【正文】 rtual work: balance equations and geometric equations of the equivalent integral form of weak virtual work principles include principle of virtual displacement and virtual stress principle, is the floorboard of the principle of virtual displacement and virtual stress theory. They can be considered with some control equation of equivalent integral weak form. Principle of virtual work: get form any balanced force system in any state of deformation coordinate condition on the virtual work is equal to zero, namely the system of virtual work force and internal force of the sum of virtual work is equal to zero. The virtual displacement principle is the equilibrium equation and force boundary conditions of the equivalent integral form of weak。s law。 Stress and strain is linear, linear elastic problem boils down to solving linear equations, so only need less putation time. If the efficient method of solving algebraic equations can also help reduce the duration of finite element analysis. Linear elastic finite element generally includes linear elastic statics analysis and linear elastic dynamics analysis from two aspects. The difference between the nonlinear problem and linear elastic problems: 1) nonlinear equation is nonlinear, and iteratively solving of general。 Virtual stress principle is geometric equation and displacement boundary condition of the equivalent integral form of weak. Mechanical meaning of the virtual displacement principle: if the force system is balanced, they on the virtual displacement and virtual strain by the sum of the work is zero. On the other hand, if the force system in the virtual displacement (strain) and virtual and is equal to zero for the work, they must balance equation. Virtual displacement principle formulated the system of force balance, therefore, necessary and sufficient conditions. In general, the virtual displacement principle can not only suitable for linear elastic problems, and can be used in the nonlinear elastic and elasticplastic nonlinear problem. Virtual mechanical meaning of stress principle: if the displacement is coordinated, the virtual stress and virtual boundary constraint counterforce in which they are the sum of the work is zero. On the other hand, if the virtual force system in which they are and is zero for the work, they must be meet the coordination. Virtual stress in principle, therefore, necessary and sufficient condition for the expression of displacement coordination. Virtual stress principle can be applied to different linear elastic and nonlinear elastic mechanics problem. But it must be pointed out that both principle of virtual displacement and virtual stress principle, rely on their geometric equation and equilibrium equation is based on the theory of small deformation, they cannot be directly applied to mechanical problems based on large deformation theory. 3, the minimum total potential energy method of minimum total potential energy method, the minimum strain energy method of minimum total potential energy method, the potential energy function in the object on the external load will cause deformation, the deformation force during the work done in the form of elastic energy stored in the object, is the strain energy. The convergence of the finite element method, the convergence of the finite element method refers to when the grid gradually encryption, the finite element solution sequence converges to the exact solution。 Article 4 is coordination requirements, meet the coordination unit coordination unit。是由一些簡單的單元形狀，單元連接通過節(jié)點(diǎn)，并在一定的負(fù)載。在這類問題中，材料的應(yīng)力和應(yīng)變的線性關(guān)系，符合廣義虎克定律；應(yīng)力和應(yīng)變是線性的，線性彈性問題歸結(jié)為求解線性方程組，所以只需要更少的計(jì)算時(shí)間。有限元求解非線性問題可分為以下三類：1）材料非線性應(yīng)力應(yīng)變問題是非線性的，但應(yīng)力應(yīng)變很小，此時(shí)應(yīng)變與位移呈線性關(guān)系，這種問題屬于材料非線性問題。當(dāng)位移較大時(shí)，應(yīng)力應(yīng)變關(guān)系為非線性關(guān)系。3）非線性邊界問題的處理，如密封問題，接觸和摩擦的作用的影響不容忽視，屬于高度非線性接觸邊界。利用不同形式的權(quán)函數(shù)和插值函數(shù)，構(gòu)成不同的有限元方法。加權(quán)殘值法是求解微分方程近似解的一種有效方法。已使用的試函數(shù)的冪級數(shù)和三角級數(shù)，樣條函數(shù)，貝賽爾，切比雪夫，勒讓德多項(xiàng)式，等等。顯然，任何獨(dú)立完備的函數(shù)集都可以作為權(quán)重函數(shù)。他們可以考慮一些控制方程的等效積分“弱”形式。另一方面，如果力系統(tǒng)在虛位移（應(yīng)變）與虛和等于零為功時(shí)，則必須平衡方程。另一方面，如果虛擬力系統(tǒng)中它們是零和為零的工作，則它們必須滿足協(xié)調(diào)。3 ,最小總勢能法最小總勢能法、最小總勢能法最小應(yīng)變能方法，潛在的目標(biāo)能量函數(shù)在外部荷載會引起變形，在工作過程中的變形力在彈性勢能的形式儲存在對象中，是應(yīng)變能。2）在單元內(nèi)，位移函數(shù)必須包含常應(yīng)變。3）在單元內(nèi)，位移函數(shù)必須包括剛體位移。由于某一單元涉及到另一個單元，其他單元做剛體位移變形時(shí)會發(fā)生驅(qū)動單元，從而，模擬一個單元的實(shí)際位移，假設(shè)單元位移函數(shù)必須包含剛體位移。一般單元和協(xié)調(diào)，以確保相鄰小區(qū)邊界位移的連續(xù)性。收斂的完整性要求是必要的，所有四個滿足，構(gòu)成收斂的充分必要條件。介紹支撐條件，每個節(jié)點(diǎn)位移5。區(qū)域單元劃分為編制有限元方法，這部分的工作量比較大，除了細(xì)胞和節(jié)點(diǎn)數(shù)和確定彼此之間的關(guān)系，也表示節(jié)點(diǎn)坐標(biāo)，同時(shí)還需要列出自然邊界和本質(zhì)邊界節(jié)點(diǎn)個數(shù)和相應(yīng)的邊界值。（5）整體綜合：在有限元方程中，根據(jù)有限元方程中所有元素的面積，根據(jù)一定的積累原理，形成一般的有限元方程。求解有限元方程（7）：基于一般有限元方程的邊界條件是固定的，都是封閉方程的未