Abstract
In this paper, we propose an optimization method for designing microstructural geometry to maximize the vibration eigenvalues of a laminated shell structure. The material properties of the porous material are calculated using the homogenization method, and the homogenized elastic tensor and density obtained are applied to the macrostructure mathematically linking the microstructures and the macrostructure. In maximizing the vibration eigenvalues, a KS function is introduced to avoid the repeated eigenvalue problem. The area-constrained microstructure optimization problem is formulated as a distributed-parameter optimization problem, and the shape gradient function is theoretically derived using the Lagrange multiplier method. The microstructures are optimized with the H1 gradient method, using the shape gradient function derived. The optimization system was constructed combining a C language program with a commercial FEM code. Numerical results showed that the microstructural shapes are optimized with increasing vibration eigenvalues for the cantilever macro-model.
