Accurate integration of trimmed cells based on Bezier approximation

In this work, a new adaptive integration method for simulation of two-dimensional linear elasticity problems is presented. The main benefit of the proposed method is the reduction of the computational cost by lowering the number of integration points required to reach a certain level of accuracy. The main concept of the proposed method is to calculate new weights for trimmed cells employing the advantage of Bezier parametric curves. Within this concept, it is possible to map a square to a triangle with one curved edge where any curved edge is approximated by a parametric Bezier curve. In this way, a new set of Gaussian quadrature points is introduced for each trimmed cell in a fast and robust way. Besides main mapping cases, the integration method includes supplementary cases as well to increase the robustness and generality of the method. In the next step, the proposed method is implemented in a two-dimensional fictitious domain code in MATLAB to solve structural problems. The results will be compared to those obtained through the commercial finite element code ABAQUS. It is shown that the proposed method is accurate and robust.