本文關(guān)鍵詞：骨骼重建拓撲優(yōu)化方法的理論研究和數(shù)值模擬　出處：《北京工業(yè)大學》2009年碩士論文　論文類型：學位論文

  更多相關(guān)文章： 骨骼重建 ICM方法 拓撲優(yōu)化 數(shù)值模擬

【摘要】： 本文基于隋允康教授提出的ICM(Independent Continuous and Mapping,即獨立、連續(xù)、映射)結(jié)構(gòu)拓撲優(yōu)化方法,建立了骨骼重建的拓撲優(yōu)化模型,并運用對偶方法進行模型轉(zhuǎn)換,用序列二次規(guī)劃方法進行了求解,研究了連續(xù)體結(jié)構(gòu)拓撲優(yōu)化方法在骨骼重建方面的應(yīng)用。并利用PCL語言對MSC.Patran進行二次開發(fā),通過數(shù)值算例,將理論研究與數(shù)值模擬相結(jié)合,為實際應(yīng)用提供了重要的理論依據(jù)。本文主要研究內(nèi)容為: (1)研究了在應(yīng)力作用下骨骼重建的拓撲優(yōu)化。以骨骼結(jié)構(gòu)的質(zhì)量最小為目標,以應(yīng)力為約束,利用應(yīng)力全局化方法將局部應(yīng)力約束轉(zhuǎn)化為結(jié)構(gòu)總應(yīng)變能約束,建立了骨骼重建的拓撲優(yōu)化模型,并運用對偶規(guī)劃理論對模型進行了求解。 (2)采用ICM優(yōu)化方法對不同骨骼結(jié)構(gòu)的模型進行了數(shù)值模擬。對于相同的骨骼模型,分別對結(jié)構(gòu)在不同應(yīng)力、不同網(wǎng)格、不同載荷、不同材料參數(shù)及優(yōu)化模型中取不同過濾函數(shù)的情況進行了研究。數(shù)值模擬的結(jié)果與實際骨骼結(jié)構(gòu)類似,證明了該方法的可行性。 (3)根據(jù)上述優(yōu)化模型和解法,利用PCL語言對MSC.Patran軟件進行了二次開發(fā),對在應(yīng)力約束下的二維、三維骨骼重建拓撲優(yōu)化問題生成了優(yōu)化模塊,為骨骼重建拓撲優(yōu)化理論從概念設(shè)計走向?qū)嶋H應(yīng)用提供了一條新途徑。
[Abstract]:This paper is based on the topology optimization method of ICM(Independent Continuous and mapping proposed by Professor Sui Yunkang. The topology optimization model of bone reconstruction is established, and the dual method is used to transform the model, and the sequential quadratic programming method is used to solve the problem. The application of topology optimization method of continuum structure in bone reconstruction is studied, and the secondary development of MSC.Patran is carried out by using PCL language, and a numerical example is given. The combination of theoretical research and numerical simulation provides an important theoretical basis for practical application. The main contents of this paper are as follows: 1) the topological optimization of bone reconstruction under stress is studied. The minimum mass of bone structure is the objective and the stress is the constraint. The local stress constraint is transformed into the total strain energy constraint by using the stress globalization method, and the topological optimization model of bone reconstruction is established, and the model is solved by dual programming theory. (2) the ICM optimization method is used to simulate the different bone structure models. For the same bone model, the different stresses, different grids and different loads are applied to the same bone model. Different material parameters and different filtering functions in the optimization model are studied. The results of numerical simulation are similar to the actual skeleton structure, which proves the feasibility of this method. 3) according to the above optimization model and solution, the MSC.Patran software is redeveloped by using PCL language, and the two dimensions under the stress constraint are analyzed. The topology optimization problem of three-dimensional bone reconstruction generates an optimization module, which provides a new way for the theory of topology optimization of bone reconstruction from conceptual design to practical application.
【學位授予單位】：北京工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2009
【分類號】：R346

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