This work extends the recent US-ATFH8 element to 3D hyper-elastic finite deformation analysis. Using two sets of shape functions, the new 3D element comprises of 8 nodes and 24 DOFs. The first set of shape functions represent the test functions that come from the conventional isoparametric interpolation, and the second set, representing the trial functions, are constructed from the homogenous solutions for linear elasticity governing equations, termed analytical trial functions (ATFs). This study considers finite deformation for hyper-elastic materials, but it is assumed that the analytical solutions associated with hyper-elastic materials can be updated to hold approximately in each incremental step. Moreover, the deformation information required for stress computation is updated by using the incremental deformation gradient, which is constructed from the updated ATFs. Numerical examples show that without additional pressure DOF, the element US-ATFH8 still behaves well in nearly incompressible hyper-elastic 3D problems with finite deformation, even when the meshes are extremely distorted.
A high-performance shape-free arbitrary polygonal hybrid stress/displacement -function flat shell finite element method is proposed for linear and geometrically nonlinear analyses of shells. First, an arbitrary polygonal Mindlin-Reissner plate element and an arbitrary polygonal membrane element with drilling degrees of freedom are constructed based on hybrid displacement-function and hybrid stress-function methods, respectively. Both elements have only two corner nodes along each edge. Second, by assembling the plate and the membrane elements, an arbitrary polygonal flat shell element is constructed. Third, based on the corotational method, a proper best-fit corotated frame for geometrically nonlinear polygonal elements is designed. By updating the analytical trial functions of shell element in each increment step, the original linear flat shell element is generalized to a geometrically nonlinear model. Numerical examples show that the new element possesses excellent performance for both linear and geometrically nonlinear analyses, and possesses outstanding flexibility in dealing with complex loading distributions and mesh shapes.
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