TOPOLOGY OPTIMIZATION OF LARGE DEFORMABLE ELASTIC PLATES

Abstract

 Brace structures have been used for a lot of steel buildings because they can give high stiffness and strength to buildings economically. However, brace members have a possibility that buckling or yielding occur in early stage under major earthquakes. In 2016 Kumamoto earthquake, tensile fractures and buckling residual deflection for braces were observed. In addition, damages of many column bases and foundations were observed. Therefore it was surmised that there might have been gymnasiums which could not be used as emergency evacuation. There are a lot of studies to improve hysteresis property of braces, i.e. NC braces, buckling restrained braces and metallic yielding damper braces. However, seismic upgrading by adding above braces needs attentions on large variation of natural periods and increase of seismic load on foundation structures.

 On the other hand, large deformable elastic devices have been studied by authors, which show only slight variation in natural period and seismic load of foundation for the upgraded structures. Large deformable elastic devices can realize elastic performance under even major earthquakes. In previous studies, the various devices were produced by trial and error using laser cutting machine from steel plates. It was overserved from previous tensile tests that the devices kept elastic performance until around 1.5% of the original length and from previous time history analyses that the devices reduced maximum and residual response of story drift.

 This paper explore effective topologies of the devices which show larger elastic deformation capacity by a topology optimization technique from a rectangle two dimensional plate shown in Fig. 1. The optimization technique uses a formulation with a function similar to Inverse Fourie Transformation and real coded Genetic algorithm.

 Concluding remarks are as follows.

 (1) No checkerboard patterns are found from Fig. 10-Fig. 25 and Fig. 27 by using a function similar to Fourier Inverse transformation for topology optimization.

 (2) It is observed from Fig. 11-Fig. 26 and Fig. 27 that the optimization technique can give regular periodical patterns by setting of large values of γ₁.

 (3) It is observed from numerical results in Table 1-Table 3 .that using high strength steel can give very large elastic performance until 2.5% of the original length and using even standard steel can give large elastic performance until 1.4% of the original length.

 (4) Mechanism of the optimization technique of this study is shown by visualization of Function F(x_k, y_k) in Fig. 2-Fig. 7.

 (5) Small differences between elastic linear analyses and material and geometrical nonlinear analyses are observed until 2% to original length of elastic deformation.