Abstract We propose an approach to modeling nonlinear membranes deformation by the method of hyperelastic nodal forces. The method is based on interpolation properties of barycentric coordinates and the principle of minimum potential energy; this permits one to derive all necessary formulas in an analytical, concise representation. To verify the approach, we run a number of numerical benchmark tests and demonstrate coincidence of the solutions produced by our approach with known analytical or numerical solutions.

中文翻译：

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非线性膜变形的超弹性节点力法

摘要 我们提出了一种通过超弹性节点力的方法来模拟非线性膜变形的方法。该方法基于重心坐标的插值性质和势能最小原理；这允许人们以一种分析性的、简明的表示形式推导出所有必要的公式。为了验证该方法，我们运行了许多数值基准测试，并证明了我们的方法产生的解决方案与已知解析或数值解决方案的一致性。