Generalized finite element approaches for analysis of localized thermo-structural effects

This work addresses computational modeling challenges associated with structures subjected to sharp, local heating, where complex temperature gradients in the materials cause three-dimensional, localized, intense stress and strain variation. Because of the nature of the applied loadings, multiphysics analysis is necessary to accurately predict thermal and mechanical responses. Moreover, bridging spatial scales between localized heating and global responses of the structure is nontrivial. A large global structural model may be necessary to represent detailed geometry alone, and to capture local effects, the traditional approach of pre-designing a mesh requires careful manual effort. These issues often lead to cumbersome and expensive global models for this class of problems. To address them, the authors introduce a generalized FEM (GFEM) approach for analyzing three-dimensional solid, coupled physics problems exhibiting localized heating and corresponding thermomechanical effects. The capabilities of traditional hp-adaptive FEM or GFEM as well as the GFEM with global-local enrichment functions are extended to one-way coupled thermo-structural problems, providing meshing flexibility at local and global scales while remaining competitive with traditional approaches. The methods are demonstrated on several example problems with localized thermal and mechanical solution features, and accuracy and (parallel) computational efficiency relative to traditional direct modeling approaches are discussed.