The quasi-static and dynamic responses of a linear viscoelastic beam are solved numerically by using the hybrid Laplace transform/finite element method In the analysis, the Timoshenko beam theory, which includes the transverse shear and rotatory inertia effect and conventional beam theory, are used to solve this problem The temperature field is assumed to be constant and homogeneous and that the relaxation modulus has the form of the Prony series In the hybrid method, the Laplace transform with respect to time is applied to the coupled equations and the finite element model is developed by applying Hamilton's variational principle without any integral transformation The numerical results of quasi-static and dynamic responses for the models of Maxwell fluid and three parameter solid types are presented and discussed

The hybrid Laplace transform/finite element method applied to the quasi‐static and dynamic analysis of viscoelastic Timoshenko beams

This paper deals with the transient response of one-dimensional axisymmetric quasistatic coupled thermoelastic problems. Laplace transform and finite difference methods are used to analyze the problems. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in the transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. We obtain solutions for the temperature and thermal stress distribution in a transient state. Moreover, the computational procedures established in this article can solve the generalized thermoelasticity problem for a multilayered hollow cylinder with orthotropic material properties.

Transient thermal stress analysis of multilayered hollow cylinder

Application of the hybrid method to inverse heat conduction problems

Hybrid Laplace transform technique for non-linear transient thermal problems

http://eportfolio.lib.ksu.edu.tw/user/T/0/T093000109/repository/hyper/1994%20Numerical%20solution%20of%20hyperbolic%20heat.pdf

Tzer-Ming Chen

Papers

Hybrid Laplace transform/finite element for one-dimensional transient heat conduction problems