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SUMMARYThis paper presents a versatile low order locking-free mixed solid-shell element that can be readily employed for a wide range of linear elastic structural analyses, that is, from thick isotropic structures to multilayer anisotropic composites. This solid-shell element has eight nodes with only displacement degrees of freedom and few assumed stress parameters that provide very accurate interlaminar stress calculations through the element thickness. These elements can be stacked on top of each other to model multilayer structures, fulfilling the interlaminar stress continuity at the interlayer surfaces and zero traction conditions on the top and bottom surfaces of the laminate. The element formulation is based on the well-known Fraeijs de VeubekeHu-Washizu mixed 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 stress field in multilayer structures, which is achieved by the introduction of a constraint equation on the interlaminar stresses in the Fraeijs de Veubeke-Hu-Washizu principle-based enhanced assumed strains formulation. The intelligent computer coding of the present formulation makes the present element appropriate for a wide range of structural analyses. To assess the present formulation's accuracy, a variety of popular numerical benchmark examples related to element convergence, mesh distortion, and shell and laminated composite analyses are investigated and the results are compared with those available in the literature. These benchmark examples reveal that the proposed formulation provides very good results for the structural analysis of shells and multilayer composites.

In this paper we introduce a low order partial hybrid stress solid-shell element based on the composite energy functional for the analysis of laminated composite structures. This solid-shell element has eight nodes with only displacement degrees of freedoms, and three-dimensional constitutive models can be directly employed in the present formulation without any additional treatment. The assumed interlam-inar stress field provides very accurate interlaminar stress calculation through the element thickness. These elements can be stacked on top of each other to model multilayer structures, fulfilling the interlaminar stress continuity at the interlayer surfaces and zero traction conditions on the top and bottom surfaces of the laminate. The present solid-shell does not show the transverse shear, trapezoidal and thickness locking phenomenon, and passes both the membrane and the bending patch tests. To assess the present formulation's accuracy, a variety of popular numerical benchmark examples related to element convergence, mesh distortion, shell and laminated composite analyses are investigated and the results are compared with those available in the literature. The numerical results show the accuracy of the presented solid-shell element for the analysis of laminated composites.

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.

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