Abstract
In order to overcome numerical instabilities such as checkerboards, meshdependence in topology optimization of continuum structures, a new implementation combined with homogenization method without introducing any additional constraint parameter is presented. To overcome the shortcoming of continuous material distribution by the introduction of finite element approximation, moving least square or modified filter functions are adopted as interpolation function. The method can be viewed as a nature extension of node-based homogenization method and named as material point homogenization method. Continuous size field and continuous density field are constructed, and structural responses' sensitivities are derived. Several representative numerical examples are presented to demonstrate the capability and the efficiency of the proposed approach against some classes of numerical instabilities.
Highlights
Topology optimization refers to optimal design problems in which the topology of the structure is allowed to change in order to improve the performance of the structure
To overcome the shortcoming of continuous material distribution by the introduction of finite element approximation, moving least square or modified filter functions are adopted as interpolation function
The method can be viewed as a nature extension of node-based homogenization method and named as material point homogenization method
Summary
Topology optimization refers to optimal design problems in which the topology of the structure is allowed to change in order to improve the performance of the structure. A simple method for shape and layout optimization, called “evolutionary structural optimization” (ESO), has been proposed by Xie and Steven which is based on the idea of gradually removing inefficient material to achieve an optimal design [3] Following this basic approach, there have been a number of modifications and refinements such as BESO, where are elements removed but are added in high stressed areas [4]. We propose a checkerboard-free and mesh-independence topology optimization method without introducing any additional constraint scheme This aim is accomplished by the introduction of continuous material distribution. Representative numerical examples are presented to demonstrate the capability of the proposed method
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