# A boundary element formulation for two-step thermoelastic analysis without internal cells

## Palavras-chave:

Boundary Element Method, Cell-less thermoelastic analysis, Radial Integration Method, Moving Least Square Interpolation## Resumo

Uncoupled (two-step) thermoelastic analysis is addressed by a new boundary element method formula-

tion that eliminates the use of internal cells. The first step is a steady-state thermal analysis. The second step is a

mechanical analysis, which uses the temperature field obtained in the first step as part of the applied loads. Domain

integrals in temperature, displacement and stress boundary integral equations are transformed to boundary by the

radial integration method. The radial integration method is a simple and powerful method based on a pure mathe-

matical treatment, which transforms any domain integral into a boundary and a radial ones. The radial integral is

independent of geometry and no discretization is necessary for its evaluation, while the boundary integral can be

solved using the existing boundary mesh. Since temperature has been evaluated only at discrete points, namely the

boundary nodes and a set of internal points, the moving least square procedure is used to calculate temperature at

numerical integration points during evaluation of radial integrations of the second step. The moving least square

is a technique usually adopted to generate shape functions in Meshfree methods. Two representative examples are

presented to demonstrate the accuracy and robustness of the proposed formulation.