An improved assumed strain solid–shell element formulation with physical stabilization for geometric non‐linear applications and elastic–plastic stability analysis

Abstract

SUMMARYIn this paper, the earlier formulation of the SHB8PS finite element is revised in order to eliminate some persistent membrane and shear locking phenomena. This new formulation consists of a solid-shell element based on a purely three-dimensional approach. More specifically, the element has eight nodes, with displacements as the only degrees of freedom, as well as an arbitrary number of integration points, with a minimum number of two, distributed along the 'thickness' direction. The resulting derivation, which is computationally efficient, can then be used for the modeling of thin structures, while providing an accurate description of the various through-thickness phenomena. A reduced integration scheme is used to prevent some locking phenomena and to achieve an attractive, low-cost formulation. The spurious zero-energy modes due to this in-plane one-point quadrature are efficiently controlled using a physical stabilization procedure, whereas the strain components corresponding to locking modes are eliminated with a projection technique following the assumed strain method. In addition to the extended and detailed formulation presented in this paper, particular attention has been focused on providing full justification regarding the identification of hourglass modes in relation to rank deficiencies. Moreover, an attempt has been made to provide a sound foundation to the derivation of the co-rotational coordinate frame, on which the calculations of the stabilization stiffness matrix and internal load vector are based. Finally to assess the effectiveness and performance of this new formulation, a set of popular benchmark problems is investigated, involving geometric non-linear analyses as well as elastic-plastic stability issues.

On the comparison of two solid-shell formulations based on in-plane reduced and full integration schemes in linear and non-linear applications

“…Where J ipi and W ipi are the determinant of the Jacobian matrix (11) and the weights at the Gauss points. To fulfill the equation of the variational principle (1), the residual R α should be equal to zero while R u represents the internal forces of the element which should be in equilibrium with the externally applied forced (whose virtual work is included in ext π (η) ).…”

“…In this context, several published works were focused on the development of solid-shell elements (e.g. see [5][6][7][8][9][10][11][12][13]) which form a class of finite element models that are intermediate between the conventional solid and shell elements. Despite their attractive features, low-order solid-shell displacement-based finite elements suffer from different types of locking effects.…”

An Explicit Dynamics Approach to the Simulation of Crack Propagation in Thin Shells Using Reduced Integration Solid-Shell Elements

“…A cylindrical shell hinged on two sides and free on the other two sides, subjected to a transversal concentrated center load, has been analyzed using the 16 × 16 SHB8PS (see [13]) solid-shell element mesh shown in Figure 3. The problem has been used in [14] to test the application of the scaled director conditioning technique [15] in explicit dynamics simulations.…”

A new assumed strain solid-shell formulation “SHB6” for the six-node prismatic finite element

“…Since they are intended to compete with shell elements, solid-shell elements are expected to have two key features: they contain only displacements as degrees of freedom, and they are able to reproduce the behavior of thin structures by means of a single layer of elements through the thickness. In the last decade, several examples of such formulations have been proposed, and can be found in Domissy [23], Cho et al [24], Hauptmann and Schweizerhof [25], Lemosse [26], Sze and Yao [27], Hauptmann et al [28], Sze and Chan [29], Abed-Meraim and Combescure [30,31], Legay and Combescure [32], Vu-Quoc and Tan [33], Sze et al [34], Chen and Wu [35], Kim et al [36], Alves de Sousa et al [37][38][39], and Reese [40]. It should be noted that most of the methods developed earlier were based on the enhanced assumed strain method proposed by Simo and co-workers (Simo and Rifai [41], Simo and Armero [42], Simo et al [43]), and consisted of either the use of a conventional integration scheme with appropriate control of all locking phenomena or the application of a reduced integration technique with associated hourglass control.…”

“…This represents the main motivation of the present work, in which a new prismatic solid-shell element, denoted SHB6, is developed. This element is formulated following a scheme similar to that used for the recently developed hexahedral solid-shell element, denoted SHB8PS, and based on a purely three-dimensional approach [31,32]. Recall that in order to improve the efficiency of this element and to alleviate some shear and thickness locking phenomena, the reduced integration technique was used.…”