基于离散单元法的单层网壳结构冲击破坏数值模拟研究
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摘要
基于传统离散单元法的接触模型,通过能量守恒定律推导适用于杆系结构的离散元模型接触刚度。将分层梁理论引入到离散单元法中,给出接触的塑性判断准则以及推导接触进入塑性后的刚度系数,从而可以应用离散元方法解决杆系结构的弹塑性问题。通过定义离散单元法基于应变的断裂准则,将其应用于解决杆件的断裂问题。选取适用于碰撞问题的赫兹模型,给出赫兹模型刚度的设置方法。最后应用改进后的离散单元法对单层网壳冲击试验进行了考虑弹塑性、断裂、碰撞的全过程模拟,验证了该方法的正确性。并对Kiewitt单层球面网壳单点冲击和多点冲击进行数值模拟研究,分析了单点和多点冲击下单层网壳的破坏模式、冲击力、节点位移和支座反力的异同点。
In this study, the contact stiffness of discrete element model for beam structure is deduced by energy conservation law based on the contact model of traditional discrete element method. By introducing the layered beam theory into the discrete element method, the judging criterion of plasticity of contact is given and the stiffness coefficient of contact after going into plasticity is derived, so that the discrete element method can be used to solve the elasto-plastic problem of beam structures. The strain-based fracture criterion of the discrete element method is defined, and then it is applied to solving the fracture problem of beam structure. The Hertz model suitable for collision problem is selected, and the setting method of Hertz model stiffness is given. Finally,the improved discrete element method is used to simulate the whole impact testing process of single-layer reticulated shell with elastoplasticity, fracture and collision considered, so that this method can be verified.Numerical simulations on single point and multi-point impacts of Kiewitt single-layer spherical reticulated shells are carried out. The differences in failure mode, impact force, joint displacement and support reaction of single-layer reticulated shell subjected to single point and multi-point impact are analyzed.
In this study, the contact stiffness of discrete element model for beam structure is deduced by energy conservation law based on the contact model of traditional discrete element method. By introducing the layered beam theory into the discrete element method, the judging criterion of plasticity of contact is given and the stiffness coefficient of contact after going into plasticity is derived, so that the discrete element method can be used to solve the elasto-plastic problem of beam structures. The strain-based fracture criterion of the discrete element method is defined, and then it is applied to solving the fracture problem of beam structure. The Hertz model suitable for collision problem is selected, and the setting method of Hertz model stiffness is given. Finally,the improved discrete element method is used to simulate the whole impact testing process of single-layer reticulated shell with elastoplasticity, fracture and collision considered, so that this method can be verified.Numerical simulations on single point and multi-point impacts of Kiewitt single-layer spherical reticulated shells are carried out. The differences in failure mode, impact force, joint displacement and support reaction of single-layer reticulated shell subjected to single point and multi-point impact are analyzed.
引文
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[20]Ye J,Qi N.Progressive collapse simulation based on DEM for single-layer reticulated domes[J].Journal of Constructional Steel Research,2017,128:721-731
[2]Gupta N K.Experimental and numerical studies of dynamic axial compression of thin walled spherical shells[J].International Journal of Impact Engineering,2004,30(8/9):1225-1240
[3]Alzheimer W E,Forrestal M J.Dynamic response of a circular elastic shell to circumferentially moving forces[J].American Institute of Aeronautics and Astronautics Journal,1968,6(11):2231-2232
[4]Tan S,Astaneh-Asl A.Cable-based retrofit of steel building floors to prevent progressive collapse[D].Berkeley:University of California in Berkeley,2003
[5]Eagar T W,Musso C.Why did the world trade center collapse?Science,engineering,and speculation[J].JOM,2001,53(12):8-11
[6]谭双林.单层球面网壳在冲击荷载下的动力响应与失效模式研究[D].哈尔滨:哈尔滨工业大学,2009(Tan Shuanglin.Dynamic responses and failure modes analysis of single-layer reticulated domes under impact loads[D].Harbin:Harbin Institute of Technology,2009(in Chinese))
[7]范峰,王多智,支旭东,等.K8型单层球面网壳抗冲击荷载性能研究[J].工程力学,2009,26(6):75-81(Fan Feng,Wang Duozhi,Zhi Xudong,et al.Performance for kiewitt8 single-layer reticulated domes subjected to impact load[J].Engineering Mechanics,2009,26(6):75-81(in Chinese))
[8]喻莹,罗尧治.基于有限质点法的结构倒塌破坏研究Ⅱ:关键问题与数值算例[J].建筑结构学报,2011,32(11):27-35(Yu Ying,Luo Yaozhi.Structural collapse analysis based on finite particle methodⅡ:key problems and numerical examples[J].Journal of Building Structure,2011,32(11):27-35(in Chinese))
[9]Feng R Q,Ye J,Yan G,et al.Dynamic nonlinearity and nonlinear single-degree-of-freedom model for cable net glazing[J].Journal of Engineering Mechanics,2013,139(10):1446-1459
[10]Zhu B C,Feng R Q,Wang X.3D discrete solid element method for elastoplastic problems of continuity[J].Journal of Engineering Mechanics,2018.doi.10.1061/(ASCE)EM.1943-7889.0001459
[11]Blandford G E.Progressive failure analysis of inelastic space truss structures[J].Computers&Structures,1996,58(5):981-990
[12]Zhang Z,Paulino G H,Celes W.Extrinsic cohesive modelling of dynamic fracture and microbranching instability in brittle materials[J].International Journal for Numerical Methods in Engineering,2010,72(8):893-923
[13]Cundall P A,Strack O D L.A discrete numerical mode for granular assemblies[J].Géotechnique,1979,29(1):47-65
[14]Cundall P A,Hart R D.Numerical modelling of discontinua[J].Engineering Computations,1993,9(2):231-243
[15]Hakuno M,Meguro K.Simulation of concrete-frame collapse due to dynamic loading[J].Journal of Engineering Mechanics,1993,119(9):1709-1723
[16]Meguro K,Tagel-Din H.Applied element method for structural analysis:Theory and application for linear materials[J].Structural Engineering Earthquake Engineering,2000,17(1):21-35
[17]Meguro K,Tagel-Din H.Applied element simulation of RC structures under cyclic loading[J].Journal of structural engineering,2001,127(11):1295-1305
[18]Utagawa N,Kondo I,Yoshida N.Simulation of demolition of reinforced concrete buildings by controlled explosion[J].Computer-Aided Civil and Infrastructure Engineering,2008,7(2):151-159
[19]顾祥林,印小晶,林峰,等.建筑结构倒塌过程模拟与防倒塌设计[J].建筑结构学报,2010,31(6):179-187(Gu Xianglin,Yin Xiaojing,Lin Feng,et al.Simulation of collapse process and design method to resist collapse for building structures[J].Journal of Building Structure,2010,31(6):179-187(in Chinese))
[20]Ye J,Qi N.Progressive collapse simulation based on DEM for single-layer reticulated domes[J].Journal of Constructional Steel Research,2017,128:721-731
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