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同一梁单元内材料具有不同性质时,传统梁单元的单元位移插值函数不能合理地描述梁内部的位移变化,导致计算精度较低。给出了一种计算同一单元内具有分布材料特性的梁反应的有限元方法,有效解决了传统梁单元的局限性。同时,给出了同一单元内具有分布材料特性的梁单元的一致等效节点荷载和一致质量矩阵的建立方法。与传统梁单元相比,使用该方法进行静力分析和特征值分析均可获得较高的计算精度,并且使用一个单元即可给出精确的单元内力和位移分布。此研究为分析同一单元内具有分布材料特性的梁的静力与动力反应问题提供了简单的方法和有价值的理论基础。
When the materials in the same beam element have different properties, the displacement displacement function of the traditional beam element can not reasonably describe the displacement inside the beam, which leads to the low accuracy. A finite element method for calculating beam response with distributed material properties in the same cell is given, which effectively solves the limitations of traditional beam elements. At the same time, a uniform equivalent node load and uniform mass matrix method for beam elements with distributed material properties in the same element are given. Compared with the traditional beam element, the static analysis and eigenvalue analysis using this method can obtain higher calculation accuracy, and the accurate internal force and displacement distribution of the element can be obtained by using one element. This study provides a simple method and valuable theoretical basis for the analysis of the static and dynamic response of beams with distributed material properties in the same cell.