【摘要】：當前，基于無網(wǎng)格方法的拓撲優(yōu)化雖還處在初步的探討階段，應(yīng)用尚不廣泛，但是相對于有限元法而言，無網(wǎng)格法本身具有一些先天性優(yōu)勢，這使得基于無網(wǎng)格法的拓撲優(yōu)化擁有誘人的前景�；跓o網(wǎng)格方法的拓撲優(yōu)化目前仍存在許多缺點，如計算缺乏穩(wěn)定性、優(yōu)化效率較低等。本文以無網(wǎng)格Galerkin數(shù)值計算方法為基礎(chǔ)，結(jié)合漸進結(jié)構(gòu)拓撲優(yōu)化方法，對二維連續(xù)體結(jié)構(gòu)拓撲優(yōu)化進行了研究，主要研究內(nèi)容如下： 1.基于有限元ANSYS軟件平臺，利用其參數(shù)化設(shè)計語言對二維連續(xù)體結(jié)構(gòu)拓撲優(yōu)化過程進行了編程模擬，通過對漸進結(jié)構(gòu)優(yōu)化法中材料拒絕率、進化率等參數(shù)的不斷嘗試，初步確定了這些參數(shù)的大致選擇范圍。 2.闡述了基于無網(wǎng)格Ga lerkin法的漸進結(jié)構(gòu)拓撲優(yōu)化流程；討論了拓撲優(yōu)化過程中被刪節(jié)點對結(jié)構(gòu)分析的影響；針對被刪節(jié)點對結(jié)構(gòu)分析中關(guān)鍵矩陣的影響，提出了直接剔除被刪節(jié)點、直接處理形函數(shù)與“生死節(jié)點”三種處理方法；對每種處理方法，利用MATLAB編程語言，以二維連續(xù)體結(jié)構(gòu)為研究對象，編寫了基于無網(wǎng)格Galerkin法的漸進結(jié)構(gòu)拓撲優(yōu)化程序，詳細討論了每種方法的可行性，結(jié)果表明直接處理形函數(shù)與“生死節(jié)點”的處理方法是可行的。 3.對無網(wǎng)格Galerk in法中節(jié)點密度、權(quán)函數(shù)影響域尺寸等參數(shù)對拓撲優(yōu)化結(jié)果的影響進行了詳細討論，總結(jié)了其規(guī)律，給出了選擇相應(yīng)參數(shù)的規(guī)律性參考。 4.介紹了基于無網(wǎng)格Ga lerkin法及變密度法的拓撲優(yōu)化原理，比較了該方法與基于無網(wǎng)格Galerkin法的漸進結(jié)構(gòu)拓撲優(yōu)化方法的優(yōu)化效率，，結(jié)果表明結(jié)合無網(wǎng)格Galerkin法及漸進結(jié)構(gòu)拓撲優(yōu)化法進行拓撲優(yōu)化能夠有效提高無網(wǎng)格拓撲優(yōu)化效率。 本文以無網(wǎng)格Galerkin法為結(jié)構(gòu)分析方法，結(jié)合漸進結(jié)構(gòu)拓撲優(yōu)化方法，對二維連續(xù)體結(jié)構(gòu)的拓撲優(yōu)化進行了深入的研究，有效地提高了無網(wǎng)格拓撲優(yōu)化效率。本文的研究為無網(wǎng)格拓撲優(yōu)化提供了一個新的思路。
[Abstract]:At present, although the topology optimization based on meshless method is still in the preliminary stage of discussion and its application is not extensive, compared with the finite element method, the meshless method itself has some congenital advantages. This makes the topology optimization based on meshless method have attractive prospects. At present, there are still many shortcomings in topology optimization based on meshless method, such as lack of computational stability, low optimization efficiency and so on. Based on the meshless Galerkin numerical calculation method and the progressive structure topology optimization method, the topology optimization of two-dimensional continuum structure is studied in this paper. the main research contents are as follows: 1. Based on the finite element ANSYS software platform, the topology optimization process of two-dimensional continuum structure is simulated by using its parametric design language. Through the continuous attempt of material rejection rate, progress rate and other parameters in the progressive structure optimization method, The approximate selection range of these parameters is preliminarily determined. two銆

本文編號：2495490