Among various methods for seismic retrofit, installation of shear wall composed of light weight blocks to existing frame is an effective approach in view of reduction of construction cost because they can resist compression (contact to wall) only and complex anchoring and/or welding is not necessary. However, shape of block in practical design tends to be regular due to simplicity in manufacturing process. The second author developed a method of shape optimization of latticed blocks based on ground structure approach. Since a nonlinear programming approach is used, very thin lattice members existed in the optimal solutions. To prevent this difficulty, a combinatorial method has been presented for layout optimization of blocks with given pattern. In both studies, location of the node is fixed, and the latticed block is discretized into beam element.
This paper presents a new method of shape optimization of a shear wall consisting of latticed blocks, where the lattice members are discretized into plane stress shell elements and the location of node and the width of diagonal elements of latticed blocks are adopted as design variables, respectively. In the first phase of proposed method, the geometry of lattice is optimized with fixed topology and width of lattice members. In the second phase, the width of lattice members are optimized with fixed topology and geometry. Each phase is repeated alternatively, and the members with small width are removed to change the topology before restarting the first phase. In each phase, an optimization problem is formulated to maximize the lateral reaction force for specified inter-story drift angle. Simulated Annealing (SA) is used for solving the optimization problem. Moreover, to obtain various shapes, force density method is utilized to move the nodes without modifying topology. In this approach, force density is treated as an auxiliary parameter for arrangement of latticed element.
Numerical examples are presented to demonstrate effectiveness of the proposed method. In numerical examples, it can be confirmed that various kinds of optimal solution are obtained. And it is shown that a truss frame which each member is arranged diagonally for smooth stress transmission through optimization process. Optimal solutions can resist the shear force 1.09-1.34 times larger than that of the initial shape. By using this proposed method, it can be confirmed that optimal solution can be archived maximizing the lateral reaction force.