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Finite and Boundary Element Methods

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Thermal Stresses – Advanced Theory and Applications

Part of the book series: Solid Mechanics and its Applications ((SMIA,volume 158))

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Because the analytical solutions to coupled and generalized thermoelasticity problems are mathematically complicated, the numerical methods, such as the finite and the boundary element methods, have become powerful means of analysis. This chapter presents a new treatment of the finite and the boundary element methods for this class of problems. The finite element method based on Galerkin technique is employed in order to model the general form of the coupled equations, and the application is then expanded to the two- and one-dimensional cases. The generalized thermoelasticity problems for a functionally graded layer, a thick sphere, a disk, and a beam are discussed using Galerkin finite element technique. To show the strong rate of convergence of Galerkin-based finite element, a problem for a radially symmetric loaded disk with three types of shape functions, linear, quadratic, and cubic, is solved. It is shown that the linear solution rapidly converges to that of the cubic solution. The chapter concludes with the boundary element formulation for the generalized thermoe-lasticity. A unique principal solution satisfying both the thermoelasticity and the coupled energy equations is employed to obtain the boundary element formulation

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(2009). Finite and Boundary Element Methods. In: Thermal Stresses – Advanced Theory and Applications. Solid Mechanics and its Applications, vol 158. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9247-3_9

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