本文選題：三維粱(桿)系結(jié)構(gòu) + 離散單元法��； 參考：《東南大學(xué)》2015年碩士論文

【摘要】：離散單元法(Discrete Element Method,DEM)是主要模擬非連續(xù)介質(zhì)力學(xué)行為的數(shù)值分析方法。該方法的基本思想是將研究區(qū)域劃分成離散的、獨(dú)立運(yùn)動(dòng)的單元,單元間允許發(fā)生相對運(yùn)動(dòng)和碰撞,無需刻意滿足變形協(xié)調(diào)條件和連續(xù)條件。離散單元法利用顯示的動(dòng)態(tài)松弛法按時(shí)步迭代求解各個(gè)單元的運(yùn)動(dòng)狀態(tài),無需集成結(jié)構(gòu)剛度矩陣,避免了由于剛度矩陣奇異造成的計(jì)算不收斂。本文利用改進(jìn)的DEM單元模型,實(shí)現(xiàn)了分析過程由連續(xù)體到非連續(xù)體的順利過渡。同時(shí),詳細(xì)討論了模型各參數(shù)的取值方法及其對計(jì)算結(jié)果的影響。最后,運(yùn)用本文改進(jìn)的DEM模型對結(jié)構(gòu)倒塌全過程包含的線彈性、幾何非線性、材料非線性、斷裂、碰撞等多個(gè)問題進(jìn)行了數(shù)值模擬分析。主要內(nèi)容和結(jié)論如下：(1)基于顆粒流連結(jié)模型和接觸型模型建立了連續(xù)介質(zhì)的離散單元模型,通過桿端力和桿端位移關(guān)系推導(dǎo)了適用于多種截面形式的二維離散元接觸剛度系數(shù)。為選取合理的離散元模型參數(shù),對單元形狀和數(shù)量、單元排列形式、單元接觸模型、模型邊界條件的處理、實(shí)際荷載等效方式、時(shí)間步長以及阻尼系數(shù)等參數(shù)的取值進(jìn)行了系統(tǒng)研究。改進(jìn)顆粒流模型,將DEM模型由二維擴(kuò)展到三維。通過桿端力和桿端位移關(guān)系推導(dǎo)了三維DEM模型的接觸剛度系數(shù),并利用等效質(zhì)量和等效剛度修正單元質(zhì)量和轉(zhuǎn)動(dòng)慣量,以確保分析過程正確有效。(2)利用離散單元法對不同結(jié)構(gòu)形式進(jìn)行幾何非線性靜/動(dòng)力響應(yīng)、材料非線性數(shù)值模擬。本文基于Mises屈服準(zhǔn)則確立了廣義應(yīng)力(單元內(nèi)力)屈服條件,進(jìn)而建立了DEM彈塑性接觸本構(gòu)關(guān)系。利用塑性鉸模型和考慮截面塑性發(fā)展的模型推導(dǎo)了簡單內(nèi)力狀態(tài)下的DEM塑性接觸剛度系數(shù),同時(shí),利用廣義應(yīng)力屈服面的正交性推導(dǎo)了復(fù)雜內(nèi)力狀態(tài)下的離散單元塑性剛度系數(shù)矩陣。通過多個(gè)算例驗(yàn)證了改進(jìn)的DEM模型求解連續(xù)介質(zhì)非線性問題的可行性。(3)建立了構(gòu)件斷裂、單元碰撞模型,編寫程序檢測單元間接觸關(guān)系,更新單元連結(jié),計(jì)算碰撞接觸力。利用本文各部分研究成果模擬分析了K6型單層球面網(wǎng)殼振動(dòng)臺(tái)倒塌過程和框架結(jié)構(gòu)爆炸倒塌過程,并將計(jì)算結(jié)果與試驗(yàn)結(jié)果進(jìn)行了比較,驗(yàn)證了接觸檢測程序的正確性以及DEM法在分析結(jié)構(gòu)由連續(xù)介質(zhì)過渡到非連續(xù)介質(zhì)問題的可行性。(4)本文采用Fortran語言編寫了二維、三維DEM法計(jì)算程序,并將彈塑性分析、單元斷裂、碰撞檢測、碰撞接觸力計(jì)算等分別編寫為獨(dú)立模塊,需要時(shí)調(diào)用即可。通過對不同結(jié)構(gòu)形式(包括簡單機(jī)構(gòu)、框架、桁架、網(wǎng)殼等)的力學(xué)行為進(jìn)行模擬,并將其計(jì)算結(jié)果與其它方法得到的結(jié)果進(jìn)行了對比,驗(yàn)證了本文DEM方法在分析結(jié)構(gòu)動(dòng)靜力響應(yīng)、彈塑性大變形及斷裂碰撞等問題中的適用性。
[Abstract]:Discrete Element method (DEM) is a numerical method for simulating the mechanical behavior of discontinuous media. The basic idea of this method is to divide the study area into discrete and independent moving units. The relative motion and collision are allowed between the elements without the need to satisfy the deformation coordination condition and the continuous condition. The discrete element method uses the displayed dynamic relaxation method to solve the motion state of each element step by step on time without the need to integrate the stiffness matrix of the structure so as to avoid the non-convergence of the calculation caused by the singularity of the stiffness matrix. In this paper, the improved DEM element model is used to realize the smooth transition from continuum to discontinuum. At the same time, the method of choosing each parameter of the model and its influence on the calculation results are discussed in detail. Finally, the improved DEM model is used to simulate the linear elasticity, geometric nonlinearity, material nonlinearity, fracture, collision and so on. The main contents and conclusions are as follows: (1) based on the particle flow connection model and the contact model, the discrete element model of continuous medium is established, and the contact stiffness coefficients of two-dimensional discrete elements suitable for various cross-section forms are derived by means of rod end force and pole end displacement relationship. In order to select reasonable parameters of discrete element model, to deal with the shape and quantity of element, the form of arrangement of element, the contact model of element, the boundary condition of model, the equivalent mode of actual load, The time step and damping coefficient are studied systematically. The particle flow model is improved and the DEM model is extended from two to three dimensions. The contact stiffness coefficient of the three-dimensional DEM model is derived by the relationship between the end force and the displacement of the rod, and the mass and moment of inertia of the element are corrected by using the equivalent mass and the equivalent stiffness. In order to ensure that the analysis process is correct and effective, the discrete element method is used to simulate the geometric nonlinear static / dynamic responses of different structures and the material nonlinear numerical simulation. In this paper, the generalized stress (internal force) yield condition is established based on the Mises yield criterion, and then the DEM elastoplastic contact constitutive relation is established. The plastic contact stiffness coefficient of DEM under simple internal force is derived by using the plastic hinge model and the model considering the plastic development of section. By using the orthogonality of the generalized stress yield surface, the plastic stiffness coefficient matrix of discrete elements under complex internal forces is derived. The feasibility of the improved DEM model for solving the nonlinear problem of continuum medium is verified by several examples.) the component fracture, the element collision model, the program to check the contact relationship between the elements, the renewal of the element connection, and the calculation of the collision contact force are established. The collapse process of K6 single-layer spherical reticulated shell vibration table and the explosion collapse process of frame structure are simulated and analyzed by using the research results of each part of this paper, and the calculated results are compared with the experimental results. The correctness of the contact detection program and the feasibility of DEM method in analyzing the transition of structure from continuous medium to discontinuous medium are verified. In this paper, the two-dimensional and three-dimensional DEM program is compiled by Fortran language, and the elastic-plastic analysis and element fracture are carried out. Collision detection, collision contact force calculation and so on are written as independent modules, which can be called when needed. The mechanical behavior of different structural forms (including simple mechanism, frame, truss, latticed shell, etc.) is simulated, and the calculated results are compared with those obtained by other methods. The applicability of the DEM method in the analysis of structural dynamic and dynamic responses, large elastic-plastic deformation and fracture collisions is verified.
【學(xué)位授予單位】：東南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：TU311

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本文編號(hào)：1961377