基于杆系离散元理论的结构屈曲显式弧长法研究  

AN EXPLICIT ARC-LENGTH METHOD FOR STRUCTURAL BUCKLING ANALYSIS BASED ON MEMBER DISCRETE ELEMENT THEORY

作　　者：叶继红 许强[1,2] YE Ji-hong;XU Qiang(Jiangsu Key Laboratory Environmental Impact and Structural Safety in Engineering,China University of Mining and Technology,Xuzhou,Jiangsu 221116,China;Xuzhou Key Laboratory for Fire Safety of Engineering Structures,China University of Mining&Technology,Xuzhou,Jiangsu 221116,China)

机构地区：[1]中国矿业大学江苏省土木工程环境灾变与结构可靠性重点实验室,江苏徐州221116 [2]中国矿业大学徐州市工程结构火灾安全重点实验室,江苏徐州221116

出　　处：《工程力学》2024年第3期9-18,共10页Engineering Mechanics

基　　金：国家自然科学基金面上项目(51978655)。

摘　　要：基于杆系离散元理论,提出了一种显式弧长法用于结构弹性屈曲全过程分析。建立了新型接触单元-铰固接触单元的本构模型,分别采用离散元法和结构力学方法对铰固接触单元在已知端部位移工况下进行受力分析,并通过端部内力相等建立方程,推导了接触刚度系数;采用动力阻尼技术简化了颗粒运动方程的求解过程,然后引入总位移约束弧长法,详细阐述了与离散元法相结合的求解策略和实施过程,并给出了相关分析参数的计算公式;通过算例验证了该方法的准确性和适用性。在追踪结构屈曲平衡路径时,该方法无需组集刚度矩阵、不涉及矩阵奇异等不收敛问题,且参数少、稳定性好,与传统有限元弧长法相比更具优越性,为结构分析提供了新的算法工具。An explicit arc-length method is proposed upon the discrete element theory to analyze the whole process of structural elastic buckling behavior.The constitutive model of a new contact element—a hinged-fixed contact element is established.The discrete element method and the structural mechanics method are used to analyze the hinged-fixed contact element under the condition of known end displacement respectively,then the contact stiffness coefficient is deduced by equalizing the internal forces obtained through these two methods.The dynamic damping technology is used to simplify the solution process of the particle motion equation.The arclength method with total displacement constraints is introduced into the discrete element method,and the solution strategy and implementation process of combination are described in detail,also,the calculation formulas for the relevant analysis parameters are developed.The accuracy and applicability of the method are verified by some examples.The method proposed can simulate the buckling behavior of the structure without assembling the stiffness matrix and involving matrix singularity.Also,it has few parameters and good stability compared with the traditional finite element arc length method,providing a new algorithmic for structural analysis.

关 键 词：杆系离散元法 弧长法 接触本构模型 屈曲分析 数值模拟 

分 类 号：TU323[建筑科学—结构工程] TU311.2