Transient analysis of orthotropic, viscoelastic thick plates in the Laplace domain

The present study aims to investigate the transient behavior of orthotropic, viscoelastic thick plates under dynamic loads. The material of the plate is assumed to be orthotropic and linear viscoelastic. The governing equations of motion for thick plates are first obtained in the time domain. Subsequently, Laplace transform is applied and the linear algebraic equations are solved numerically. In viscoelastic modeling, the Kelvin model is employed. In the viscoelastic material case, according to the correspondence principle, the material constants are replaced with their complex counterparts in the Laplace domain. The solutions obtained are transformed to the time domain using the modified Durbinʹs numerical inverse Laplace transform method. For this purpose, a finite element analysis program is coded in FORTRAN. Verification of the numerical procedure is performed by comparing the results with those of an analytical solution available in the literature for a partial uniformly-distributed dynamic load. Moreover, the results of the present method are compared with the results obtained by Newmark method in the time domain. The results obtained in this study are found to be in good agreement with those available in the literature. Obtaining the equation first discretely in the time domain using finite element method (FEM) and then applying the Laplace transform has proved to be a procedure highly accurate and efficient compared to other numerical methods available in the literature.