AN ISOGEOMETRIC APPROACH FOR THE SIMULATION OF SOLID MECHANICS PROBLEMS

Abstract

The NURBS based Isogeometric analysis offers a seamless integration between the CAD and subsequent finite element analysis and has been shown to be very effective for wide classes of problems due to its accurate geometric description. NURBS can accurately define any shape. Therefore, NURBS based Isogeometric analysis for solving problems of FEA becomes quite accurate. NURBS are used widely today due to their ability to construct an - exact geometric model in several practical applications. A NURBS based Isogeometric approach has been used in the present work. The FEM formulation was developed based on NURBS basis functions to solve two-dimensional plane problems. Two problems were solved, an infinite plate with hole in tension and a hollow , cylinder with uniform internal pressure. The results obtained by isogeometric analysis were compared with those obtained by exact method and ANSYS. This concept is further extended to three-dimensional problems. The concept of multiple patches is introduced to solve those problems which are difficult to solve by the single patch. Two problems were solved using multiple patch program. To model and simulate discontinuities (cracks and holes) in the plate, the Isogeometric analysis is combined with XFEM. A mathematical formulation is given for extended Isogeometric analysis (XIGA). The nine problems are solved using the developed MATLAB program. The values of Stress intensity factor were compared with those obtained by exact results. These simulations show that XIGA is quite accurate for solving problems of discontinuous domains. 0