Abstract
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.
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