Linear and geometric nonlinear spline finite element analysis for trimmed cad models and its extension to meshfree analyses

Abstract

Trimming technique is a powerful and efficacious way of endowing an arbitrary complex topology to CAD files created by using NURBS. In this work, spline FEM for trimmed CAD surfaces in linear and geometric nonlinear elasticity problem is presented. The main benefit of the proposed method is that no additional modeling for the analysis of the trimmed NURBS surfaces is necessary. As a pioneering attempt to deal with the trimmed surfaces in spline FEM, the information on the trimming curves and trimmed surfaces exported from CAD system is directly utilized for analysis. For this, a specific searching algorithm and an integration scheme of trimmed elements are introduced. For analyses, 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. It is observed that the proposed method gives the theoretical convergence rate. Multiple-holes problems which are difficult to analyze with conventional spline FEM are easily treated with the proposed method. Moreover, if the domain boundaries are described by trimming curves only, with the extension of the classical concepts of trimming curves, it is supposed that the proposed method has a lot of advantages over conventional methods. First, any problems of arbitrary complex topology can be handled. The flexibility for describing complex domain is significantly improved, because the complicated boundaries are easily represented by NURBS curves. Circular or any degrees of polygonal shapes are manageable. It is shown that any complex multiply-connected NURBS domain can be described by using trimming curves only. Schemes for imposing essential and traction boundary conditions on trimming curves are presented. It has been demonstrated that with the presented schemes boundary conditions on trimming curves can be successfully treated. Second, when p...