A Mindlin plate finite element with semi-analytical shape design sensitivities

A hybrid-stress Mindlin plate finite element and its sensitivity derivatives are presented. The element is triangular and has a simple nodal configuration with three corner nodes and Co type nodal variables. The use of independent field assumptions for displacements and stresses removes the necessity for an in-plane shear correction factor. The element can effectively be used as the bending part of facet shell elements. Its simplicity and accuracy makes it ideal for large-scale analysis and design problems. The sensitivity derivatives are obtained by analytical and semi-analytical methods for the thickness and shape design variables, respectively. The well-known deficiency of the classical semi-analytical method in the shape design of flexural systems is alleviated by using a series approximation for the sensitivity derivatives and considering the higher order terms. The accuracy of the proposed formulations in computing displacements, stresses and sensitivity derivatives is verified by numerical examples.