Improvement of Plate and Shell Finite Elements by Mixed Formulations

Mixed formulations are introduced as a means for reducing severe constraints in finite-element derivations. For plate bending elements to include transverse shear effect and to be applicable also to thin plates, the method can reduce the conditions of constraints of zero transverse shear strain energy. For shell elements, the constraints of rigid-body modes can be lessened similarly. Certain mixed formulations have been shown to be equivalent to displacement models with reduced integration scheme. But the present approach provides a general and rational method for the finite-element development. Illustrative examples include plate, circular arch, and shell elements.