Time-dependent p-delta analysis of Timoshenko viscoelastic beams and Mindlin viscoelastic plates with different shapes

Abstract

This research introduces a closed-form solution for the time-dependent p-delta analysis of a viscoelastic plate based on the linear static analysis of an elastic plate for the first time, by defining an exponential time function having three unknown coefficients. The new point of the proposed method is that the time response of a Mindlin viscoelastic plate subjected to transversal load and in-plane compression simultaneously is explicitly formulated in the time domain with low computational cost. By finding the minimum eigenvalue in the Laplace-Carson domain, and satisfying the equilibrium equation at two asymptotic times, the three unknown coefficients of the time function are determined. The stress-strain relations are written for linear viscoelasticity with constant bulk modulus according to the Boltzmann integral law. The simple hp cloud meshfree method is utilized for discretizing the equations in the space domain. Numerical results are compared with other available references to demonstrate the accuracy of the proposed formulation. The effect of geometrical, material, and loading parameters on the coefficients of the time function is investigated.