Adrian Egger

Research

Analysis of composite structures using the scaled boundary finite element method

The scaled boundary finite element (SBFEM), a semi-analytical fundamental solution-less boundary element method based on finite elements, is a recently developed numerical structural analysis method that combines many of the advantages of the well-established finite element method (FEM) and the boundary element method (BEM), while alleviating most of their respective shortcomings and simultaneously introducing significant benefits of its own. This stems from the fact that an analytical solution is sought in the radial direction, whereas the method of weighted residuals is employed in the circumferential direction and thus leading to a FEM-like formulation, which may be readily coupled with existing FEM and BEM.

Some of SBFEM’s more noteworthy advantages include but are not limited to:
• The reduction of the special dimension by one as only the boundary must be discretized, thus reducing data preparation as well as computational costs
• The analytical solution in the radial direction permits analytical calculations of stresses and stress singularities extracted directly from their definitions without the need for a priori knowledge
• The transition between and the presence of power and power-logarithmic singularities, as they are frequently encountered in multi-material test cases, are evaluated with a single stable algorithm

Quantities relevant to crack related phenomena, such as stress intensity factors (SIFs) and T-stresses, can be easily extracted from the unmodified displacement solution procedure without the need for asymptotic expansion or tip enrichment commonly found in the extended finite element method (XFEM). Further, a newly proposed error estimator for SIFs and T-stresses based on the super-convergent patch recovery theory allows for accurate estimations with comparatively few degrees of freedom (DOF) at negligible additional computational cost.

These insights can be directly applied to modelling composite structures, a field only recently tested and implemented for Civil Engineering applications. Within a damage mechanics framework (i.e. crack initiation, crack propagation and delamination), problems previously rendered practically unsolvable due to excessive computational requirements are now again solvable using SBFEM. Furthermore, the numerical error in crack initiation and propagation can now be efficiently and accurately quantified.