基于边界元法的液压试验台静刚度解析
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摘要
对于由多个梁单元组成的复杂机械结构系统的静刚度解析,理论力学难以求解其超静定问题,有限元法需要进行结构建模和单元划分,耗时长、精度不高。针对由多杆组成的液压试验台的静刚度求解问题,采用边界元法,考虑到梁单元间的复杂连接关系,提出了一种基于不同合成条件下梁单元间的复合合成方法,构造了由梁单元组成的液压试验台机械系统的边界元静刚度解析模型,根据梁单元的基本参数及受力状态即可解析出系统及各主要构件的受力与变形情况。通过实例解析并与理论力学计算结果比较,该方法可以获得精确的理论解,适用于以梁单元组成的各种机械系统的静刚度计算。
For the static stiffness analysis on complex mechanical systems composed of multiple beam elements, theoretical mechanics fails to solve the hyper-static problem. The finite element method requires structural modeling and unit division,which takes a long time and has low precision. In this article, for the static stiffness of hydraulic linkage testing bed composed of multiple poles, BEM is adopted to present a compound combination method based on different compound conditions, with the complex connection relationship among beam elements taken into account. The BEM static stiffness model of the hydraulic linkage testing bed's mechanical system composed of beam elements is set up, in order to analyze the force and deformation of the system and its major components, according to the basic parameters and the force state of the beam elements. The results are compared with those based on theoretical mechanics. Thanks to this method, accurate theoretical solutions can be obtained,which are suitable for the static stiffness analysis on various mechanical systems composed of beam elements.
For the static stiffness analysis on complex mechanical systems composed of multiple beam elements, theoretical mechanics fails to solve the hyper-static problem. The finite element method requires structural modeling and unit division,which takes a long time and has low precision. In this article, for the static stiffness of hydraulic linkage testing bed composed of multiple poles, BEM is adopted to present a compound combination method based on different compound conditions, with the complex connection relationship among beam elements taken into account. The BEM static stiffness model of the hydraulic linkage testing bed's mechanical system composed of beam elements is set up, in order to analyze the force and deformation of the system and its major components, according to the basic parameters and the force state of the beam elements. The results are compared with those based on theoretical mechanics. Thanks to this method, accurate theoretical solutions can be obtained,which are suitable for the static stiffness analysis on various mechanical systems composed of beam elements.
引文
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[4]李善德,黄其柏,张潜.快速多极边界元方法在大规模声学问题中的应用[J].机械工程学报,2011,47(7):82-89.
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[11]李艳,王媛,汤琴,等.考虑结合部耦合的结构梁的边界元解析方法研究[J].机械强度,2015,37(2):300-306.
[12]黄玉美,韩旭炤,高峰,等.基于边界元法的平面运动并联机构静力学解析[J].机器人,2010,32(3):384-389.
[13]杨霞,鄢闯,黄庆学.滚动体几何相似条件在轴承边界元法中的应用[J].计算力学学报,2015,32(3):404-410.
[14]肖宏,杨霞,陈泽军,等.赫兹接触理论在采用边界元法分析轧机轴承载荷中的应用[J].中国机械工程,2010,21(21):2532-2535,2540.
[15]王冬,刘中宪,武凤娇,等.弹性波三维散射快速多极子间接边界元法求解[J].工程力学,2017,34(1):33-44.
[16]牛忠荣,张晨利,王秀喜.边界元法分析狭长体结构[J].计算力学学报,2003(4):391-396.
[2]朱华锋,谭建荣,贾高顺.机械结构可靠性预测的边界元逆分析法建模[J].中国机械工程,2001,11(7):801-804.
[3]杨霞,肖宏,陈泽军.基于轴承边界元法的轴承座对轧机滚动轴承载荷的影响[J].机械设计,2013,30(5):59-63.
[4]李善德,黄其柏,张潜.快速多极边界元方法在大规模声学问题中的应用[J].机械工程学报,2011,47(7):82-89.
[5]吴海军.基于快速多极子边界元方法的大规模声学计算方法与应用研究[D].上海:上海交通大学,2013.
[6]陈铭,胥云,翁定为.水平井多段压裂多裂缝扩展形态计算方法[J].岩石力学与工程学报,2016,35(S2):3906-3914.
[7]李义强,杨自豪,杨志强.随机复合材料统计多尺度边界元算法研究[J].航空工程进展,2017,8(2):199-205.
[8]Madhukar Vable,Jaihind Reddy Maddi.Boundary element analysis of inclusions with corners[J].Engineering Analysis with Boundary Elements,2007,31:762-770.
[9]Sahli A,Guemmour M B,Kebdani S,et al.Independent meshing of contact surfaces in 3D boundary element method contact analysis[J].Journal of Applied Mechanics,2008,75:041021.1-041021.8.
[10]Zhang Yao-Ming,Gu Yan,Chen Jeng-Tzong.Internal stress analysis for single and multilayered coating systems using the boundary element method[J].Engineering Analysis with Boundary Elements,2011,35:708-717.
[11]李艳,王媛,汤琴,等.考虑结合部耦合的结构梁的边界元解析方法研究[J].机械强度,2015,37(2):300-306.
[12]黄玉美,韩旭炤,高峰,等.基于边界元法的平面运动并联机构静力学解析[J].机器人,2010,32(3):384-389.
[13]杨霞,鄢闯,黄庆学.滚动体几何相似条件在轴承边界元法中的应用[J].计算力学学报,2015,32(3):404-410.
[14]肖宏,杨霞,陈泽军,等.赫兹接触理论在采用边界元法分析轧机轴承载荷中的应用[J].中国机械工程,2010,21(21):2532-2535,2540.
[15]王冬,刘中宪,武凤娇,等.弹性波三维散射快速多极子间接边界元法求解[J].工程力学,2017,34(1):33-44.
[16]牛忠荣,张晨利,王秀喜.边界元法分析狭长体结构[J].计算力学学报,2003(4):391-396.