| Author Name | Affiliation | | Lei Huang | School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, Liaoning, China | | Zengxuan Hou | School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, Liaoning, China | | Dijing Zhang | School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, Liaoning, China | | Youhang Zhao | School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, Liaoning, China |
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| Abstract: |
| A novel variable stiffness model was proposed for analyzing elastic-plastic bending problems with arbitrary variable stiffness in detail. First, it was assumed that the material of a rectangular beam is an ideal isotropic elastic-plastic material, whose elastic modulus, yield strength, and section height are functions of the axial coordinates of the beam respectively. Considering the effect of shear on the deformation of the beam, the elastic and elastic-plastic bending problems of the axially variable stiffness beam were studied. Then, the analytical solutions of the elastic and elastic-plastic deformation of the beam were derived when the cross-section height and the elastic modulus of the material were varied by special function along the length of the beam respectively. The elastic and elastic-plastic analysis of the variable stiffness beam was carried out using Differential Quadrature Method (DQM) when the bending stiffness varied arbitrarily. The influence of the axial variation of the bending stiffness on the elastic and elastic-plastic deformation of the beam was analyzed by numerical simulation, DQM, and finite element method (FEM). Simulation results verified the practicability of the proposed mechanical model, and the comparison between the results of the solutions of DQM and FEM showed that DQM is accurate and effective in elastic and elastic-plastic analysis of variable stiffness beams. |
| Key words: elastic-plastic bending problems variable stiffness cross-section DQM plastic deformation |
| DOI：10.11916/j.issn.1005-9113.2021.01.005 |
| Clc Number:TP391.9 |
| Fund: |
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| Descriptions in Chinese: |
| 关于抗弯刚度变化的弯曲梁弹塑性变形问题的研究 黄磊，侯增选，张迪婧，赵有航 （大连理工大学 机械工程学院，大连 116024） 摘要：本文构建一种新的可变刚度悬臂梁力学模型，以用于深入分析任意变刚度梁的弹性塑性弯曲问题。首先设定所要分析的梁是一种理想的各项同性的弹塑性材料，并且梁的各项材料参数如弹性模量惯性矩等均沿梁的轴线方向不断变化,同时考虑剪切对梁弯曲变形的影响。当梁在受到垂直集中力作用于梁的自由端时,分别给出在弹性阶段、塑性阶段全梁的挠度、转角微分方程。对于刚度任意变化的塑性阶段的变形分析，本文采用一种优化的微分求积分进行数值求解。最后分别通过MATLAB数值计算、DQM计算和abaqus有限元仿真分别分析了弯曲刚度轴向变化对悬臂梁的弹塑性变形的影响。数值仿真结果验证了该力学模型的实用性，并通过将微分求积法DQM的计算结果与有限元法的计算结果进行精度和效率的比较，结果表明DQM法在变刚度梁的复杂弹塑性行为的分析中不失为一种十分有效的科学方法。 关键词：剪切变形；弯曲问题；可变刚度；横截面；DQM法；弹塑性变形 |
