Geometrically Nonlinear and Post-Buckling Analyses of Solids and Shells by a Hierarchical Quadrature Element Method

In this work, the three-dimensional hexahedron/wedge hierarchical quadrature elements are formulated and applied to geometrically nonlinear analyses of solid and shell structures. Large deformation as well as post-buckling analyses are considered. Numerical benchmark examples demonstrate that the proposed formulations accurately capture various geometrically nonlinear behaviors with high precision and efficiency. The proposed method also accurately captures the buckling response of thin shell structures with initial imperfections and predicts mode jumping in the post-buckling phase. Due to the advantage of easy assembly, the proposed hierarchical quadrature elements enable straightforward local p-refinement and blending different element types. Numerical tests show that the flexible local p-refinement capability of the proposed elements delivers results with high accuracy using significantly reduced degrees of freedom. Different from conventional high-order finite element method, the Hierarchical Quadrature Element Method (HQEM) permits independent node distribution at the vertices, edges, faces and interior of each element. This capability facilitates flexible p-refinement and blending of diverse element types, thereby enabling the generation of meshes that conform more accurately to complex geometric configurations.