: This paper presents a geometrically nonlinear analysis of viscoelastic Mindlin plates with various shapes and different boundary conditions using the Laplace-Carson transformation. Nonlinear bending analysis of viscoelastic plates subjected to transversal loading is presented with no need to follow the time-displacement path. The equations are derived based on the Von-Karman assumptions and total Lagrangian formulations. The mechanical properties of the materials are assumed to be linear viscoelastic with constant bulk modulus. The displacement field is assumed to be a known function of time. Incremental decomposition method is applied to achieve linear equations from nonlinear ones. 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. Simple hp cloud meshless method is used to discretize the domain of plate. The suitability and efficiency of the proposed method for the geometrically nonlinear analysis of moderately thick viscoelastic plates is studied for the first time. Key words : Geometrically nonlinear analysis, Incremental decomposition metod, Laplace-Carson transformation, Viscoelastic Mindlin plate. 1. Introduction
