A non-intrusive iterative generalized finite element method for multiscale coupling of 3-D solid and shell models

Fully 3-D models can be prohibitively expensive when dealing with industrial-scale problems while plate and shell models are not able to capture localized 3-D effects around cracks, welds, and other structural features. This paper presents an iterative multiscale Generalized Finite Element Method (GFEM) able to automatically couple 3-D solid and shell models and capture interactions among structural scales. Three scales and corresponding models and discretizations are considered: A global shell model that captures only the overall behavior of a structure; a 3-D mesoscale model that bridges the solutions between the global and finer scales; and a 3-D fine-scale model, denoted local model, used to simulate localized defects, such as cracks, or structural features, such as welds. The coupling between global and mesoscale models is done using the iterative global-local algorithm and a Generalized Finite Element Method with analytically or numerically defined enrichments is used for the meso and local scales coupling. The proposed multiscale framework combines software with complementary capabilities. The shell problem is solved with the commercial software Abaqus while the meso and local scale problems are solved with an in-house GFEM solver. Another contribution of this work is a staggered algorithm for the solution of the coupled problems defined at the global, meso, and local scales. The performance of the methodology is compared against fully 3-D models and the sub-modeling approach which is widely adopted in engineering practice for the analysis of problems with multiple spatial scales of interest.