Minimal assumed moments and optimal local coordinates for plate elements based upon the complementary energy functional

Abstract

In most plate/shell elements founded on the complementary energy functional, the assumed mement spaces are not minimal. The reason of introducing additional moment modes is to build elements with sufficient stiffness. A new method of using incompatible deflections to select the minimal moment modes is attempted. A square 4-node and a square semiLoof plate elements are derived. They are both stable and not overflexible. To generalize the elements for distorted geometry, three different local coordinates are employed. Unexpectedly, the skew coordinates formed by the covariant base vectors of the natural coordinates are least desirable. © 1994 Springer-Verlag.