CS-IGA: A new cell-based smoothed isogeometric analysis for 2D computational mechanics problems

In this work a new cell based strain smoothing formulation for isogeometric finite element analysis is proposed. The new CS-IGA method is formulated by incorporating cell-wise strain smoothing operation into IGA method. The compatible strain fields are smoothed based on smoothing domains associated with entities of isogeometric elements and the smoothed Galerkin weak form based on these smoothing domains is then applied to compute the system stiffness matrix. Unlike IGA, this new approach avoids gradient computation and the assembling of stiffness matrices. A transformation method is employed to accurately solve the problem and enforce properly the essential boundary conditions. Several numerical examples are investigated to verify the validity and accuracy of the proposed method. It has been found that numerical results obtained from CS-IGA can achieve very satisfactory accuracy and improved convergence rate.