Large deformation analysis of moderately thick viscoelastic plates

Abstract

This paper presents a new formulation for the geometrically nonlinear analysis of viscoelastic Mindlin plates with low computational cost and high computational precision. The equations are derived according to the Von-Karman assumptions and total Lagrangian formulations. The displacement field is approximated by the product of two separate functions, a function of geometrical parameters and a function of time parameter. Incremental decomposition method is applied to achieve linear equations from nonlinear ones. Simple hp cloud meshless method is used for constructing the approximation functions. Illyushin approximation method is utilized to approximate tangent stiffness matrix and residual force vector by some known kernels in the Laplace–Carson domain. Finally, by applying the inverse of Laplace–Carson transformation the equations are obtained in the time domain. We show that the geometrically nonlinear responses of time-dependent viscoelastic plates can be obtained by finding coefficients of a time function without using any time integration or Laplace transformation. The suitability and efficiency of the proposed method for the large deformation analysis of viscoelastic plates is studied for the first time. Also, asymptotic behavior of viscoelastic plates is predicted.