Multiscale SBFEM analysis

Real world structures pose a significant computational challenge. A methodology to circumvent this issue is the introduction of multiscale methods. Here, we propose exploiting SBFEM on the fine scale to account for damage related phenomena and solve the governing equation on a significantly reduced coarse mesh of representation volume elements (RVEs). These scales are linked with numerically computed mapping functions according to the extended multiscale finite element method, which are only computed once at the start of analysis. Hence, we call this approach the multiscale scaled boundary finite element method (MsSBFEM).

The behaviour of different types of RVEs possesing either 4/8/12/16 coarse nodes using the example of a masonry wall is explored.

Enlarged view: Masonry wall comprised of a 6 x 5 RVE grid, clamped at bottom and loaded in shear at top — Masonry wall comprised of a 6 x 5 RVE grid, clamped at bottom and loaded in shear at top

Enlarged view: Von Mises stress using RVEs with 4 coarse nodes (Q4 elements) — Von Mises stress using RVEs with 4 coarse nodes (Q4 elements)

Enlarged view: Von Mises stress using RVEs with 12 coarse nodes (Q12 elements) — Von Mises stress using RVEs with 12 coarse nodes (Q12 elements)

Enlarged view: Von Mises stress of SBFEM reference solution fully resolving the domain without the useof RVEs — Von Mises stress of SBFEM reference solution fully resolving the domain without the useof RVEs

Enlarged view: Von Mises stress using RVEs with 8 coarse nodes (Q8 elements) — Von Mises stress using RVEs with 8 coarse nodes (Q8 elements)

Enlarged view: Von Mises stress using RVEs with 16 coarse nodes (Q16 elements) — Von Mises stress using RVEs with 16 coarse nodes (Q16 elements)

Computational gains

Substantial computational gains can be achieved, when utilizing multiscale methods, while maintaining most of the model's fidelity.

Enlarged view: Reduction of computational cost and complexity — Reduction of computational cost and complexity