Study On Topology Optimization Based On Modified MPM

As a new method of meshless topology optimization, Moving particle method(MPM) can successfully eliminate the numerical instabilities appeared in theoptimization process. However, the method may be at exploring stage so that there aresome problems. For example, selection of parameters for MPM is not mature anddegradation of density can be occurred, which restrict its application in engineeringpractice. This article mainly discusses the influence factors of topology optimizationefficiency from the aspects of degradation of density and determination of the movingstep length, the main courses are summarized as follows：1. Based on the basic theory of moving least-squares (MLS) and MPM, asminimization compliance is objective function, A model of topology optimization fortwo-dimensional continuum structures is obtained. Relative examples about topologyoptimization are analyzed by compiling programs.2. The reason that the least nodal density degenerated in MPM is analyzed. Anadaptive moving step length for insertion point method is presented, and the movingstep length is determined corresponding to nodal density in the iterative process.Relative examples are analyzed and numerical results show the advantage of the newMPM. The correlation for convergence density value and the result of topologyoptimization is retained by compiling programs. The correlations betweenconvergence density value and iterations as well as continuity of final topologystructure provide the reference for the improved algorithm.3. The analysis of correlations between nodal density and the length of movingstep and considering the minimization distance, a new method about adaptive movingstep length is obtained. It may be applied in the optimization process and the processof topology optimization for structures is obtained. Relative examples are analyzedand numerical results show the advantage of the modified MPM. The last, it considersthe effect of the number of nodes on topology results.In a word, the modified MPM is successfully used in structural topologyoptimization in this paper, and the improved method can effectively eliminate thedegradation of density so that it can obtain some clear results for structural topologyoptimization and pioneer a new way for continuum structure mode topologyoptimization.