers the stiffness degradation and irreversible deformation during concrete unloading. In view of the non-negative characteristics of equivalent strain, a tension-compression conversion processing method is proposed, so that distinguishing between tension and compression damage is no longer necessary when solving damage variables, and the mathematical form of the model is concise as a result. Meanwhile, the realization process does not depend on the four-parameter model, and the realization method is applicable to various concrete equivalent strain models. By simulating the uniaxial cyclic load test and the dynamic damage process of the Koyna dam, the correctness and reliability of the model in this paper are verified.
An elastic-plastic damage model describing the complex mechanical behavior of concrete under cyclic loading is established. The model uses the four-parameter equivalent strain to convert the complex multi-axis problem into the uniaxial equivalent strain space, and considers the stiffness degradation and irreversible deformation during concrete unloading. In view of the non-negative characteristics of equivalent strain, a tension-compression conversion processing method is proposed, so that distinguishing between tension and compression damage is no longer necessary when solving damage variables, and the mathematical form of the model is concise as a result. Meanwhile, the realization process does not depend on the four-parameter model, and the realization method is applicable to various concrete equivalent strain models. By simulating the uniaxial cyclic load test and the dynamic damage process of the Koyna dam, the correctness and reliability of the model in this paper are verified.
2023, 40(4): 162-171.
doi: 10.6052/j.issn.1000-4750.2021.10.0788
Abstract:
A damping modification factor (DMF) model for adjusting the vertical acceleration response spectrum of offshore ground motions with a damping ratio of 5% is proposed. Based on 5680 offshore vertical ground motion records from S-net network, the influence of earthquake types on DMF is analyzed by using DMF ratios and Z tests. A DMF model is proposed through considering damping ratios and spectral periods, and compared with the onshore DMF model, by which the vertical response spectra are obtained for other damping ratios. Finally, the residuals and standard deviations of the model are analyzed. The results show that the influence of earthquake types on DMF can be ignored. The influence of damping ratio on DMF can be simulated by a cubic polynomial. Due to the characteristics of offshore ground motions, there are significant differences between offshore and onshore DMF models. The damping ratios can affect the spectral value of one standard deviation of the response spectrum of 5% damping ratio. Residual analysis shows that moment magnitude, fault depth and source distance can be introduced to improve the fitting of DMF model. The DMF model for vertical response spectrum proposed provides a reference for the determination of multi-damping ratios seismic design spectra of offshore engineering.
A damping modification factor (DMF) model for adjusting the vertical acceleration response spectrum of offshore ground motions with a damping ratio of 5% is proposed. Based on 5680 offshore vertical ground motion records from S-net network, the influence of earthquake types on DMF is analyzed by using DMF ratios and Z tests. A DMF model is proposed through considering damping ratios and spectral periods, and compared with the onshore DMF model, by which the vertical response spectra are obtained for other damping ratios. Finally, the residuals and standard deviations of the model are analyzed. The results show that the influence of earthquake types on DMF can be ignored. The influence of damping ratio on DMF can be simulated by a cubic polynomial. Due to the characteristics of offshore ground motions, there are significant differences between offshore and onshore DMF models. The damping ratios can affect the spectral value of one standard deviation of the response spectrum of 5% damping ratio. Residual analysis shows that moment magnitude, fault depth and source distance can be introduced to improve the fitting of DMF model. The DMF model for vertical response spectrum proposed provides a reference for the determination of multi-damping ratios seismic design spectra of offshore engineering.
2023, 40(4): 172-183.
doi: 10.6052/j.issn.1000-4750.2021.10.0791
Abstract:
The seismic capability of pier column is important to the safety of the whole bridge structure. To reduce residual deformation and damage, and to resume normal functions with no or minimal repair after earthquake, an innovative pier column with self-centering capability based on Shape Memory Alloy (SMA) and Engineering Cement Composite (ECC) was proposed. In the plastic hinge zone of the self-centering pier column, the longitudinal reinforcements and concrete were replaced by SMA bars and ECC. Therefore, the self-centering capability of the pier column can be achieved through SMA with the energy dissipation capacity being improved. Damage of pier column can be reduced by ECC with strain hardening characteristics. Five specimens were produced, i.e., ordinary reinforced concrete bridge pier (R/C-BP), reinforced ECC bridge pier (R/ECC-BP), steel strands reinforced bridge pier (SS/C-BP), steel strands reinforced ECC bridge pier (SS/ECC-BP), and SMA reinforced ECC bridge pier (SMA/ECC-BP). Based on low cyclic loading tests, the failure characteristics, bearing capacity, ductility and energy dissipation capability of pier column specimens were analyzed. The test results show that the SMA material can effectively enhance the displacement ductility coefficient and improve the ductility performance of the structure, and can reduce the residual deformation of the structure. The ECC material can significantly improve the ductility of the structure and reduce the speed of cracking and increase the energy dissipation capacity of the structure. Compared with the ordinary specimen, SMA-ECC pier column was less damaged with remarkable self-centering capability. Furthermore, it also exhibit excellent ductility and seismic performance.
The seismic capability of pier column is important to the safety of the whole bridge structure. To reduce residual deformation and damage, and to resume normal functions with no or minimal repair after earthquake, an innovative pier column with self-centering capability based on Shape Memory Alloy (SMA) and Engineering Cement Composite (ECC) was proposed. In the plastic hinge zone of the self-centering pier column, the longitudinal reinforcements and concrete were replaced by SMA bars and ECC. Therefore, the self-centering capability of the pier column can be achieved through SMA with the energy dissipation capacity being improved. Damage of pier column can be reduced by ECC with strain hardening characteristics. Five specimens were produced, i.e., ordinary reinforced concrete bridge pier (R/C-BP), reinforced ECC bridge pier (R/ECC-BP), steel strands reinforced bridge pier (SS/C-BP), steel strands reinforced ECC bridge pier (SS/ECC-BP), and SMA reinforced ECC bridge pier (SMA/ECC-BP). Based on low cyclic loading tests, the failure characteristics, bearing capacity, ductility and energy dissipation capability of pier column specimens were analyzed. The test results show that the SMA material can effectively enhance the displacement ductility coefficient and improve the ductility performance of the structure, and can reduce the residual deformation of the structure. The ECC material can significantly improve the ductility of the structure and reduce the speed of cracking and increase the energy dissipation capacity of the structure. Compared with the ordinary specimen, SMA-ECC pier column was less damaged with remarkable self-centering capability. Furthermore, it also exhibit excellent ductility and seismic performance.
2023, 40(4): 184-192.
doi: 10.6052/j.issn.1000-4750.2021.10.0816
Abstract:
Quantitative analysis of frost resistance of concrete materials is one of the basic requirements of digital concrete era. Based on the comprehensive analysis of the factors affecting the frost resistance of concrete and the existing hypothesis of freeze-thaw damage of concrete, the theoretical model of freeze-thaw damage of concrete is deduced. The model uses internal and external independent variables, and takes the micro-structure evolution of the material as the core, so as to realize the quantitative analysis of the frost resistance of concrete. The calculation analysis of the model shows that the physical and mechanical properties, bubble content and pore size distribution, minimum temperature, cooling rate, stress level, material overflow distance and other internal and external factors of cement hydration products affect the freeze-thaw damage characteristics of cement-based materials from different angles and to different degrees. Reasonable design of bubble content and bubble aperture can effectively improve the frost resistance durability of concrete. The above analysis is in good agreement with the existing research results. The research results can provide reference for the freezing resistance design of concrete.
Quantitative analysis of frost resistance of concrete materials is one of the basic requirements of digital concrete era. Based on the comprehensive analysis of the factors affecting the frost resistance of concrete and the existing hypothesis of freeze-thaw damage of concrete, the theoretical model of freeze-thaw damage of concrete is deduced. The model uses internal and external independent variables, and takes the micro-structure evolution of the material as the core, so as to realize the quantitative analysis of the frost resistance of concrete. The calculation analysis of the model shows that the physical and mechanical properties, bubble content and pore size distribution, minimum temperature, cooling rate, stress level, material overflow distance and other internal and external factors of cement hydration products affect the freeze-thaw damage characteristics of cement-based materials from different angles and to different degrees. Reasonable design of bubble content and bubble aperture can effectively improve the frost resistance durability of concrete. The above analysis is in good agreement with the existing research results. The research results can provide reference for the freezing resistance design of concrete.
2023, 40(4): 193-204, 256.
doi: 10.6052/j.issn.1000-4750.2021.10.0817
Abstract:
Most wind farms in China are inevitably built in earthquake-prone areas, and thus it is highly possible that earthquake occurs when the wind turbine is working under the wind load. This paper investigated a 2.5 MW wind turbine in Northwest China as a prototype to study the response of a wind turbine tower considering the blade rotation effect under the coupling effect of wind and earthquake. The harmonic superposition method was used to generate a simulated fluctuating wind speed considering the spatial coherence of the blade and the tower. The impeller load considering the blade rotation effect was calculated based on the blade element momentum theory, and the wake model was used to calculate the load on the tower surface in the wake area. A finite element model considering the eccentricity of the blades and the nacelle as a concentrated mass was established through ABAQUS to analyze the response of the wind turbine under wind-earthquake coupling. The influence of the input time of ground motions on the response of wind turbine under wind-earthquake coupling was discussed. The results show that the impeller rotation effect and the wake have significant influence on the calculation of wind load. The wind-earthquake coupling effect may make the top displacement of the wind turbine tower smaller than that under the wind load, and the base stress is close to that under the sole action of earthquake. The input time of ground motion has significant influence on the result when the wind-earthquake coupling is analysed and should be considered in the design.
Most wind farms in China are inevitably built in earthquake-prone areas, and thus it is highly possible that earthquake occurs when the wind turbine is working under the wind load. This paper investigated a 2.5 MW wind turbine in Northwest China as a prototype to study the response of a wind turbine tower considering the blade rotation effect under the coupling effect of wind and earthquake. The harmonic superposition method was used to generate a simulated fluctuating wind speed considering the spatial coherence of the blade and the tower. The impeller load considering the blade rotation effect was calculated based on the blade element momentum theory, and the wake model was used to calculate the load on the tower surface in the wake area. A finite element model considering the eccentricity of the blades and the nacelle as a concentrated mass was established through ABAQUS to analyze the response of the wind turbine under wind-earthquake coupling. The influence of the input time of ground motions on the response of wind turbine under wind-earthquake coupling was discussed. The results show that the impeller rotation effect and the wake have significant influence on the calculation of wind load. The wind-earthquake coupling effect may make the top displacement of the wind turbine tower smaller than that under the wind load, and the base stress is close to that under the sole action of earthquake. The input time of ground motion has significant influence on the result when the wind-earthquake coupling is analysed and should be considered in the design.
2023, 40(4): 205-214.
doi: 10.6052/j.issn.1000-4750.2021.10.0776
Abstract:
In order to accurately calculate the actual contact area ratio of the steel-BFPC joint surface, a virtual material simulation method for the contact performance of the steel-BFPC joint surface based on discrete method was established. The calculation method of the actual contact area ratio of the steel-BFPC joint surface was established by discretizing the contact rubbings of the joint surface, and the corresponding calculation program was compiled to analyze the influence law of different joint surface pressure on actual contact area ratio. Based on the calculated actual contact area ratio, a virtual material simulation analysis model of the steel-BFPC joint surface was established. Through virtual material simulation and experiment, the modal characteristics of steel-BFPC joint surface piece were studied respectively, and the results of the two methods were compared and analyzed. The results show that the maximum relative error between the natural frequency of the two is +6.48% and the vibration mode is consistent. The accuracy of the discrete calculation method of the actual contact area ratio of the steel-BFPC joint surface and the virtual material simulation method has been proved.
In order to accurately calculate the actual contact area ratio of the steel-BFPC joint surface, a virtual material simulation method for the contact performance of the steel-BFPC joint surface based on discrete method was established. The calculation method of the actual contact area ratio of the steel-BFPC joint surface was established by discretizing the contact rubbings of the joint surface, and the corresponding calculation program was compiled to analyze the influence law of different joint surface pressure on actual contact area ratio. Based on the calculated actual contact area ratio, a virtual material simulation analysis model of the steel-BFPC joint surface was established. Through virtual material simulation and experiment, the modal characteristics of steel-BFPC joint surface piece were studied respectively, and the results of the two methods were compared and analyzed. The results show that the maximum relative error between the natural frequency of the two is +6.48% and the vibration mode is consistent. The accuracy of the discrete calculation method of the actual contact area ratio of the steel-BFPC joint surface and the virtual material simulation method has been proved.
2023, 40(4): 215-225.
doi: 10.6052/j.issn.1000-4750.2021.10.0780
Abstract:
Cracks are the main diseases of concrete structures. Finding out the depth of cracks can provide reliable information for the durability and safety evaluation of structures, but it is also one of the difficulties in the detection of concrete structures. A data-driven learning algorithm is proposed to predict the crack depth by investigating the signal of wave propagation through the cracked structure. The wave propagation process in the cracked massive concrete structure is simulated by using the extended finite element methods (XFEM) and the boundary absorbing layer model, and the observation signal of the receiving point is paired with the crack information. Based on the machine learning model of artificial neural network, a fracture depth prediction model based on XFEM datasets is established. For the concrete structure with unknown crack information, through the measured observation point signals, the established machine learning model is utilized to realize the real-time prediction of crack depth. The performance of the algorithm is verified by two numerical examples. The results show that the proposed algorithm can accurately predict the crack depth.
Cracks are the main diseases of concrete structures. Finding out the depth of cracks can provide reliable information for the durability and safety evaluation of structures, but it is also one of the difficulties in the detection of concrete structures. A data-driven learning algorithm is proposed to predict the crack depth by investigating the signal of wave propagation through the cracked structure. The wave propagation process in the cracked massive concrete structure is simulated by using the extended finite element methods (XFEM) and the boundary absorbing layer model, and the observation signal of the receiving point is paired with the crack information. Based on the machine learning model of artificial neural network, a fracture depth prediction model based on XFEM datasets is established. For the concrete structure with unknown crack information, through the measured observation point signals, the established machine learning model is utilized to realize the real-time prediction of crack depth. The performance of the algorithm is verified by two numerical examples. The results show that the proposed algorithm can accurately predict the crack depth.
2023, 40(4): 226-232.
doi: 10.6052/j.issn.1000-4750.2022.02.0163
Abstract:
Aiming at the problem of motion blur in complex measurement environment or high dynamic measurement, a blind deblurring method for speckle image based on the combination of gray sparsity prior and reference image gradient prior is proposed. This method takes the norm of the peak value of the gray histogram and the gradient of the reference image as the regular terms, uses the quadratic splitting method to estimate the clear image, and evaluates the convolution kernel in an alternating iterative way. After the fuzzy kernel estimation is completed, the Richardson-Lucy non-blind deconvolution method is used to restore the speckle image. Experimental results show that compared with the classical method for natural image and text image, the proposed method achieves better image deblurring results and improves the accuracy and robustness of digital image correlation measurement.
Aiming at the problem of motion blur in complex measurement environment or high dynamic measurement, a blind deblurring method for speckle image based on the combination of gray sparsity prior and reference image gradient prior is proposed. This method takes the norm of the peak value of the gray histogram and the gradient of the reference image as the regular terms, uses the quadratic splitting method to estimate the clear image, and evaluates the convolution kernel in an alternating iterative way. After the fuzzy kernel estimation is completed, the Richardson-Lucy non-blind deconvolution method is used to restore the speckle image. Experimental results show that compared with the classical method for natural image and text image, the proposed method achieves better image deblurring results and improves the accuracy and robustness of digital image correlation measurement.
2023, 40(4): 233-242.
doi: 10.6052/j.issn.1000-4750.2021.10.0755
Abstract:
Although lower limb amputation has been identified as a possible risk factor of cardiovascular disease, the underlying biomedical mechanisms are not completely understood. The purpose of this study was to examine the cardiovascular hemodynamic status of lower limb amputees at different postoperative periods and life status to evaluate the impact of abnormal hemodynamics on cardiovascular system. In this paper, a centralized parameter model of the cardiovascular system with lower limb arteries was established to simulate three common conditions of amputation patients, i.e., postoperation, postoperation residual limb atrophy and postoperation both limb atrophy. The diameter of lower limb artery measured by ultrasound in 7 patients with lower limb amputation was used as the reference for parameter setting of the model. By comparing the blood pressure and blood flow waveform of the normal person model and the lower limb amputation model, we found that the amplitude of the systolic and diastolic blood pressure increased after amputation, and the peak value of the arterial flow in the abdominal aorta and below decreased significantly. In postoperation residual limb atrophy and postoperation both limb atrophy, the peak blood pressure in the central aorta increased during diastole. Such abnormal hemodynamic changes may be a risk factor of cardiovascular diseases such as hypertension and ventricular hypertrophy in lower limb amputees. The centralized parameter model established in this paper provides the change rule of hemodynamics after amputation, which can provide theoretical guidance of rehabilitation treatment and cardiovascular disease prevention of amputation patients in the future.
Although lower limb amputation has been identified as a possible risk factor of cardiovascular disease, the underlying biomedical mechanisms are not completely understood. The purpose of this study was to examine the cardiovascular hemodynamic status of lower limb amputees at different postoperative periods and life status to evaluate the impact of abnormal hemodynamics on cardiovascular system. In this paper, a centralized parameter model of the cardiovascular system with lower limb arteries was established to simulate three common conditions of amputation patients, i.e., postoperation, postoperation residual limb atrophy and postoperation both limb atrophy. The diameter of lower limb artery measured by ultrasound in 7 patients with lower limb amputation was used as the reference for parameter setting of the model. By comparing the blood pressure and blood flow waveform of the normal person model and the lower limb amputation model, we found that the amplitude of the systolic and diastolic blood pressure increased after amputation, and the peak value of the arterial flow in the abdominal aorta and below decreased significantly. In postoperation residual limb atrophy and postoperation both limb atrophy, the peak blood pressure in the central aorta increased during diastole. Such abnormal hemodynamic changes may be a risk factor of cardiovascular diseases such as hypertension and ventricular hypertrophy in lower limb amputees. The centralized parameter model established in this paper provides the change rule of hemodynamics after amputation, which can provide theoretical guidance of rehabilitation treatment and cardiovascular disease prevention of amputation patients in the future.
2023, 40(4): 243-256.
doi: 10.6052/j.issn.1000-4750.2021.10.0777
Abstract:
The ice resistance is an important factor in the navigation process of ships in ice areas, which brings serious challenges to the navigation performance and navigation safety of ships. In this study, the dilated polyhedron based discrete element method (DPDEM) is used to establish a three-dimensional discrete element method (DEM) of the ice-ship dynamic interaction process, based on the approximate relationship between ship propulsion power and propulsion force, and considering propeller thrust, ice load, rudder force and hydrodynamic load separately, the ice resistance and motion response of 6-DOF nonlinear manoeuvre straight navigate of constant power icebreaker are calculated. In order to verify the reliability of the DEM, the results of DUBROVIN and LINDQVIST ice resistance formulas in a broken ice region and a flat ice region were compared and analyzed. Based on the simulation results of the ice resistance on ship under different propulsion power and complex ice conditions, the influencing factors of ship speed are analyzed. Accordingly, the simulation results of ship motion response in ice areas, such as ship heave, roll and pitch, and the prediction results of ice-breaking performance of polar ships are analyzed. Finally, the ice load and the motion response both in a broken ice field and in a level ice one are compared and analyzed. This method can effectively calculate the ice resistance of ship, and the simulation results can provide an important reference for the motion response and navigation safety early-warning of ships in ice-covered regions.
The ice resistance is an important factor in the navigation process of ships in ice areas, which brings serious challenges to the navigation performance and navigation safety of ships. In this study, the dilated polyhedron based discrete element method (DPDEM) is used to establish a three-dimensional discrete element method (DEM) of the ice-ship dynamic interaction process, based on the approximate relationship between ship propulsion power and propulsion force, and considering propeller thrust, ice load, rudder force and hydrodynamic load separately, the ice resistance and motion response of 6-DOF nonlinear manoeuvre straight navigate of constant power icebreaker are calculated. In order to verify the reliability of the DEM, the results of DUBROVIN and LINDQVIST ice resistance formulas in a broken ice region and a flat ice region were compared and analyzed. Based on the simulation results of the ice resistance on ship under different propulsion power and complex ice conditions, the influencing factors of ship speed are analyzed. Accordingly, the simulation results of ship motion response in ice areas, such as ship heave, roll and pitch, and the prediction results of ice-breaking performance of polar ships are analyzed. Finally, the ice load and the motion response both in a broken ice field and in a level ice one are compared and analyzed. This method can effectively calculate the ice resistance of ship, and the simulation results can provide an important reference for the motion response and navigation safety early-warning of ships in ice-covered regions.
