A Two-Field Formulation in Isogeometric Analysis to Alleviate Locking

Abstract

In recent past, isogeometric analysis (IGA) has gained significant popularity as a numerical technique in computational mechanics. The systematic framework of IGA allows maintaining the exact geometry during discretization regardless of how coarse the mesh is, and furthermore, it also eliminates the dependency on computer-aided design (CAD) once the initial mesh is created. IGA often referred as a generalized version of finite element analysis (FEA) or with a different perspective FEA can be seen as a special case of IGA. Though IGA performs superior to FEA in several ways, it does exhibit similar limitations sooner or later like its FE counterpart. One such limitation is locking which appears during the analysis of thin structural parts and for incompressible or nearly incompressible material. However, on the promising side, the techniques available in FEA to tackle such limitations can be successfully modified to work with IGA as well. In the present work, a two-field hybrid formulation is explored in the framework of IGA which performs convincingly well in situations where the problem demands incompressibility or near incompressibility of material or to solve problems of beam/plate/shell geometries and so on. As per our best knowledge, the stated method is yet to be studied in context of IGA, despite the fact that the same formulation will eliminate different types of locking. Finally, the proposed formulation has been successfully implemented on several examples with promising results.