An Improved Isogeometric Analysis Using the Lagrange Multiplier Method

Isogeometric analysis (IGA) is a novel computational approach recently developed by Hughes et al. [1]with the aim of integrating computer aided design (CAD) into structural analysis. It uses non uniform rational B-splines (NURBS) for both description of the geometry and approximation of thesolution field. NURBS are the most common basis functions in the CAD systems. Using CAD basis functions directly in the finite element analysis (FEA), leads to eliminate the existing time-consuming data conversion process between CAD systems and finite element packages in engineering problems. This is one of the main ideas behind developing isogeometric analysis and vastly simplifies mesh refinement of complex industrial geometries [1].Although IGA has attracted many research interests and successfully has been applied in diverse engineering problems, but it still suffers from a number of drawbackswhich require further investigation. One of the key challenges with IGA is the imposition of essential boundary conditions; hence, some specific techniques have to be used. As the NURBS basis functions in isogeometric analysis,similar to many meshfreebasis functions, are not interpolatory; they do not satisfy the kronecker-delta property. Therefore, imposition of inhomogeneous essential boundary conditions is not a straightforward task, as it is the case in a homogeneous one.To impose the essential boundary conditions in numerical methods with non-interpolatory basis function, several strategies have been proposed [2]. Since the Lagrange multiplier method [3] has been widely applied in various engineering simulations, it is now selected for improving the imposition of essential boundary conditions in IGA.