A LINEARIZED METHOD FOR MINIMAL SURFACE FORM-FINDING OF MEMBRANE STRUCTURES AND ITS FEMOL SOLUTION

The minimal surface form-finding analysis of membrane structures is a nonlinear problem. Its strong nonlinearity makes its computation to be a great challenge which usually needs a lot of iterations and a rational initial solution to guarantee the convergence of the solution process. This paper substantially simplifies this problem into a linear problem by using the integral mean-value theorem and normalization technique, the solution of which approaches the minimal surface with high accuracy. This method can be used either for an approximate form of the membrane surface in the primary design stage or for an initial solution for further computation of the original nonlinear problem. The error of the present method mainly comes from the non-uniformity of the mapping parameters, and thus this method works very well for most membranes whose shapes are close to parallelogram. As a semi-analytical method based on ordinary differential equation (ODE) techniques, the finite element method of lines (FEMOL) is very suitable for membrane problems due to its semi-analytical property and smoothness of its solutions. FEMOL is applied to the linearized problem proposed in the paper. Numerical examples given show that this linearized method is simple, efficient and reliable with highly satisfactory accuracy.