Modification of the quadratic 10‐node tetrahedron for thin structures and stiff materials under large‐strain hyperelastic deformation

Abstract

Summary The concept of energy‐sampling stabilization is used to develop a mean‐strain quadratic 10‐node tetrahedral element for the solution of geometrically nonlinear solid mechanics problems. The development parallels recent developments of a “composite” uniform‐strain 10‐node tetrahedron for applications to linear elasticity and nonlinear deformation. The technique relies on stabilization by energy sampling with a mean‐strain quadrature and proposes to choose the stabilization parameters as a quasi‐optimal solution to a set of linear elastic benchmark problems. The accuracy and convergence characteristics of the present formulation are tested on linear and nonlinear benchmarks and compare favorably with the capabilities of other mean‐strain and high‐performance tetrahedral and hexahedral elements for solids, thin‐walled structures (shells), and nearly incompressible structures.

Extension of the unsymmetric 8‐node hexahedral solid element US‐ATFH8 to 3D hyper‐elastic finite deformation analysis

“…And the corresponding results are listed in Table 2. Results obtained by other element models, including the plane‐strain tapered panel with element Q1E4, 26 the mean‐strain 8‐node hexahedron element H8MSGSO, 33 the higher‐order mean‐strain 10‐node tetrahedron element T10MS, 45 and the modified higher‐order mean‐strain 10‐node tetrahedral element QT10MS, 46 are also plotted in Figure 7. The contour plots for pressure on final deformed shapes with mesh 16 × 16 × 1 are also given in Figure 8, in which the pressure is defined by $$$$ p=-\frac{1}{3}\left({\sigma}_{11}+{\sigma}_{22}+{\sigma}_{33}\right).$$…”

“…In this example, a cylinder shell problem 30,33,46 is employed for testing the present element. Owing to symmetry, the simulation is only performed on one quarter of the structure.…”

“…A hyper-elastic 3D Cook's beam structure is employed for evaluating the elements' bending behavior with finite deformation elasticity. 25,26,33,[45][46][47] Figure 6 shows the boundary conditions and geometry parameters. The left end is completely clamped.…”

“…In this example, a cylinder shell problem 30,33,46 is employed for testing the present Owing to the simulation is only performed on one quarter of the structure. The top surface undertakes a uniform line load q, which is along the y direction.…”

Rapid free‐vibration analysis with model reduction based on coherent nodal clusters

“…The rectangular surface at the back is assumed to be clamped. In this example, the quadratic assumed-strain tetrahedral finite elements 45 is employed. The partitioning of the nodes into clusters is in this case complicated by the non-convex geometry.…”