Thermo-stress in multi-layered elastic half space solved with stiffness matrix method

In the paper, thermo-stress in multilayered elastic half space is presented. Firstly, the stiffness matrix for a layer is derived based on the fundamental elasticity equations and some mathematic methods such as Hankel integral transformation. Then the global stiffness matrix is established for multilayered elastic half space using the finite element concepts in which layers are completely contacted. Therefore, explicit solution for axisymmetrical problems in multilayered elastic half space is obtained from the solution of the algebraic equation formed by global stiffness matrix and the inverse Hankel integral transformation. Because positive exponential function is not included in the element of matrix, the calculation is not overflowed. Therefore, the shortages of transfer matrix method are overcome. This method is clear in concept, and the corresponding formulas given in the paper are not only simple but also convenient for application. More important is that this method can be used to solve other problems of multilayered elastic half space such as thermo field and dynamics. An example of road surface deflection is presented to prove the calculated results.