さまざまな形状のユニットで構成された耐震補強ブロック壁の組合せ最適化

Abstract

Seismic performance of an existing building frame can be improved using various devices such as shear walls, shear dampers, buckling restrained brace, base isolator, etc. If we construct shear walls using latticed blocks, we can have much ventilation and transparency compared with the solid walls. In our previous study, we presented a nonlinear programming approach to optimize the topology of latticed blocks to maximize the horizontal stiffness, and also to minimize the increase of shear force in the existing beam. However, it has been found that very thin members exist in the optimal solutions, if the thicknesses of members are considered as continuous variables. In this study, a combinatorial optimization approach is presented for topology design of a latticed shear wall. The existing beams and columns, as well as the lattice members in blocks, are modeled using beam elements. The connections between the latticed blocks as well as those between the blocks and existing members are modeled using the zero-length bi-linear elastic elements. The response against forced shear deformation is evaluated through an incremental geometrically and materially nonlinear analysis. The types of unit blocks that can be selected are given in view of the results of optimization using the nonlinear programming approach. A heuristic approach called simulated annealing is used for optimizing combination of unit blocks. The following three problems are solved: 1. Minimization of structural volume under constraints on horizontal stiffness and stress. 2. Maximization of horizontal stiffness under constraints on structural volume and stress. 3. Minimization of shear force of the upper beam under constraints on horizontal stiffness, structural volume, and maximum stress of lattice members. It is confirmed through numerical examples that various optimal combinations of latticed blocks can be generated using the proposed approach. A latticed shear wall with small structural volume can be found through combinatorial optimization while maintaining the horizontal stiffness and limiting the additional force in the existing frame members. Appropriate choice of types of units that can be selected is important to obtain mechanically efficient latticed shear walls.