Beginning with augmentation of experimental boundary-data with numerical methods in early hybrid methods (HMs), HMs have evolved in various states of hybridization amalgamating combinations of theoretical, numerical and experimental analysis techniques. In this work, an HM coupling coarse-mesh FE boundary-data with a theoretical solution in the 2D elastostatic framework is proposed and explored. Utilizing Michell solution—a generalized Airy stress function in polar coordinate—the harmonic regression analysis carried out on the FEA hole-boundary displacement data renders coefficients embedded with Airy constants. These constants are determined from the equations furnished by imposing the boundary conditions strongly on the hole and by comparing the coefficients with the corresponding field variables. The method is illustrated for square and hexagonal perforated plates under symmetric, anti-symmetric and asymmetric loadings. von Mises stress calculated by the coarse-mesh based HM is corroborated with FEA employing a refined mesh. The results show good correspondence over a sizeable part of the domains, demonstrating the efficacy of the method. In addition, an extension of the HM incorporating experimental techniques to estimate remote-data from accessible boundary-data, the potential scope as a mesh-reduction technique and an alternative complex-variable formulation are discussed.

中文翻译：

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用于弹性静力学的耦合分析-有限元混合方法

从在早期混合方法 (HMs) 中用数值方法增加实验边界数据开始，HMs 已经在各种混合状态中发展起来，融合了理论、数值和实验分析技术的组合。在这项工作中，提出并探索了将粗网格有限元边界数据与二维弹性静力学框架中的理论解决方案相结合的 HM。利用 Michell 解——极坐标中的广义艾里应力函数——对 FEA 孔边界位移数据进行的调和回归分析呈现嵌入艾里常数的系数。这些常数是通过将边界条件强加在孔上并通过将系数与相应的场变量进行比较而提供的方程确定的。该方法针对对称、反对称和非对称载荷下的方形和六边形穿孔板进行了说明。由基于粗网格的 HM 计算出的 von Mises 应力得到了采用细化网格的 FEA 的证实。结果显示了相当大一部分域的良好对应，证明了该方法的有效性。此外，还讨论了 HM 的扩展，它结合了实验技术以从可访问的边界数据中估计远程数据，讨论了作为网格减少技术的潜在范围和替代的复杂变量公式。证明该方法的有效性。此外，还讨论了 HM 的扩展，它结合了实验技术以从可访问的边界数据中估计远程数据，讨论了作为网格减少技术的潜在范围和替代的复杂变量公式。证明该方法的有效性。此外，还讨论了 HM 的扩展，它结合了实验技术以从可访问的边界数据中估计远程数据，讨论了作为网格减少技术的潜在范围和替代的复杂变量公式。