Non-conforming multi-patch isogeometric topology optimization for plate and shell structures based on Nitsche’s method

This paper presents a multi-patch isogeometric topology optimization (MITO) method for plates and shells based on Nitsche’s method, which can effectively address compliance minimization problems of complex structures comprised of non-conforming multiple NURBS patches. 5-DOFs Reissner-Mindlin (RM) degenerate elements are used to discretize complex plate and shell structures. Meanwhile, NURBS-based isogeometric analysis (IGA) can accurately described the geometry of the mid-surfaces of both RM plates and shells, where Nitsche’s method is used to couple different patches for several typical interface formulations, with a broader parameter stability domain in penalty factor than traditional penalty method. In addition, the tensor-product decomposed explicit filter is employed to substitute traditional sensitivity filter in our presented MITO approach. Several benchmark examples are presented to verify the effectiveness and robustness of the proposed MITO method for thin wall structures. Compared to the traditional sensitivity filter, the compliance value and design variable update time obtained by the tensor-product decomposed explicit filter are maximumly reduced by 14.8% and 50.6%, respectively. In summary, the proposed MITO method is an effective tool of performing innovative design for complex thin wall structures.