考虑几何非线性的杆系结构弯曲变形样条有限点法

Considering Geometric Nonlinearity of Truss Structural Bending Deformation Spline Finite Point Method

研究了杆系结构考虑几何非线性的大挠度弯曲变形问题,推算并验证了一种考虑几何非线性的杆系结构弯曲变形计算新方法.以三次B样条函数为基函数,采用广义参数法,构造出梁的样条基函数,通过最小势能原理,建立了杆系结构考虑几何非线性的刚度方程,对处于弹性范围内的杆系结构的大变形弯曲问题进行了计算,提出了考虑几何非线性时杆系结构弯曲变形计算的样条有限点法.结果表明:方法不用进行单元坐标变换、划分等分数少、收敛速度快且计算精度较高,是一种较传统有限元法更简单且可行的方法.

Truss structure was studied considering geometric nonlinear problem of large deflection bending deformation,calculate and validate a considering geometric nonlinearity of truss structure is a new method to calculate the bending deformation;With cubic B spline function as the base functions,using the generalized parameter method,constructs the beam of the b-spline basis function,through the principle of minimum potential energy,truss structure is established considering the geometric nonlinear stiffness equations,in the elastic bar system within the scope of large deformation of the structure of bending problem was calculated,proposed considering geometric nonlinear truss structural bending deformation calculation of the spline finite point method.Results show that the method need not unit coordinate transform,the dividing points less,such as fast convergence rate,and high calculation accuracy is a more traditional finite element method is simple and feasible method.