Topology optimization of isotropic beam cross section accounting for stiffness and strength constraints

This paper presents a topology optimization framework for the design of isotropic beam cross section. The optimization question is formulated using the solid isotropic material with penalization method. The objective is to minimize the weight per unit of length of the beam, while the constraints can account not only for stiffness and strength requirements, but also for the position of the normal stress center and shear center, as well as the orientation of principal axis. During the optimization process, the cross-section analysis is performed by a dedicated two-dimensional finite element code, while the sensitivity information is efficiently computed by resorting to the adjoint method, significantly speeding up the optimization procedure. Numerical examples are presented to illustrate the effect of different constraint on the optimal cross-section topology. Finally, fully constrained optimizations are performed to demonstrate both the effectiveness of the proposed method and its applicability to practical cross-section design.