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A trapezoidal hierarchical finite element for nonlinear free and forced vibration analyses of skew and trapezoidal Mindlin plates is introduced. Legendre orthogonal polynomials are used as enriching shape functions to avoid the shear-locking problem. The element matrices are analytically integrated in closed form. With the enriching degrees of freedom, the accuracy of the computed results and the...
Three new Fourier p-elements of rectangular, skew and trapezoidal shapes are given analytically for plane viscoelastic vibration problems. The natural frequencies of the plane viscoelastic structures with complex Young's modulus are computed by a complex eigenvalue solver. With the additional Fourier degrees of freedom, the accuracy of the computed natural frequencies is greatly increased. Since trigonometric...
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