Improved numerical integration of thick shell finite elements

Abstract

SUMMARYA quadratic thick shell element derived from a three-dimensional isoparametric element was first introduced by Ahmad and co-workers in 1968. This element was noted, however, to be relatively inefficient in representing bending deformations in thin shell or thin plate applications. The present paper outlines a selective integration scheme for evaluating the stiffness matrix of the element, in which each component of the strain energy is evaluated separately using a different Gaussian integration grid for each contribution. By this procedure, the excessive bending stiffness of the element, which results from the use of the quadratic interpolation functions, is avoided.The improved performance of this element, as compared with the original thick shell element, is demonstrated by analyses of a variety of thin and thick shell problems.*

Discretization by finite elements of a model parameter dependent problem

“…Reduced integration -the artifice of lowering the order of the integration rule used to compute certain contributions to the stiffness matrix in order to achieve better approximation -has received much attention in the engineering literature over the past decade [5][6][7][8][9][10]12,13]. Its principle success has been in thin plate problems (the two dimensional analogue of the problem considered here) and in modelling nearly incompressible materials.…”

On a Four-Node Quadrilateral Plate for Laminated Composites

“…As it was soon detected that uniform reduced-order integration schemes were not fully effective, selective reduced-order integration schemes were then proposed as an improvement over the uniform schemes. The reader is referred to the pioneering works by Pawsey and Clough (1971), and by . However, such selective schemes introduced spurious zero-energy modes, which motivated the development of the "Heterosis" element by Hughes and Haroum (1978).…”

Supernatural QUAD4: A template formulation

“…Full Reduced Integration (FRI) and Selective Reduced Integration (SRI) emerged during 1969-72 [13,36,48,64] as tools to improve the in-plane bending behavior of isoparametric displacement models. Initially labeled as "variational crimes" by Strang [56,57] they were eventually justified through lawful association with mixed variational methods [30][31][32][33].…”