Higher-order assumed strain plane element immune to mesh distortion

Purpose This paper aims to propose a new robust membrane finite element for the analysis of plane problems. The suggested element has triangular geometry. Four nodes and 11 degrees of freedom (DOF) are considered for the element. Each of the three vertex nodes has three DOF, two displacements and one drilling. The fourth node that is located inside the element has only two translational DOF. Design/methodology/approach The suggested formulation is based on the assumed strain method and satisfies both compatibility and equilibrium conditions within each element. This establishment results in higher insensitivity to the mesh distortion. Enforcement of the equilibrium condition to the assumed strain field leads to considerably high accuracy of the developed formulation. Findings To show the merits of the suggested plane element, its different properties, including insensitivity to mesh distortion, particularly under transverse shear forces, immunities to the various locking phenomena and convergence of the element are studied. The obtained results demonstrate the superiority of the suggested element compared with many of the available robust membrane elements. Originality/value According to the attained results, the proposed element performs better than the well-known displacement-based elements such as linear strain triangular element, Q4 and Q8 and even is comparable with robust modified membrane elements.

A Selective Reduced Integration 8-Node Hexahedral Element by Assumed Strain for Coining Simulation

A selective reduced integration 8-node hexahedral element for coining simulation is developed in this paper. The element is free of volume locking by assumed strain method. The standard velocity gradient matrix is derived in which the shear items are ignored to avoid shear locking. Hourglass modes are successfully suppressed without user-input parameters. The element is successfully employed in the coining simulation package - COINFORM. Numerical tests and experiments of a typical coin are carried out to show the good performances of the element.

EAS 3D triangular and quadrangular shell elements

A new 3D solid shell element is developed in SAMCEF™ code. The purpose of this element is to make the meshing easier starting from a 3D definition of the structure, it is not necessary to extract the mean surface of the shell. Here, we are not concerned by the meshing; we only are concerned by the element formulation. In order to improve the quality of the results, we add internal degrees of freedom as suggested by Simo and co-authors. We use the Enhanced Assumed Strain method. A special handling of the transverse shear is performed in order to pass successfully the plate patch test (constant bending) and to avoid shear locking. The formulation is based on the work of Bathe and Dvorkin for classical shell. The element has been developed in linear and non-linear analysis; it can be a mono or multilayer element.

A new prismatic solid-shell element ‘SHB6’: Assumed-strain formulation and evaluation on benchmark problems

In this paper, the formulation of a new six-node solid–shell element denoted (SHB6) is proposed. This prismatic element is based on a purely three-dimensional approach, and hence has displacements as the only degrees of freedom. A reduced integration scheme is adopted consisting of one-point in-plane quadrature and an arbitrary number of integration points, with a minimum number of two, distributed along the ‘thickness’ direction. Moreover, in order to enhance its performance and to greatly reduce most locking effects, specific projections are introduced based on the assumed-strain method. The resulting derivation can then be used to model thin structural problems, while taking into account the various through-thickness phenomena. A careful analysis of potential stiffness matrix rank deficiencies reveals that no hourglass modes need to be controlled. However, without assumed-strain method, the element exhibits some shear and thickness-type locking, which is common in linear triangular elements associated with constant strain states. After the formulation of the element is detailed, its performance is assessed through a set of representative benchmark problems illustrating its capabilities in various situations. More specifically, this prismatic solid–shell element proves to be an essential complement to the SHB8PS hexahedral element in meshing arbitrarily complex geometries.