An optimal versatile partial hybrid stress solid‐shell element for the analysis of multilayer composites

Abstract

SUMMARY In the present contribution we propose an optimal low‐order versatile partial hybrid stress solid‐shell element that can be readily employed for a wide range of geometrically linear elastic structural analyses, that is, from shell‐like isotropic structures to multilayer anisotropic composites. This solid‐shell element has eight nodes with only displacement degrees of freedom and only a few internal parameters that provide the locking‐free behavior and accurate interlaminar shear stress resolution through the element thickness. These elements can be stacked on top of each other to model multilayer composite structures, fulfilling the interlaminar shear stress continuity at the interlayer surfaces and zero traction conditions on the top and bottom surfaces of composite laminates. The element formulation is based on the modified form of the well‐known Fraeijs de Veubeke–Hu–Washizu multifield variational principle with enhanced assumed strains formulation and assumed natural strains formulation to alleviate the different types of locking phenomena in solid‐shell elements. The distinct feature of the present formulation is its ability to accurately calculate the interlaminar shear stress field in multilayer structures, which is achieved by the introduction of the assumed interlaminar shear stress field in a standard enhanced assumed strains formulation based on the Fraeijs de Veubeke–Hu–Washizu principle. The numerical testing of the present formulation, employing a variety of popular numerical benchmark examples related to element patch test, convergence, mesh distortion, shell and laminated composite analyses, proves its accuracy for a wide range of structural analyses.Copyright © 2012 John Wiley & Sons, Ltd.

An improved enhanced solid shell element for static and buckling analysis of shell structures

“…In comparison to other solid shell formulations in the literature (Q8A3E5, Q8A3E7, and Q8S12), our developed formulation and those obtained with Vu-Quoc and Tan [15] show superior convergence behavior. However, the comparison of the present solid shell element with the one presented in Rah et al [10] confirms that 7 EAS parameters are sufficient for wide geometrically linear elastic structural analyses. This proves the accuracy and efficiency of the present solid shell formulation for the linear elastic structural analysis of shells.…”

“…Based on this method, Alves de Sousa et al [8] proposed a volumetric and shear locking-free solid element a Corresponding author: mondherwali@yahoo.fr formulation. The application of the EAS method for wide range of geometrically linear elastic structural analyses was presented in the works of Andelfinger and Ramm [9] and Rah et al [10,11]. The extension to non-linear aspects was carried out by Büchter et al [12] and Bischoff and Ramm [13] among others.…”

Modeling of cylindrical composite shell structures based on the Reissner’s Mixed Variational Theorem with a variable separation method

“…Alternative hybrid approaches take into account the transverse normal effect. The Fraeijs de VeubekeHuWashizu multifield variational principle [55,56] and the Reissner Mixed Variational Theorem [57] are used assuming the transverse shear stresses only. Note that Sgambitterra et al [14] have introduced a mixedfield assumptions (γ α3 and σ 33 ) to derive a hybrid formulation enforcing the compatibility straindisplacement relations to be least-squares compatible through the shell thickness.…”