弹塑性DEM方法在杆系结构中的应用研究

Application of discrete element method in member structures:elastoplastic analysis

在颗粒离散元(DEM)方法应用于杆系结构弹性分析基础上,进一步对材料非线性行为进行了研究。引入纤维模型,将DEM方法中连接颗粒与颗粒之间的弹簧用分布式弹簧进行等效,并将分布式弹簧看作是粘结截面的若干根纤维,建立了可考虑截面塑性发展的DEM纤维模型。推导了弹塑性接触本构模型内力增量计算公式,编制了计算程序并通过算例验证了此方法在结构弹塑性分析中的适用性和正确性。最后,以跨度40m的单层球面网壳结构为例,对其进行地震弹塑性动力时程分析,模拟了结构动力响应以及杆件截面塑性发展程度。此方法可有效克服传统有限元方法在非线性分析时存在的刚度矩阵奇异、迭代不易收敛等问题。

Based on the application of elastic analysis in member structure by particle discrete element method （DEM） , this pa-per further investigates the material nonlinear behavior. A DEM model considering section plasticity development is established by introducing the fiber model, where the contact spring connected two particles is equivalent to distributed springs which can be viewed as several fiber of contact section. Derivation of internal incremental force formula for elastic-plastic contact constitu-tive model is addressed. On this basis？ a computer program is developed and the applicability and accuracy of the static and dy-namic elastic-plastic analyses are verified by numerical examples. In the end, taking an example of a 40 m span single-layer re-ticulated shell, the dynamic elastic-plastic time history analysis under earthquake action is studied, including the simulation of structural dynamic response and the development degree of plasticity of member section. It is indicated that the proposed meth-od is effective in nonlinear analysis of member structures to overcome the problems in traditional finite element method such as stiffness matrix singularity and iterative convergence difficulty.