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本文提出了膜结构形状确定的三类问题：第一类问题是给定边界条件的等应力最小曲面确定问题。第二类问题是给定边界条件的平衡曲面确定问题，第三类问题是给定曲面几何的最均匀应力分布确定问题。对第一、第二类问题，本文采用动力松弛方法求解；对第三类问题，本文提出了最小二乘法的计算理论和求解方法。数值算例表明了本文方法的实用性和优越性。本文方法具有概念明晰、推导简单和计算快速的优点。
This paper presents three types of problems in the determination of the shape of the membrane structure. The first type of problem is the determination of the minimum isometric surface for a given boundary condition. The second type of problem is the problem of determining the equilibrium surface for a given boundary condition. The third type of problem is the determination of the most uniform stress distribution for a given surface geometry. For the first and the second kind of problems, this paper uses the dynamic relaxation method to solve; for the third kind of problem, this paper proposes the least square method of calculation theory and solution method. Numerical examples show the practicality and superiority of this method. This method has the advantages of clear concept, simple derivation and fast calculation.