Arbitrarily-shaped layered polar orthotropic domains: elastostatics using analytical and coupled analytical-FE approaches

Polar orthotropic materials as wood and filament-wound composites are ubiquitous in nature and technological applications, respectively. With annular domains rendering themselves naturally for polar orthotropy, applications featuring annular domains have received considerable attention; however, arbitrarily-shaped domains are less explored. In an attempt to address this gap, the present work explores elastostatics of arbitrarily-shaped layered 2D domains. After identifying the refinement required in an earlier work to yield a physically and mathematically consistent solution, the work considers analytically homogenous and layered polar orthotropic annular domains and corroborates the results with FEA. Subsequently, the arbitrarily-shaped layered domains—including octagonal-shaped, cruciform-shaped and annular domains—are analyzed by employing a coupled FE-analytical technique combining coarse-mesh boundary displacement-data from FEA and the refined solution. Results for the illustrative cases under symmetric and anti-symmetric loadings are depicted as contours over the domains for the resultant displacements and von Mises stresses. A comparison with converged FE results and L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{2}$$\end{document}-error norms indicate a good correspondence between the two—demonstrating the efficacy of the coupled technique. The potential extension of the technique to hybrid-experimental strategies, asymmetric cases, composite cylindrical FGMs and a complex-variable based formulation for the coupled technique is briefly discussed.