Exact convergence studies on static and dynamic analyses of plates by using the double U-transformation and the finite-element method

This paper presents exact static and dynamic analyses of simply supported rectangular plates. The analytical solutions for displacements, natural frequencies and dynamic responses are obtained by using the double U-transformation and the finite-element method. These explicit solutions then can easily be used to accurately study the convergence rates of the finite-element solutions. Two non-conforming plate elements are taken as examples to demonstrate the proposed procedure. The analytical finite-element solutions, the exact error expressions and convergence rates are derived. Moreover, the convergent speeds of the two elements are discussed.