弹性DEM方法在杆系结构中的应用研究

基于颗粒离散元方法（DEM），结合杆系结构的特点，提出了一种适于杆系结构问题分析的DEM模型。对颗粒元相应的质量和转动惯量计算公式进行了修正；通过能量等效原理推导了杆系DEM模型分析时弹簧接触刚度系数表达式；将瑞利阻尼引入到DEM方法之中，给出了阻尼常数计算公式并用算例进行了验证。将该方法应用于杆系结构弹性分析，包括静动力与几何非线性大变形问题的空间框架结构和网壳结构等多个算例，计算结果与有限元方法结果吻合良好。DEM方法的特点是将动力分析和几何非线性分析自动包含在运动方程的计算之中，不用组集刚度矩阵，无需迭代求解。杆系DEM模型非常适宜处理杆系结构大变形及动力非线性问题，尤其是在结构进入强非线性之后的模拟分析。

APPLICATION OF ELASTIC DISCRETE ELEMENT METHOD IN MEMBER STRUCTURES

Based on particle discrete element method (DEM), combined with the characteristics of member structures, a DEM model is proposed for member structures analysis. The calculated and modified formulas of the mass and the moment of inertia of the particle are presented and the spring contact stiffness expression for analysis of member structures was derived based on the principle of energy equivalence. Rayleigh damping was adopted to account for the effect of structural damping and the formula of damping constant was given and verified. According to its application in structural elastic analysis such as spatial frame under seismic action and single-layer reticulated shells subjected to impact loads, the calculation results agree well with the finite element method (FEM). The DEM takes dynamic and geometric nonlinear analysis under consideration automatically during solving the equations of motion without assembling stiffness matrixes and iterations during nonlinear analysis. Therefore, the presented DEM is reliable in dealing with large deformation and dynamic nonlinear problems, especially for the analysis of structures with strong nonlinearity.