Interface shape optimization of 3D structures composed of dissimilar materials in natural vibration problem

Abstract

This paper focuses on the design optimization of clad structures composed of different materials, which are expected to earn better characteristic physical and mechanical properties than structures with single materials. In particular, a non-parametric shape optimization method is proposed for designing the interface shapes of three dimensional composite structures composed of dissimilar materials in natural vibration problem. The objective functional consisting of a set of specified vibration eigenvalues with weighting coefficients is maximized under the volume constraint and repeated eigenvalues. Because the positive weighting coefficient maximizes the eigenvalue, whereas the negative weighting coefficient minimizes the eigenvalue, this optimization method makes it possible to control the sum or the gap of the specified eigenvalues by setting positive of negative of the weighting coefficients of the specified eigenmodes. The shape gradient function is derived using the Lagrange multiplier method and the material derivative method, and is applied in shape update based on the H1 gradient method. A cantilever cylinder composed of 2 different materials with repeated eigenvalues and a composite inlaid plate are optimized in this work with two patterns of weighting coefficients to illustrate the shape optimization algorithm. The results show that the proposed interface shape optimization method can successfully control the vibration eigenvalues, while maintaining the smoothness of the interface boundary.

Keywords

• shape optimization
• natural vibration
• interface shape
• solid structure
• composite structures
• non-parametric optimization
• repeated eigenvalues