Non-parametric shape design optimization of elastic-plastic shear panel dampers under cyclic loading

Abstract

In this work, we develop a non-parametric shape optimization method for designing low yield steel shear panel dampers (SPDs) under cyclic loading to enhance their energy dissipation capacity and verify it by experiments. Considering material nonlinearity (elastic-plastic) and geometric nonlinearity (large deformation), we formulate a shape optimization problem based on the variational method for 3D solid continua under cyclic loading, in which the plastic work in terms of von Mises equivalent stress is used as the objective function under a volume constraint. Considering the optimality conditions for the plastic work maximization problem, we theoretically derive the shape gradient function based on the Lagrange multiplier method, the material derivative formula, and the adjoint variable method. The derived shape gradient function is used to the H1 gradient method for designing the optimal shapes of 3D solid continua. We apply the developed shape optimization method to design SPDs made of low yield steel, which is an elastic-plastic material owning high-energy dissipation capacity. Cyclic enforced displacements acting on SPDs are used for simulating cyclic loading and evaluating the capacity of energy absorption of SPDs. To evaluate the nonlinear finite element analysis, we also perform cyclic loading test on SPDs. Two design examples of SPDs without and with holes are optimized to verify the validity of the developed shape optimization method. The results show that the developed optimization method works effectively to enhance the plastic work of SPDs. As a feature, this method can design SPDs more efficiently when considering the variation in the thickness direction.