Multi-material polygonal topology optimization for incompressible structures under harmonic force excitation
Hieu P. Ban,Thanh T. Banh,Soomi Shin,Dongkyu Lee
Abstract
This paper introduces a practical method for multi-material topology optimization of continuum structures subjected to harmonic load excitation, encompassing a broad range of materials from compressible to incompressible. The approach leverages a specialized polytopal composite finite element (PCE) framework capable of addressing diverse material behaviors, effectively mitigating volumetric locking issues commonly observed in nearly incompressible materials. Furthermore, a generalized harmonic load model, incorporating damping effects, is employed to deliver a comprehensive solution for multi-material optimization. This innovative method accommodates various elemental geometries, such as triangles, quadrilaterals, and polygons, across both compressible and nearly incompressible material regimes. The paper provides rigorous mathematical formulations for optimizing the topology of multi-material structures and demonstrates the method's efficiency and accuracy through a series of numerical examples. The proposed approach is validated by comparing optimized designs with those derived from traditional methods, highlighting its advantages. Additionally, the influence of varying excitation frequencies, damping coefficients, and force amplitudes on the optimized results is thoroughly examined, underscoring the critical importance of considering such factors in the design of resonant structures.
