A variational justification of the assumed natural strain formulation of finite elements—II. The C0 four-node plate element

Abstract

In Part II the four-node $C^{0}$ plate bending element is used to explore some of the possibilities opened by the theory presented in Part I [C. Militello and C. A. Felippa, Comput. Struct.34, 431–438 (1990)]. This element is chosen because the version presented by Bathe and Dvorkin [Int. J. Numer. Meth. Engng21, 367–383 (1985)], MITC4, can be considered the simplest assumed natural strain element that allows several possibilities to be studied in a straightforward manner. Attention is focused on the governing functionals R and H presented in Part I, assuming independent strain fields only for the transverse shear strains. Besides MITC4, three formulations (two mixed and one hybrid) are considered that collectively represent a variational justification for the assumed strain technique. In addition, reduced and selective-integration elements are examined to compare their behavior with that of the present assumed strain elements.