Simple quadrilateral plate element is developed based on the Hellinger-Reissner hybrid/mixed variational principle with independently assumed displacement and stress field, in this study.
Note is to show a way for using incompatible displacement for plate bending problems by the Hellinger-Reissner principle. Initial choice of stress terms are assumed with complete polynomials to be unconstrained, and added internal displacements such that corresponding strain terms are also taken to satisfy the completeness and consistency with the assumed stresses. The additional displacements are used as Lagrangian multipliers to enforce the stress equilibrium constraint. Approach for the choosing the stress terms for a hybrid stress element is based on the condition of vanishing of the virtual work along the element boundary due to the stress terms higher than constant and the additional incompatible displacement.
Through the numerical examples, the verification of the developed element is considered by comparing with the other element and more improved results are obtained.
