大挠度Euler-Bernoulli梁单元的算法研究

Algorithm research on the Euler-Bernoulli beam considering large deflection

通过有限元方法研究Euler-Bernoulli梁变形的求解。形状函数矩阵通过Lagrange插值函数和两节点Hermite单元构造。然后根据形状函数矩阵推导大挠度几何非线性单元刚度矩阵。再利用C++编程,开发出一套可用于求解梁杆结构大挠度问题的算法。最后通过典型算例来验证本算法的计算精度。

This paper focuses on the algorithm to solve the large deflection of Euler-Bernoulli beam by the Finite Element Method. The shape function matrix is constructed via the Lagrange interpolation function and two-node Hermite element. According to the shape function matrix,the geometrically nonlinear element stiffness matrix is obtained. The algorithm is implemented in C ＋ ＋ language to simulate the beam structure considering large deflection. Finally,a typical example is used to verify the accuracy of the algorithm.