Abstract
This paper presents a non-parametric shape optimization method for a solid structure under cyclic elasto-plastic loading. A distributed-parameter optimization problem for cyclic deformation considering material non-linearity and geometrical non-linearity is formulated, in which the plastic work is maximized under a volume constraint, and the shape gradient function and the optimality conditions for this problem are theoretically derived using the adjoint variable method. The adjoint analysis is thinned out under the assumption that the piecewise proportional loading holds true in spite of the plastic deformation. The shape gradient function derived is applied to the H1 gradient method to obtain the optimal three-dimensional shape, where the negative shape gradient function is used to move the design domain. The objective functional, the plastic work equivalent to the energy dissipation capacity, is maximized in the iterative process while maintaining the mesh regularity without re-meshing. This method is applied to design a shear panel damper (SPD) with high energy dissipation capacity which is made of low yield steel and can dissipate seismic energy by plastic deformation. The calculated results show the validity of this method for efficient designing a non-linear structure for cyclic elasto-plastic loading efficiently.
