A coupled analytical–FE hybrid approach for elastostatics

Abstract

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.