本文選題：離散元 + 有限元　； 參考：《浙江大學(xué)》2013年博士論文

【摘要】：界面元是指兩種連續(xù)結(jié)構(gòu)或連續(xù)結(jié)構(gòu)與離散介質(zhì)在接觸界面一定范圍內(nèi)的有限單元集或有限單元/粒子單元集。界面元方法是研究界面元區(qū)域內(nèi)單元之間的力作用和結(jié)點屬性等效傳遞的一種數(shù)字化模擬方法。本文提出界面元方法來模擬和分析裝備工作過程中連續(xù)結(jié)構(gòu)與離散介質(zhì)、連續(xù)結(jié)構(gòu)與連續(xù)結(jié)構(gòu)在相互作用界面的作用力計算、單元結(jié)點屬性的等效傳遞問題,研究工作主要體現(xiàn)在以下五個方面： 1針對界面元方法預(yù)處理階段需要快速生成離散顆粒集問題,提出一種幾何和物理相結(jié)合的顆粒集生成算法,充分利用離散介質(zhì)顆粒單元的幾何特性和顆粒下落時的物理特性,構(gòu)建了幾何與物理特性相結(jié)合的顆粒堆積移動模型,快速生成二維域圓形顆粒集和三維域球形顆粒集,生成顆粒集的時間與顆粒數(shù)量成線性關(guān)系,且顆粒集密度高,生成時間短。 2為了模擬和計算連續(xù)結(jié)構(gòu)與離散介質(zhì)之間的相互作用力,提出基于單元/粒子接觸的界面元方法,根據(jù)有限單元與粒子單元之間的幾何接觸情形,采用線彈性模型直接計算單個離散顆粒與有限元面片間的作用力,再將計算得到的作用力等效至有限元節(jié)點,進一步計算有限元節(jié)點的受力和位移,可視化顯示了離散介質(zhì)的受力、變化狀況和連續(xù)結(jié)構(gòu)的受力、應(yīng)變狀況。 3針對大規(guī)模粒子集在機械結(jié)構(gòu)作用下的應(yīng)力、應(yīng)變分析問題,提出基于單元／粒子交迭的界面元模型,將直接受結(jié)構(gòu)作用的區(qū)域及其近鄰區(qū)域用離散元表示,較遠區(qū)域則用六面體有限單元表示,兩種單元區(qū)域在它們的相互作用界面有一定程度的交迭。在交迭區(qū),將有限單元內(nèi)離散粒子的質(zhì)量、受力等效傳遞至有限元節(jié)點,得有限元節(jié)點加速度,將有限元節(jié)點的速度、加速度等參插值至離散單元,得離散粒子所在位置的應(yīng)變和應(yīng)力,同時以交迭區(qū)有限單元的受力作為邊界條件求解整個區(qū)域的受力和變形狀況。 4為了解決多個有限元網(wǎng)格在接觸界面的節(jié)點不匹配而導(dǎo)致節(jié)點屬性不能光滑傳遞的問題,提出異構(gòu)網(wǎng)格界面元方法,構(gòu)建了二維異構(gòu)的四邊形單元節(jié)點及其錯位節(jié)點形函數(shù),實現(xiàn)異構(gòu)四邊形單元網(wǎng)格在接觸界面屬性的光滑傳遞,將該方法進一步延伸至四邊形網(wǎng)格與三角形網(wǎng)格之間的界面元分析；同時研究了三維異構(gòu)的六面體單元網(wǎng)格之間結(jié)點屬性的光滑傳遞方法。通過一個異構(gòu)網(wǎng)格接觸實例驗證了方法的正確性,并將方法應(yīng)用于齒輪的接觸分析。 5提出了主/輔網(wǎng)格節(jié)點屬性等效集成方法，，以解決異構(gòu)有限元網(wǎng)格多場信息難以集成顯示的問題。將多個有限元網(wǎng)格模型中的一個作為主網(wǎng)格,其它作為輔網(wǎng)格,將輔網(wǎng)格單元節(jié)點信息向主網(wǎng)格節(jié)點等效轉(zhuǎn)移,最終在主網(wǎng)格單元節(jié)點中實現(xiàn)多場信息的集成顯示。研究結(jié)果分析了盾構(gòu)刀盤掘進過程中刀具和刀盤受到的應(yīng)力場和溫度場綜合作用分布和多場作用的最強區(qū)域,為刀具和刀盤設(shè)計提供了依據(jù)。
[Abstract]:The interface element refers to the finite element set or the finite element / particle unit set of two continuous structures or continuous structures and discrete media within a certain range of contact interfaces. The interface element method is a digital simulation method to study the force action and the equivalent transfer of node properties between the elements in the interface element region. The simulation and analysis of the continuous structure and the discrete medium, the calculation of the interaction force of the continuous structure and the continuous structure in the interaction interface and the equivalent transfer of the attribute of the unit node in the process of equipment work are mainly reflected in the following five aspects:
1 in view of the need to quickly generate the discrete particle set problem in the preprocessing phase of the interface element method, a particle collection algorithm combining geometry and physics is proposed, which makes full use of the geometric characteristics of the granular element and the physical characteristics of the particle falling, and constructs a particle accumulation moving model combining geometric and physical properties. Two dimensional circular particles and three dimensional spherical particle sets are formed. The time of generating particle sets is linearly related to the number of particles, and the particle density is high and the generation time is short.
2 in order to simulate and calculate the interaction force between the continuous structure and the discrete medium, an interface element method based on the element / particle contact is proposed. According to the geometric contact between the finite element and the particle element, the linear elastic model is used to calculate the force between the single discrete particle and the finite element face, and then the calculated effect is obtained. The force is equivalent to the finite element node, and the force and displacement of the finite element node are further calculated. The visualization of the force, the change state of the discrete medium and the stress of the continuous structure and the strain state are visualized.
3 in view of the stress and strain analysis of large-scale particle sets under the action of mechanical structure, an interface meta model based on the overlapping of elements / particles is proposed, which will be expressed directly by the discrete element in the region and adjacent area of the structure, and the far region is expressed with the hexahedral finite element, and the two element regions are in their interaction interfaces. A certain degree of overlap. In the overlapping area, the mass of discrete particles in the finite element is transferred to the finite element node, and the finite element node acceleration is obtained. The velocity and acceleration of the finite element nodes are interpolated to the discrete element, and the strain and stress of the position of the discrete particle are obtained, while the force of the finite element in the overlapping area is taken as the edge. Boundary conditions are used to solve the stress and deformation conditions of the whole area.
4 in order to solve the problem that the node properties of multiple finite element grids are not matched at the contact interface, the heterogeneous grid interface element method is proposed. The two-dimensional heterogeneous quadrilateral element node and its misplaced node shape function are constructed to realize the smooth transfer of the heterogeneous quadrilateral single grid in the contact interface properties. The method is further extended to the interface element analysis between the quadrilateral mesh and the triangular mesh, and the smooth transfer method of the node properties between the three dimensional heterogeneous hexahedral meshes is studied. The method is verified by a heterogeneous grid contact case, and the method is applied to the contact analysis of the gear.
5 the equivalent integration method of the main / auxiliary grid node attribute is proposed to solve the problem that the multi field information of the heterogeneous finite element mesh is difficult to integrate. One of the multiple finite element mesh models is used as the main grid and the other is used as the auxiliary grid. The node information of the auxiliary grid unit is transferred to the node of the main grid equivalent, and finally in the main grid unit node. The integrated display of multi field information is realized. The research results are made to analyze the distribution of the stress field and the temperature field and the strongest area of the multi field effect on the cutting tool and the cutter disk during the tunneling of the shield cutter disk, and provide the basis for the design of the cutter and the cutter disk.
【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2013
【分類號】：TH122

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