Abstract: By applying the virtual work principle, the stiffness and mass matrices of an arbitrary non-uniform plane beam element are derived in the paper. For the simplicity and convenience in application, a bi-linear non-uniform plane beam model is recommended. Its stiffness matrix, mass matrix and influence lines by kinematic method can be formulized explicitly. A numeric example demonstrates its accuracy in comparison with the analytic results and indicates that its results coincide with those of the d

Key words: non-uniform beams, beam elements, stiffness matrices, mass matrices, influence lines

摘要： 从变形体虚功原理出发,推导了平面任意变截面梁单元的刚度阵和质量阵;从用户使用方便简单的角度提出 了一种双线性变截面模型,在此基础上得到了梁单元的刚度阵、质量阵以及机动法求影响线公式的显式表达式.算 例表明双线性变截面梁单元符合位移有限元的特点,在应用方便情况下能有效地提高精度,具有一定的实用性

关键词: 变截面, 梁单元, 刚度阵, 质量阵, 影响线