By Xiaojun Wang,杆系结构有限元分析,王晓军 航空科学与工程学院固体力学研究所, By Xiaojun Wang,杆系结构有限元分析,杆系是工程中常见的结构体系，比较简单，其中每一个杆件都可以看作是一个单元，单元受力与位移的关系很容易求得而且物理概念清晰、直观。结构力学中介绍的矩阵位移法是采用经典的方法讲述的，它是利用转角位移方程来建立单元特性公式，所以只适用于杆系。有限元方法是在结构矩阵分析的矩阵位移法基础上发展起来的，在建立位移场的过程中采用的是最有普遍意义的方法，即建立单元位移场函数，通过最小势能原理进行单元和整体分析。, By Xiaojun Wang,杆单元,拉(压)杆单元 一般规定, By Xiaojun Wang,杆单元,位移函数, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元,几何关系和物理关系, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元,平衡关系, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元,扭转杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,杆单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,平面直梁单元, By Xiaojun Wang,总体刚度矩阵,直接刚度法（定位向量）, By Xiaojun Wang,总体刚度矩阵, By Xiaojun Wang,总体刚度矩阵, By Xiaojun Wang,总体刚度矩阵, By Xiaojun Wang,总体刚度矩阵, By Xiaojun Wang,总体刚度矩阵, By Xiaojun Wang,总体刚度矩阵, By Xiaojun Wang,总体刚度矩阵, By Xiaojun Wang,总体刚度矩阵,产生带状矩阵的结点编号, By Xiaojun Wang,总体刚度矩阵, By Xiaojun Wang,总体刚度矩阵, By Xiaojun Wang,总体刚度矩阵, By Xiaojun Wang,总体刚度矩阵, By Xiaojun Wang,刚度矩阵的物理意义, By Xiaojun Wang,刚度矩阵的物理意义, By Xiaojun Wang,刚度矩阵的物理意义, By Xiaojun Wang,刚度矩阵的物理意义, By Xiaojun Wang,刚度矩阵的物理意义, By Xiaojun Wang,刚度矩阵的物理意义, By Xiaojun Wang,刚度矩阵的物理意义, By Xiaojun Wang,刚度矩阵的物理意义, By Xiaojun Wang,刚度矩阵的性质, By Xiaojun Wang,刚度矩阵的性质, By Xiaojun Wang,刚度矩阵的性质, By Xiaojun Wang,刚度矩阵的性质, By Xiaojun Wang,刚度矩阵的性质, By Xiaojun Wang,刚度矩阵的性质, By Xiaojun Wang,刚度矩阵的性质, By Xiaojun Wang,位移边界条件, By Xiaojun Wang,位移边界条件, By Xiaojun Wang,位移边界条件, By Xiaojun Wang,位移边界条件, By Xiaojun Wang,位移边界条件, By Xiaojun Wang,位移边界条件, By Xiaojun Wang,位移边界条件, By Xiaojun Wang,位移边界条件, By Xiaojun Wang,位移边界条件, By Xiaojun Wang,总刚度平衡方程的求解, By Xiaojun Wang,总刚度平衡方程的求解, By Xiaojun Wang,总刚度平衡方程的求解, By Xiaojun Wang,总刚度平衡方程的求解, By Xiaojun Wang,总刚度平衡方程的求解, By Xiaojun Wang,总刚度平衡方程的求解, By Xiaojun Wang,总刚度平衡方程的求解, By Xiaojun Wang,总刚度平衡方程的求解, By Xiaojun Wang,总刚度平衡方程的求解, By Xiaojun Wang,平面桁架算例, By Xiaojun Wang,平面桁架算例, By Xiaojun Wang,平面桁架算例, By Xiaojun Wang,平面桁架算例, By Xiaojun Wang,平面桁架算例, By Xiaojun Wang,平面桁架算例, By Xiaojun Wang,平面桁架算例, By Xiaojun Wang,平面桁架算例, By Xiaojun Wang,小结,对于杆系结构，由于单元位移场是无节间载荷作用的真实位移，因此当仅受结点载荷作用时，分析结果是完全精确的。当除结点载荷外还有节间载荷时，可以证明所求得的结点位移和各单元的杆端力仍然是精确的。对有载荷作用单元，单元位移场并非真实位移，单元各微段在所设单元位移情况下是不平衡的。但因杆端力是精确的，所以可以由截面法精确求得单元任一截面的内力。正因这样，可以称杆系有限元分析的结果是精确的。,