Improved numerical integration of thick shell finite elements

Abstract

Abstract A 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 me 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. Editors' note: A similar development was outlined by O. C. Zienkiewicz and co‐workers in lnt. J. num. Meth. Engng , 3 , 275–290 (1971). Some important details differ between the two papers which are thus complementary.