【摘要】 固定形状的单元位移插值函数不能合理地近似变截面梁内部的位移变化,从而影响了传统梁单元用于计算变截面梁的精度。采用直接基于单元平衡的思想给出了计算变截面梁反应的有限元方法,解决了单元位移插值函数局限性所带来的问题。导出了变截面梁单元的单元刚度矩阵、单元等效节点荷载和单元一致质量矩阵。在此基础上,利用编制的程序进行了算例验证与分析。算例验证了本文理论的正确性,表明本文方法具有很高的计算精度。更多还原

【Abstract】 The element shape functions with fixed shapes cannot rationally approximate the deformation in a deformed beam with variable cross-section,which results in an inaccuracy of traditional beam elements.The paper presents a method to analyze beam with variable cross-section by using direct element-based equilibrium framework.This method avoids the inaccuracy caused by the limitation of element shape functions.The stiffness matrix,equivalent nodal load and consistent mass matrix are derived for the beam element with variable cross-section.A computer program is then developed and a numerical example is provided to verify the presented method.It is shown that the theory is correct and the method has higher accuracy than the traditional beam elements.更多还原