A NEW ADAPTIVE FEM FOR MINIMAL SURFACES FORM-FINDING OF MEMBRANE STRUCTURES

Form-finding analysis is a key step of the design of membrane structures. The minimal-surface form-finding problem of membrane structures is a highly nonlinear problem in mathematics, and no analytic solutions are available in general. Thusly, numerical methods are an important approach. In recent years, remarkable success has been made in the adaptive analysis of both 1D nonlinear finite element method (FEM) and 2D linear FEM based on element energy projection (EEP) super-convergent technique. A new adaptive strategy for 2D nonlinear FEM is developed and applied to the form-finding of membrane structures. In this method, by linearizing nonlinear problems into a series of linear problems via the Newton method, the existing 2D linear adaptive strategy based on EEP technique can be incorporated into a nonlinear solution procedure. As a result, an adaptive mesh is automatically generated and adjusted by the algorithm to guarantee to produce a satisfactory solution with the results satisfying the user-preset error tolerance by maximum norm. Pertinent numerical examples are presented to demonstrate the feasibility and effectiveness of the newly developed method.