In this study, element-free Galerkin method (EFGM), a meshless method, is proposed for wrinkling analysis of pre-stressed rectangular membranes. The mathematical model for studying wrinkling of pre-stressed membranes is derived by considering the bending stiffness, though it is negligible. Moving least-square approximation for deflection is constructed by considering three degrees of freedom per node. Essential boundary conditions are imposed using scaled transformation matrix method. Initially, compression-induced buckling of a homogeneous thin plate without pre-stress is solved to validate the method and then a pre-stressed homogeneous membrane is analyzed for both compression-induced and shear-induced wrinkling. Capabilities of the proposed method for membrane analysis are compared with that of the finite element method (FEM). Comparative study on wrinkling analysis using EFGM and different FEM element types in a commercial FEM package shows that in lower modes both methods show satisfying consistency in eigenvalues with respect to the total of number of nodes, while at higher modes EFGM shows better consistency than FEM. Further, the study is extended to wrinkling of nonhomogeneous membranes subjected to linearly-varying in-plane load. The results obtained from EFGM analysis is compared and found to be matching well with those available in the literature.

中文翻译：

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无元素伽辽金法预应力矩形膜的起皱分析

在这项研究中，提出了一种无网格方法无单元 Galerkin 方法 (EFGM)，用于预应力矩形膜的起皱分析。研究预应力膜起皱的数学模型是通过考虑弯曲刚度推导出来的，尽管它可以忽略不计。通过考虑每个节点的三个自由度来构造偏转的移动最小二乘近似。使用缩放变换矩阵方法施加基本边界条件。首先，求解无预应力的均质薄板的压缩致屈曲以验证该方法，然后分析预应力均质膜的压缩致皱和剪切致皱。所提出的膜分析方法的能力与有限元法 (FEM) 的能力进行了比较。使用 EFGM 和商业 FEM 包中的不同 FEM 单元类型对起皱分析进行的比较研究表明，在较低模式下，两种方法都显示出关于节点总数的特征值的令人满意的一致性，而在较高模式下，EFGM 显示出比 FEM 更好的一致性。此外，该研究扩展到了非均质膜在平面内线性变化载荷下的起皱。比较从 EFGM 分析获得的结果，发现与文献中可用的结果非常匹配。该研究扩展到受到线性变化的平面内载荷的非均匀膜的起皱。比较从 EFGM 分析获得的结果，发现与文献中可用的结果非常匹配。该研究扩展到受到线性变化的平面内载荷的非均匀膜的起皱。比较从 EFGM 分析获得的结果，发现与文献中可用的结果非常匹配。