Ⅴ irtual Work equation虚功方程 状态1:{p}=XY{p}=XYT 状态2:{r}=uw{}=[L{r"} 虚功方程:{}T{p} dx dy t+「{r}pdst ∫!e"}T{o} dx dy t 注:{f}"{puvX=Xu+Yv Y 6、、8、+σ、Ey+τ、r xy xy 徐汉忠第一版2000/7 弹性力学第六章有限元
徐汉忠第一版2000/7 弹性力学第六章有限元 11 Virtual Work Equation 虚功方程 状态1： {p}=[X Y]T {p}=[X Y]T {}= [x y xy ] T 状态2： {f* }=[u* v * ] T { * }=[L] {f* } 虚功方程 ： {f* } T{p}dx dy t+ {f* } T{p}ds t = { * } T{}dx dy t 注： {f* } T{p} =[ u* v * ] X =X u*+Y v* Y { * } T {} =[x * y * rxy * ] x = x x *+ y y * + xy rxy * y xy
6.2 Basic Concepts about finite Element method 62有限单元法的概念 有限单元法的计算模型 1. The continuum structure is idealized as a structure consisting of a number of individual elements connected only at nodal points. 连续的结构理想化为仅由在结点相连的 单元组成。 徐汉忠第一版2000/7 弹性力学第六章有限元 12
徐汉忠第一版2000/7 弹性力学第六章有限元 12 6.2 Basic Concepts about Finite Element Method 6.2 有限单元法的概念 有限单元法的计算模型 • 1.The continuum structure is idealized as a structure consisting of a number of individual elements connected only at nodal points. 连续的结构理想化为仅由在结点相连的 单元组成
2. Displacement boundary: place a bar support at the node where displacement is zero. 位移边界:结点位移为零处,设置连杆. 3. The system of external loads acting on the actual structure has to be replaced by an equivalent system of forces concentrated at the element nodes. This can be done by using the principle of virtual work and equating the work done by the actual loads to the work done by the equivalent nodal loads. 外力按静力等效的原则移置到结点上 徐汉忠第一版2000/7 弹性力学第六章有限元
徐汉忠第一版2000/7 弹性力学第六章有限元 13 • 2.Displacement boundary: place a bar support at the node where displacement is zero. 位移边界：结点位移为零处，设置连杆. • 3. The system of external loads acting on the actual structure has to be replaced by an equivalent system of forces concentrated at the element nodes.This can be done by using the principle of virtual work and equating the work done by the actual loads to the work done by the equivalent nodal loads. 外力按静力等效的原则移置到结点上
图6-2 徐汉忠第一版2000/7 弹性力学第六章有限元
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图6-3 徐汉忠第一版2000/7 弹性力学第六章有限元 15
徐汉忠第一版2000/7 弹性力学第六章有限元 15