An isogeometric approach to topology optimization of multi- material and functionally graded structures

Alireza H. Taheri, Krishnan Suresh* Department of Mechanical Engineering, UW-Madison, Madison, Wisconsin 53706, USA. * Corresponding author, email: [email protected] Abstract A new isogeometric density based approach for the topology optimization of multi-material structures is presented. In this method, the density fields of multiple material phases are represented using the isogeometric NURBS-based parameterization leading to exact modeling of the geometry, and removing numerical artifacts. Moreover, due to the unified parameterization of the geometry, analysis and design space, the sensitivities are computed analytically, and in a cost effective manner. An extension of the perimeter control technique is proposed where restrictions are imposed on the perimeters of density fields of all phases. Due to higher order continuity of the density fields, the gradients are calculated exactly without additional computational cost. Consequently, not only can mesh-independency be achieved, but the complexity of the optimal design can be controlled easily. The problem is formulated with constraints on either: (a) volume fractions of different material phases, or (b) the total mass of the structure. The proposed method is applied for the minimal compliance design of twodimensional structures consisting of multiple distinct materials as well as functionally graded ones. Numerical results demonstrate high quality of the obtained optimal designs, and superior performance of these structures compared to the corresponding single material topological designs.