Research On Factors That Affect Efficiency Of Topology Optimization Based On MPM

As a new structure topology optimization method, moving particle method (MPM)can successfully eliminate the numerical instabilities appeared in the optimizationprocess. However, as the same as other types of topology optimization method, thereare also problems such as long computing time and low optimization efficiency incalculation and so on exist in moving particle method, which restrict its application inengineering practice. This article mainly discusses the influence factors of topologyoptimization efficiency from the aspects of implementation method of the essentialboundary conditions and determination of the mobile step length, and a displacementconstraint equation method (DCEM) is proposed for the imposition of the essentialboundary conditions and the topology optimization solution is conducted by adaptivemobile step length insertion point method on that basis. The main courses aresummarized as follows：1. The impact on calculation efficiency caused by implementation method of theessential boundary conditions in the structure analysis based on Element-freeGalerkin method is analyzed. DCEM is proposed for implementation of the essentialboundary conditions, and the basic theory of DCEM is explained. Relative examplesare analyzed by Visual Fortran, and numerical results show that calculation efficiencycan be raised and storage demands can be reduced with the same precision by DCEM.2. The topology optimization efficiency obtained by Lagrange multiplier methodand DCEM is compared, and the preponderance of high optimization efficiency byDCEM is further validated. The reason that the least nodal density degenerated inMPM is analyzed, and an adaptive mobile step length and insertion point method ispresented. The algorithm is implemented with Visual Fortran, and results show thatadaptive mobile step length and insertion point method has the preponderance of highoptimization efficiency.3. The effect of judgment density value which decides whether node is movableon topology results and optimization efficiency is discussed. The correlations betweenjudgment density value and iterations as well as continuity of final topology structureprovide a breakthrough for presenting the improved algorithm.4. The reasons of long calculation time and more iteration numbers caused bycalculation of the least nodal density less than0.1based on adaptive mobile steplength and insertion point method are analyzed. Considering the impact on iterative process caused by judgment density value that decides whether node is movable, animproved optimization algorithm is presented. The algorithm is implemented withVisual Fortran, and numerical results show that calculation time and iterations of theleast nodal density less than0.1can be reduced and the topology optimizationefficiency is raised at the same time based on improved optimization algorithm.The least nodal density and density gradient degenerated in the iterative processis successfully eliminated when the essential boundary conditions are imposed byDCEM and topology optimization is analyzed based on adaptive mobile step lengthand insertion point method in this paper. The improved optimization algorithm whichis presented based on the above analysis can reduce calculation time of the least nodaldensity less than0.1, thereby further raising topology optimization efficiency whilemaintaining the same quality of the results.