Isogeometric analysis for trimmed CAD surfaces

In this work, an Isogeometric analysis for trimmed CAD surfaces in 2D linear elasticity problem is presented. The main benefit of the proposed method is that no additional modeling for the analysis of the trimmed surface is necessary. As a pioneering attempt to deal with the trimmed surfaces in Isogeometric analysis, the information on the trimming curves and trimmed surfaces exported from CAD system is directly utilized for analysis. For this, trimmed elements are searched through using a projection scheme. For the integration of trimmed elements, NURBS-enhanced integration scheme employed in NEFEM is adopted. For the Isogeometric analysis, the construction of the stiffness matrix based on the spline basis function is presented. In the formulation, the information on the trimming curves is used not only for obtaining integration points but also for calculating the Jacobian. Through error analyses of the verification examples, the robustness and effectiveness of the proposed method are investigated. It is observed that the proposed method gives the theoretical convergence rate. Multiple-trimming-curve problems which are difficult to analyze with conventional Isogeometric analysis are easily treated with the proposed method. An illuminating example is given. In the same example, T-spline local refinement is also employed.