【摘要】 目的推导一种新型Euler-Bernoulli梁单元,克服传统两结点梁单元在梁杆结构稳定性分析中存在的计算精度较低的问题.方法以Euler-Bernoulli梁理论和有限元插值理论为基础,首先使用五次Hermite插值函数和二次Lagrange插值函数构造了三结点Euler-Bernoulli梁单元的横向和纵向位移场;进而依据非线性有限元理论推导了该三结点梁单元的几何刚度矩阵的单元切线刚度矩阵;最后使用静力凝聚方法消除该三结点梁单元的内部结点自由度.结果通过上述推导得到了一种新型的两结点梁单元,它和传统的两结点梁单元具有相同的自由度数量和分布.结论对梁杆结构稳定性分析中的几个典型算例进行了分析,证明此新型梁单元与传统两结点梁单元相比计算精度有了大幅度地提高.更多还原

【Abstract】 Although the conventional two-node beam element has been widely used for the stability analysis of beam structures,the results’ precision is poor.More elements have to be used for improving the results’ precision.Based on the Euler-Bernoulli beam theory and the interpolation theory of the finite element method,the transverse and longitudinal displacement fields of three-node Euler-Bernoulli beam element are constructed using the quintic Hermite and quadratic Lagrange interpolation polynomials.The three-node beam element tangent stiffness matrix including the geometric stiffness matrix is developed according to the nonlinear finite element theory.A new two-node beam element with the same degrees of freedom(DOFs) and location as the conventional two-node beam element is obtained by eliminating the DOFs of the interior node of the three-node beam element using the static condensation method.The results of several classical examples in the stability of beam structures show that the results’ precision using this new two-node beam element is much higher than the one using the conventional two-node beam element.更多还原