【摘要】：數(shù)值流形法采用兩套相互獨(dú)立的網(wǎng)格(數(shù)學(xué)網(wǎng)格和物理網(wǎng)格),具備了能夠統(tǒng)一處理連續(xù)與非連續(xù)變形問題的能力,也解決了前處理工作量大的難題。但是目前采用有限元網(wǎng)格作為數(shù)學(xué)網(wǎng)格的流形法存在著關(guān)鍵部位計(jì)算精度不高、高階情況下方程組線性相關(guān)、網(wǎng)格加密不方便等問題。針對(duì)這種完全重疊的覆蓋方式帶來的問題,長(zhǎng)江科學(xué)院提出了基于獨(dú)立覆蓋的數(shù)值流形法(簡(jiǎn)稱獨(dú)立覆蓋流形法),該法采用以獨(dú)立覆蓋分析為主的方式,在局部網(wǎng)格加密和特殊區(qū)域的快速收斂等方面相比現(xiàn)有方法優(yōu)勢(shì)突出,為解決上述問題提供了新的思路。但該方法在收斂性、精度分析、自適應(yīng)等方面還有待進(jìn)一步研究�？紤]到計(jì)算精度問題是關(guān)系到新方法是否具有實(shí)用價(jià)值的關(guān)鍵性問題,所以本文基于獨(dú)立覆蓋的流形法開展精度分析和收斂性研究,具體包括以下內(nèi)容:(1)通過幾個(gè)算例對(duì)獨(dú)立覆蓋流形法現(xiàn)有的精度指標(biāo)進(jìn)行驗(yàn)證,在肯定其合理性的同時(shí),指出獨(dú)立覆蓋內(nèi)部誤差不易控制的問題,以及裂尖奇異區(qū)精度指標(biāo)不易滿足、需要研究覆蓋的合理布置問題。(2)針對(duì)獨(dú)立覆蓋內(nèi)部誤差不易控制的問題,提出了獨(dú)立覆蓋的子模型法,在單獨(dú)的獨(dú)立覆蓋內(nèi)進(jìn)行覆蓋函數(shù)的升階操作,通過高低階之間的相對(duì)誤差獲得新的誤差指標(biāo),為將來實(shí)現(xiàn)逐點(diǎn)的誤差控制打下基礎(chǔ)。給出了考慮子模型法的自動(dòng)計(jì)算實(shí)施步驟,用重力壩等算例驗(yàn)證了該方法能有效控制獨(dú)立覆蓋內(nèi)部誤差。(3)針對(duì)裂尖奇異區(qū)精度指標(biāo)不易滿足的問題,采用數(shù)值試驗(yàn)的方法探索了裂尖附近的覆蓋布置方式,找出了裂尖處的解析覆蓋和周邊數(shù)值覆蓋的分割界限(在一定大小的數(shù)值覆蓋的前提下),并從裂紋體的應(yīng)力解析解入手,說明了這種覆蓋布置方式對(duì)Ⅰ型裂紋和Ⅱ型裂紋的普遍適用性,通過算例驗(yàn)證了采用合適的覆蓋布置能夠加快收斂,并使裂尖附近數(shù)值覆蓋的精度指標(biāo)得到滿足。
[Abstract]:The numerical flow method adopts two sets of independent meshes (mathematical mesh and physical mesh), which has the ability to deal with continuous and discontinuous deformation problems in a unified way, and solves the difficult problem of large workload of pre-processing. But at present, the finite element mesh is used as the mathematical mesh in the flow form method, there are some problems, such as the accuracy of the key parts is not high, the linear correlation of the equations in the high-order case, the inconvenient mesh refinement and so on. In view of the problems caused by this completely overlapping coverage method, the Changjiang Academy of Sciences proposed a numerical fluidic method based on independent coverage (referred to as independent coverage fluidization method), which is mainly based on independent coverage analysis. Compared with the existing methods, local mesh encryption and fast convergence in special areas are superior to the existing methods, which provides a new way to solve the above-mentioned problems. However, the convergence, precision analysis, self-adaptation and other aspects of this method need to be further studied. Considering that the computational accuracy is a key problem related to the practical value of the new method, the accuracy analysis and convergence study based on the independent cover flow method is carried out in this paper. The main contents are as follows: (1) the existing accuracy indexes of the independent cover flow method are verified by several examples. While affirming its rationality, it is pointed out that the internal error of the independent cover is difficult to control, and that it is difficult to control the internal error of the independent coverage method. And the precision index of crack tip singular region is not satisfied, so it is necessary to study the reasonable arrangement of cover. (2) aiming at the problem that the internal error of independent cover is not easy to control, a sub-model method of independent cover is proposed. A new error index is obtained through the relative error between high and low order, which lays a foundation for the realization of point-by-point error control in the future. The steps of automatic calculation and implementation of the submodel method are given. Examples such as gravity dam show that the method can effectively control the internal error of independent coverage. (3) aiming at the problem that the precision index of the singular zone at the crack tip is not easily satisfied, the method can control the internal error of independent cover effectively. The method of numerical experiment is used to explore the covering arrangement near the crack tip, and the dividing boundary between the analytical cover and the surrounding numerical coverage is found (on the premise of a certain size of numerical coverage). Based on the analytical solution of the stress of the crack body, the universal applicability of the coverage arrangement to type I crack and type 鈪，

本文編號(hào)：2433935