Strain Solid-shell Element Research Articles

Buckling analysis of a laminated composite plate with delaminations using the enhanced assumed strain solid shell element

The paper deals with the validation of a recently proposed hexahedral solid-shell finite element in the buckling analysis of a laminated composite plate with delaminations. The object is to study the buckling behavior of structures with delaminations using the enhanced assumed strain (EAS) solid shell element with 5, 7 and 9 parameters. The EAS three-dimensional finite element formulation presented in this paper is free from shear locking and leads to accurate results for distorted element shapes. The developed FE model is used to study the effects of some parameters in the buckling load, such as the stacking sequences, delamination size, aspect ratio, width-to-thickness ratio. The feasibility of the proposed method is confirmed by numerical examples. Results show that using hexahedral solid-shell finite element in the buckling analysis is more efficient than using the enhanced solid finite element.

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

AbstractIn 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. Copyright © 2009 John Wiley & Sons, Ltd.

The formulation of a refined hybrid enhanced assumed strain solid shell element andits application to model smart structures containing distributed piezoelectricsensors/actuators

In the present paper, a novel refined hybrid piezoelectric element formulationis developed for mechanical analysis and active vibration control of laminatedstructures bonded to piezoelectric sensors and actuators. By invoking the electricalfield potential equation, a ‘quasi-decoupling’ method for treating the couplingelectromechanical effects is presented and a modified generalized variational principlewith a weaker interelement continuity condition is proposed. On the basis ofthis functional, a general formulation for a refined hybrid piezoelectric elementmethod is established by incorporating an orthogonal interpolation approachand enhanced assumed strain (EAS) modes. A linearly distributed transverseEAS in the thickness direction is adopted to overcome the thickness locking ofsolid shell elements. Compared with the conventional incompatible brick elementapproach, the present formulation is very reliable, more accurate, computationallyefficient and can be used to model the response of thin plates and shell structures.

A six-node pentagonal assumed natural strain solid–shell element

In this paper, a six-node pentagonal solid–shell element is formulated. Particular attention is focused on alleviating shear, trapezoidal and thickness lockings that plagues the conventional element. While assumed natural strain method is employed to alleviate shear and trapezoidal lockings, a modified generalized laminate stiffness matrix is proposed to circumvent thickness locking. Unlike the commonly adopted plane stress assumption, the modified laminate stiffness matrix enables the element to reproduce the exact thickness stress and transverse displacement when the element is loaded by thickness stress. Numerical examples reveal that the element is close in accuracy with other state-of-the-art three-node degenerated shell elements.

Stability analysis using a geometrically nonlinear assumed strain solid shell element model

A solid shell element model with six degrees of freedom per node is applied to buckling and postbuckling analysis of geometrically nonlinear shell structures. The present model allows changes in the thickness direction and does not require rotational angles or parameters for the description of the kinematics of deformation. The finite element model is constructed based on the assumed strain formulation in which an assumed strain field is chosen to prevent locking while maintaining kinematic stability. Numerical results show that the present model allows large increments in the iterative solution scheme for pre- and postbuckling analysis. In particular, it appears that the model provides a means to pinpoint a bifurcation point on the geometrically nonlinear deformation path.