基于罰函數(shù)法和雙勢能理論的DDA接觸理論研究及高階位移模式理論應(yīng)用
發(fā)布時間：2019-04-01 09:06
【摘要】：不連續(xù)變形方法(DDA)是一種基于最小勢能原理,可較為準(zhǔn)確計算塊體系統(tǒng)中塊體運(yùn)動速度和位移的理論。在使用罰函數(shù)法處理塊體間接觸時,塊體系統(tǒng)機(jī)械能計算精度較低。本文提出變剛度法和沖量法處理塊體間的接觸,以解決機(jī)械能計算不準(zhǔn)確的問題,同時結(jié)合雙勢能接觸理論和高階位移模式理論計算塊體間的接觸力和塊體上的變形和應(yīng)力,以提高計算精度。本文研究的主要內(nèi)容如下:(1)介紹了 DDA理論并對整體方程組的推導(dǎo)過程和增廣拉格朗日乘子法等關(guān)鍵內(nèi)容做出了解釋。(2)從機(jī)械能守恒和損耗的角度分析罰函數(shù)法接觸理論的優(yōu)缺點(diǎn),并提出變接觸剛度法在無摩擦力作用時解決DDA圓盤在接觸和碰撞過程中的機(jī)械能不守恒問題,分析結(jié)果表明變接觸剛度法可以有效阻止碰撞過程中機(jī)械能發(fā)生突變,但變剛度法在有摩擦力作用時失去效用,同時對移修正公式進(jìn)行了介紹。(3)在罰函數(shù)法處理接觸時,塊體系統(tǒng)機(jī)械能計算精度較低。介紹沖量法以解決上述問題,沖量法是以剛體塊體接觸前的線速度和角速度為己知量,通過沖量定理建立方程組以計算塊體接觸分離時的速度。將沖量法編入算例程序中以驗證沖量法的有效性,分析發(fā)現(xiàn)沖量法可有效的解決塊體系統(tǒng)機(jī)械能不守恒的問題。(4)將莫爾庫侖準(zhǔn)則和最大拉應(yīng)力準(zhǔn)則用于判斷塊體間的接觸狀態(tài)。將懸臂梁離散成緊湊排列的正多邊形離散體,設(shè)置較大的凝聚力和抗拉強(qiáng)度值以阻止塊體間的相對運(yùn)動。在不同多邊形尺寸下使用DDA方法模擬懸臂梁在相同位移載荷作用下的變形,提取梁上邊緣多邊形的應(yīng)變與材料力學(xué)解進(jìn)行對比,以此研究多邊形塊體與梁的相對尺寸對計算精度的影響,分析發(fā)現(xiàn)多邊形塊體相對尺寸越小時,應(yīng)變計算精度越高。(5)引入雙勢能理論,計算塊體間的接觸力。使用高階位移函數(shù)計算塊體內(nèi)部應(yīng)力和塊體上點(diǎn)的位移。將雙勢能理論和高階位移模式理論結(jié)合起來,編寫算例程序,計算塊體間接觸力和塊體變形,發(fā)現(xiàn)雙勢能接觸理論可較為準(zhǔn)確的計算塊體間接觸力,高階位移理論可精確的計算懸臂梁上點(diǎn)的應(yīng)力和位移。
[Abstract]:Discontinuous deformation method (DDA) is a theory based on the principle of minimum potential energy, which can accurately calculate the velocity and displacement of block motion in a block system. When the penalty function method is used to deal with the contact between blocks, the accuracy of mechanical energy calculation of the block system is lower. In this paper, the variable stiffness method and the impulse method are proposed to deal with the contact between blocks in order to solve the problem of inaccurate calculation of mechanical energy. At the same time, the contact force between blocks and the deformation and stress on the block are calculated by means of the theory of double potential energy contact and the theory of higher order displacement mode. In order to improve the accuracy of calculation. The main contents of this paper are as follows: (1) the DDA theory is introduced and the derivation process of the global equations and the augmented Lagrangian multiplier method are explained. (2) the mechanical energy conservation and loss are divided into two parts. To analyze the advantages and disadvantages of the contact theory of penalty function method, The variable contact stiffness method is proposed to solve the problem of non-conservation of mechanical energy in the process of contact and collision of DDA disc when there is no friction force. The results show that the variable contact stiffness method can effectively prevent the sudden change of mechanical energy in the process of collision. However, the variable stiffness method is ineffective when there is friction, and the displacement correction formula is also introduced. (3) when the penalty function method is used to deal with the contact, the accuracy of mechanical energy calculation of the block system is lower. The impulse method is introduced to solve the above problems. The impulse method is based on the linear velocity and angular velocity before the contact of the rigid block. The equations are set up by the impulse theorem to calculate the velocity of the block contact separation. The impulse method is programmed in a numerical example to verify the validity of the impulse method. It is found that the impulse method can effectively solve the problem of non-conservation of mechanical energy in block system. (4) the Mohr-Coulomb criterion and the maximum tensile stress criterion are used to judge the contact state between blocks. The cantilever is discretized into a compact arrangement of regular polygonal discrete bodies, and a larger cohesion and tensile strength value is set to prevent the relative movement of the blocks. The DDA method is used to simulate the deformation of cantilever beam under the same displacement load under different polygon sizes. The strain of the polygon on the upper edge of the beam is extracted and compared with the mechanical solution of the material. It is found that the smaller the relative size of polygonal block is, the higher the precision of strain calculation is. (5) the theory of double potential energy is introduced to calculate the contact force between blocks. The high-order displacement function is used to calculate the internal stress and displacement of points on the block. By combining the theory of double potential energy with the theory of higher order displacement model, a numerical program is compiled to calculate the indirect contact force and deformation of the block. It is found that the contact theory of double potential energy can accurately calculate the indirect contact force of the block. The higher-order displacement theory can accurately calculate the stress and displacement of the cantilever beam.
【學(xué)位授予單位】：西南交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O302
本文編號：2451434
[Abstract]:Discontinuous deformation method (DDA) is a theory based on the principle of minimum potential energy, which can accurately calculate the velocity and displacement of block motion in a block system. When the penalty function method is used to deal with the contact between blocks, the accuracy of mechanical energy calculation of the block system is lower. In this paper, the variable stiffness method and the impulse method are proposed to deal with the contact between blocks in order to solve the problem of inaccurate calculation of mechanical energy. At the same time, the contact force between blocks and the deformation and stress on the block are calculated by means of the theory of double potential energy contact and the theory of higher order displacement mode. In order to improve the accuracy of calculation. The main contents of this paper are as follows: (1) the DDA theory is introduced and the derivation process of the global equations and the augmented Lagrangian multiplier method are explained. (2) the mechanical energy conservation and loss are divided into two parts. To analyze the advantages and disadvantages of the contact theory of penalty function method, The variable contact stiffness method is proposed to solve the problem of non-conservation of mechanical energy in the process of contact and collision of DDA disc when there is no friction force. The results show that the variable contact stiffness method can effectively prevent the sudden change of mechanical energy in the process of collision. However, the variable stiffness method is ineffective when there is friction, and the displacement correction formula is also introduced. (3) when the penalty function method is used to deal with the contact, the accuracy of mechanical energy calculation of the block system is lower. The impulse method is introduced to solve the above problems. The impulse method is based on the linear velocity and angular velocity before the contact of the rigid block. The equations are set up by the impulse theorem to calculate the velocity of the block contact separation. The impulse method is programmed in a numerical example to verify the validity of the impulse method. It is found that the impulse method can effectively solve the problem of non-conservation of mechanical energy in block system. (4) the Mohr-Coulomb criterion and the maximum tensile stress criterion are used to judge the contact state between blocks. The cantilever is discretized into a compact arrangement of regular polygonal discrete bodies, and a larger cohesion and tensile strength value is set to prevent the relative movement of the blocks. The DDA method is used to simulate the deformation of cantilever beam under the same displacement load under different polygon sizes. The strain of the polygon on the upper edge of the beam is extracted and compared with the mechanical solution of the material. It is found that the smaller the relative size of polygonal block is, the higher the precision of strain calculation is. (5) the theory of double potential energy is introduced to calculate the contact force between blocks. The high-order displacement function is used to calculate the internal stress and displacement of points on the block. By combining the theory of double potential energy with the theory of higher order displacement model, a numerical program is compiled to calculate the indirect contact force and deformation of the block. It is found that the contact theory of double potential energy can accurately calculate the indirect contact force of the block. The higher-order displacement theory can accurately calculate the stress and displacement of the cantilever beam.
【學(xué)位授予單位】：西南交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O302
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