Automatic image-based analyses using a coupled quadtree-SBFEM/SCM approach

Abstract

Quadtree-based domain decomposition algorithms offer an efficient option to create meshes for automatic image-based analyses. Without introducing hanging nodes the scaled boundary finite element method (SBFEM) can directly operate on such meshes by only discretizing the edges of each subdomain. However, the convergence of a numerical method that relies on a quadtree-based geometry approximation is often suboptimal due to the inaccurate representation of the boundary. To overcome this problem a combination of the SBFEM with the spectral cell method (SCM) is proposed. The basic idea is to treat each uncut quadtree cell as an SBFEM polygon, while all cut quadtree cells are computed employing the SCM. This methodology not only reduces the required number of degrees of freedom but also avoids a two-dimensional quadrature in all uncut quadtree cells. Numerical examples including static, harmonic, modal and transient analyses of complex geometries are studied, highlighting the performance of this novel approach.