An efficient through‐thickness integration scheme in an unlimited layer doubly curved isoparametric composite shell element

Abstract

This paper presents an efficient numerical integration scheme for evaluating the matrices (stiffness, mass, stress-stiffness and thermal load) for a doubly curved, multilayered, composite, quadrilateral shell finite element. The element formulation is based on three-dimensional continuum mechanics theory and it is applicable to the analysis of thin and moderately thick composite shells.The conventional formulation requires a 2 x 2~2 or 2 x 2~ 1 Gauss integration per layer for the calculation of element matrices. This method becomes uneconomical when a large number of layers is used owing to an exccssive amount of computations. The present formulation is based on explicit separation of the thickness variable from the shell surface parallel variables. With the through-thickness variables separated, they are combined with the thickness dependent material properties and integrated separately. The element matrices are computed using the integrated material matrices and only a 2 x 2 spatial Gauss integration scheme. The response results using the present formulation are identical to those obtained using the conventional formulation. For a small number of layers, the present method requires slightly more CPU time. However, for a larger number of layers, numerical data are presented to demonstrate that the present forinulation is an order-of-magnitude economical compared to the conventional scheme.

Reliability assessment of post-buckling compressive strength of laminated composite plates and stiffened panels under axial compression

“…In order to overcome this problem, explicit through-thickness integration schemes have been developed for linear problems where the inverse of Jacobian matrix is assumed to remain either constant (Vlachoutsis, 1990) or to vary linearly across the thickness (Yunus et al, 1989). The comparison study conducted by Prema Kumar and Palaninathan (1997) showed that the model proposed by Yunus et al (1989) is more accurate than the model of Vlachoutsis (1990).…”

“…The updated Lagrangian finite element formulation with a degenerated shell element (Ahmad et al, 1970) is used for the structural analysis. To improve the computational efficiency, a new explicit throughthickness integration scheme is developed for nonlinear analysis which was based on the one of Yunus et al (1989) that was applicable only to linear problems. The Tsai-Wu criterion (Tsai and Wu, 1971) is adopted to predict the failure mechanisms and the stiffness reduction is carried out at the Gauss points of the finite element mesh depending on the mode of failure.…”

“…The postbuckling compressive strength of laminated composite plates and stiffened panels was predicted by a progressive failure analysis performed with a nonlinear finite element code developed by the authors. To improve the computational efficiency, this code implemented a new explicit through-thickness integration scheme for nonlinear analysis which was developed from the one of Yunus et al (1989) that was applicable only to linear problems. A code was also developed to perform a reliability assessment coupled with the finite element code.…”

An efficient method for nonlinear analysis of layered shells

“…The direct extension of the same to the layered shells (Panda & Natarajan 1981) becomes computationally inefficient when the number of layers in the laminate is large, which is usually the case in reality. In order to overcome this, explicit through-thickness integration schemes (Yunus et al 1989;Vlachoutsis 1990) have been formulated for linear problems. Explicit integration through the thickness becomes possible when the elements of the inverse Jacobian are assumed to either remain constant or have a particular variation through thickness.…”

Gradient reproducing kernel particle method

“…It is suitable for laminate composites and can accept up to 100 different layers. This element is discussed by Yunus et al [1989]. A planner view of this element is given in Figure 12.…”