温度依赖功能梯度Timoshenko梁的弹塑性屈曲
Elastoplastic Buckling of Temperature Dependence Functionally Graded Timoshenko Beam
DOI: 10.12677/IJM.2021.101006, PDF,   
作者: 曾成*：兰州理工大学，理学院，甘肃 兰州；陈丽科：兰州大学，土木工程与力学学院，甘肃 兰州
关键词: 功能梯度材料；Timoshenko梁；弹塑性；屈曲；辛方法；Functionally Graded Materials； Timoshenko Beam； Elastoplastic； Buckling； Symplectic Method
摘要: 考虑功能梯度材料物性参数的温度依赖性研究变化的温度场中陶瓷-金属功能梯度Timoshenko梁的弹塑性屈曲特性，其中功能梯度材料的弹塑性材料参数由TTO模型模拟、弹塑性本构方程应用线性强化模型建立。研究中利用Hamilton系统中的辛方法将问题转换为求解正则方程，临界载荷和屈曲模态对应于正则方程的辛本征值和辛本征解。精确解析求解正则方程得到梁的临界载荷和屈曲模态，并结合屈服条件获得弹塑性分界面。最后进行参数研究分析了梯度参数、几何参数和边界条件对该复合材料梁的屈曲载荷和屈曲时弹塑性变形分界面的影响。
Abstract: The elastoplastic buckling characteristics of functionally graded Timoshenko beams in varying temperature field are studied by considering the temperature dependence of material parameters. The elastoplastic material parameters of functionally graded materials are simulated by TTO model and the elastoplastic constitutive equation is established by linear strengthening model. By using the symplectic method in Hamilton system, the problem is transformed into solving canonical equations. The critical load and buckling mode correspond to the symplectic eigenvalue and eigen solution of the canonical equations, and are obtained by accurate analytical solution. At the same time, the elastoplastic interface is obtained by combining the yield condition. Finally, the influence of gradient parameters, geometric parameters and boundary conditions on the buckling load and elastoplastic deformation interface of the beam is analyzed.
文章引用：曾成, 陈丽科. 温度依赖功能梯度Timoshenko梁的弹塑性屈曲[J]. 力学研究, 2021, 10(1): 62-69. https://doi.org/10.12677/IJM.2021.101006

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