Sensitivity analysis with non-locking three node mindlin plate elements

A finite element formulation and analytical and semianalytical methods for calculating sensitivity derivatives for static analysis and design problems of Mindlin plate structures are presented. The finite element is the hybrid-stress version of the displacement model element MIN3 by Tessler and Hughes [1]. It is triangular and has a simple nodal configuration with three corner nodes and C-0 type nodal variables. The use of independent field assumptions for displacements and stresses removes the necessity for the inplane shear correction factor of MIN3. With its three-noded configuration, the element can effectively be used as the bending part of facet shell elements, and due to its simplicity and accuracy, it can be employed in large scale analysis and design problems of folded plate and shell structures. The sensitivity derivatives that are needed in the design processes 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.