Thin plate elements with relaxed Kirchhoff constraints

An analysis of thin plates by C⁰ elements is presented. The fundamental part of it is the formulation of a set of constraints that relate the rotational degrees of freedom to the translational degrees of freedom and which are weaker than the usual Kirchhoff constraints. A penalty term associated with these constraints is then introduced instead of the usual expression for the shear strain energy. It is shown that the approach is effective for both quadrilateral and triangular elements.