【摘要】：反問題是科學(xué)和工程領(lǐng)域的重要問題。相對(duì)于正問題來說,反問題的求解要復(fù)雜得多。重構(gòu)核粒子法是目前應(yīng)用和研究較為廣泛的無網(wǎng)格方法之一,而復(fù)變量重構(gòu)核粒子法由于采用一維基函數(shù)建立二維問題的逼近函數(shù),因而具有更高的計(jì)算精度和計(jì)算效率。本文采用復(fù)變量重構(gòu)核粒子法建立逼近函數(shù),提出了變系數(shù)對(duì)流擴(kuò)散問題、帶源參數(shù)的熱傳導(dǎo)反問題、彈性力學(xué)反問題和彈塑性力學(xué)反問題的復(fù)變量重構(gòu)核粒子法,具體研究工作如下:基于復(fù)變量重構(gòu)核粒子法建立逼近函數(shù),提出了變系數(shù)對(duì)流擴(kuò)散問題的復(fù)變量重構(gòu)核粒子法,推導(dǎo)了相應(yīng)的計(jì)算公式。該方法的優(yōu)點(diǎn)是可取較少的節(jié)點(diǎn),在同等精度下,相比傳統(tǒng)的重構(gòu)核粒子法減小了計(jì)算量;而在同等節(jié)點(diǎn)分布時(shí),則比傳統(tǒng)的重構(gòu)核粒子法具有較高的計(jì)算精度。在熱傳導(dǎo)正問題的基礎(chǔ)上,將復(fù)變量重構(gòu)核粒子法應(yīng)用于帶源參數(shù)的熱傳導(dǎo)反問題的求解,結(jié)合瞬態(tài)熱傳導(dǎo)問題的Galerkin積分弱形式,建立了帶源參數(shù)的熱傳導(dǎo)反問題的復(fù)變量重構(gòu)核粒子法,推導(dǎo)了相應(yīng)的計(jì)算公式�；趶�(fù)變量重構(gòu)核粒子法建立逼近函數(shù),在彈性力學(xué)的復(fù)變量重構(gòu)核粒子法的基礎(chǔ)上,建立了彈性力學(xué)反問題的復(fù)變量重構(gòu)核粒子法,推導(dǎo)了相應(yīng)的計(jì)算公式。彈性力學(xué)反問題的復(fù)變量重構(gòu)核粒子法比傳統(tǒng)的重構(gòu)核粒子法具有較高的計(jì)算精度�；趶�(fù)變量重構(gòu)核粒子法建立逼近函數(shù),建立了彈塑性力學(xué)反問題的復(fù)變量重構(gòu)核粒子法,推導(dǎo)了相應(yīng)的計(jì)算公式。彈塑性力學(xué)反問題的復(fù)變量重構(gòu)核粒子法比傳統(tǒng)的重構(gòu)核粒子法具有較高的計(jì)算精度。為了證明本文提出的復(fù)變量重構(gòu)核粒子法的有效性,本文編制了MATLAB計(jì)算程序,進(jìn)行了數(shù)值算例分析。數(shù)值算例說明了本文方法的正確性和有效性。
[Abstract]:Inverse problem is an important problem in the field of science and engineering. The solution of inverse problem is much more complicated than that of positive problem. Reconstructing kernel particle method is one of the most widely used and studied meshless methods at present. The complex variable reconstruction kernel particle method is more accurate and efficient because it uses a wiki function to establish the approximation function of two-dimensional problem. In this paper, the approximation function is established by using the complex variable reconstruction kernel particle method, and the complex variable reconstruction kernel particle method is proposed for variable coefficient convection diffusion problem, heat conduction inverse problem with source parameters, elastic mechanics inverse problem and elastoplastic mechanics inverse problem. The main work is as follows: based on the complex variable reconstruction kernel particle method, the approximation function is established, and the complex variable reconstruction kernel particle method for convection-diffusion problem with variable coefficients is proposed, and the corresponding calculation formula is derived. The advantage of this method is that it has fewer nodes and reduces the computational complexity compared with the traditional reconstruction kernel particle method under the same precision, but at the same node distribution, it has higher calculation accuracy than the traditional reconstruction kernel particle method. Based on the positive heat conduction problem, the complex variable reconstruction kernel particle method is applied to the solution of the inverse heat conduction problem with source parameters, and the Galerkin integral weak form of the transient heat conduction problem is combined. The complex variable reconstruction kernel particle method for inverse heat conduction problem with source parameters is established and the corresponding formulas are derived. Based on the complex variable reconstruction kernel particle method, the approximation function is established. Based on the complex variable reconstruction kernel particle method of elasticity, the complex variable reconstruction kernel particle method for the inverse problem of elasticity is established, and the corresponding calculation formulas are derived. The complex variable reconstruction kernel particle method for inverse problem of elasticity is more accurate than the traditional reconstruction kernel particle method. Based on the complex variable reconstruction kernel particle method, the approximation function is established, and the complex variable reconstruction kernel particle method for the inverse problem of elastoplastic mechanics is established, and the corresponding calculation formula is derived. The complex variable reconstruction kernel particle method for inverse problem of elastoplastic mechanics is more accurate than the traditional reconstruction kernel particle method. In order to prove the validity of the complex variable reconstruction kernel particle method proposed in this paper, a MATLAB program is developed and a numerical example is given. Numerical examples show that the proposed method is correct and effective.
【學(xué)位授予單位】：上海大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2017
【分類號(hào)】：O241.8

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本文編號(hào)：2330215