几类反问题的复变量重构核粒子法研究

发布时间：2018-11-13 19:31

【摘要】：反问题是科学和工程领域的重要问题。相对于正问题来说,反问题的求解要复杂得多。重构核粒子法是目前应用和研究较为广泛的无网格方法之一,而复变量重构核粒子法由于采用一维基函数建立二维问题的逼近函数,因而具有更高的计算精度和计算效率。本文采用复变量重构核粒子法建立逼近函数,提出了变系数对流扩散问题、带源参数的热传导反问题、弹性力学反问题和弹塑性力学反问题的复变量重构核粒子法,具体研究工作如下:基于复变量重构核粒子法建立逼近函数,提出了变系数对流扩散问题的复变量重构核粒子法,推导了相应的计算公式。该方法的优点是可取较少的节点,在同等精度下,相比传统的重构核粒子法减小了计算量;而在同等节点分布时,则比传统的重构核粒子法具有较高的计算精度。在热传导正问题的基础上,将复变量重构核粒子法应用于带源参数的热传导反问题的求解,结合瞬态热传导问题的Galerkin积分弱形式,建立了带源参数的热传导反问题的复变量重构核粒子法,推导了相应的计算公式。基于复变量重构核粒子法建立逼近函数,在弹性力学的复变量重构核粒子法的基础上,建立了弹性力学反问题的复变量重构核粒子法,推导了相应的计算公式。弹性力学反问题的复变量重构核粒子法比传统的重构核粒子法具有较高的计算精度。基于复变量重构核粒子法建立逼近函数,建立了弹塑性力学反问题的复变量重构核粒子法,推导了相应的计算公式。弹塑性力学反问题的复变量重构核粒子法比传统的重构核粒子法具有较高的计算精度。为了证明本文提出的复变量重构核粒子法的有效性,本文编制了MATLAB计算程序,进行了数值算例分析。数值算例说明了本文方法的正确性和有效性。
[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.
【学位授予单位】：上海大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O241.8

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