Theoretical Study On The Member DEM And Its Application In Simulation Of Structural Mechanical Behaviors

The structural system composed of members is widely used in practical engineering,for instance frame structure,large-span space structure and bridge structure.The mechanical behaviors of structures of this type mainly includes: geometric nonlinearity,material nonlinearity,static and dynamic behaviors,joint semirigidity,fracture,contact collision and composite behaviors consisting of the above behaviors,for example local damage or progressive collapse failure.It is already a difficult task for existing numerical methods to accurately process single mechanical behavior of a structure.If multiple mechanical behaviors are coupled on this basis,it will become more complicated.Therefore,to describe structural mechanical behaviors simply and accurately,in this dissertation the Member Discrete Element Method(MDEM)is employed as the analysis tool and contact elements(such as bar elements and beam elements)available for structural system composed of members are developed.A series of quantitative calculation approaches are established for structural mechanical behaviors including elastic behavior,elastoplastic behavior,strong earthquake collapse modeling,and semi-rigid joint simulation.All the existing research results assumed that the tangential spring of contact constitutive model in the MDEM is only used to represent pure shearing deformation caused by shearing force.However,in the structures composed of members,the slenderness ratio of a member is usually large and the effect of shearing deformation can be ignored.That is,according to bending beam theory,the tangential displacement(i.e.,deflection)can be supposed to emerge by bending deformation caused by shearing force,not shearing deformation caused by the shearing force.Therefore,the tangential stiffness coefficient of contact element derived based on the above assumption cannot be applied to solve structural problems of the members.To figure out this issue,the tangential spring is redefined in this dissertation,and calculation formulas of contact stiffness coefficients corresponding to six directions are systematically derived based on the principle of energy equivalence.On this basis,the basic assumptions as well as concepts of the MDEM are elaborated in detail,and the basic formulas of the MDEM for the axial force rod element,the plane beam element and the space beam element are deduced.It provides strict theoretical support for mechanical behavior simulation of complex structures.In the MDEM,the solution of geometrically nonlinear issue and dynamic response is automatically embodied in the motion control equations of the particles,which is a natural process without special treatment.Based on this feature,a unified calculation framework for static and dynamic elastic analysis of structures composed of members is constructed,and the problems encountered when dealing with elastic behaviors by the MDME are further refined.The application ways of static and dynamic loads are given in detail,and the MDEM damping model under dynamic loads is constructed.The static and dynamic elastic nonlinear behaviors of several 2D and 3D structures,including geometric large deformation,large rotation,snapthrough buckling,bifurcation,and dynamic response,are analyzed.The comparison results verify the advantages and effectiveness of the MDEM to simulate static and dynamic elastic nonlinear behaviors.For material nonlinear issue,the Refined Plastic-hinge Method of the MDEM is proposed by improving the MDEM Plastic-hinge Method.This method uses the tangent modulus and the stiffness degradation coefficient of the cross section approximately represent the weakening of the contact element stiffness by residual stress.The calculation theories of two elastoplastic analysis methods in the MDEM are elaborated respectively,including yield criterion,elastoplastic contact constitutive model,loading and unloading criterion,and correction method after internal force exceeds limit yield surface.Static elastoplastic behaviors analyses of several examples(i.e.truss,simple beam,plane frame,space frame and single-layer reticulated shell)show that the MDEM Refined Plastic-hinge Method can approximately consider the plastic development of a member,and its calculation accuracy is significantly higher than the Plastic-hinge Method,meanwhile the consuming time of the MDEM program does not increase.In addition,when the material is ideally elastoplastic or the distribution plasticity of the cross-section is not evident,the Refined Plastic-hinge Method of the MDEM is more cost-effective than the Plastic-zone Method of the MDEM.The Member Discrete Element Method(MDEM)is modified and perfected to quantitatively and accurately simulate the progressive collapse for large-span spatial steel structures.Contact constitutive model that can consider strain rate effect under earthquake action is first established.Then,the Displacement Method and the Large Mass Method are introduced to determine the multi-support excitation for the MDEM,and further the parallel implementation strategies for the MDEM is initially constructed.The collapse simulation of a 1/3.5-scaled single-layer reticulated dome shaking table test model under multi-support excitation is carried out.Additionally,the collapse test can also be used to calibrate the structural key parameters of the Member Discrete Element Method(MDEM)in the progressive collapse analysis.To further model the semi-rigid behavior of beam-column joints,a novel and effective algorithm based on the Member Discrete Element Method is presented for static and dynamic analysis of space steel frames with semi-rigid connections,which incorporates nonlinear semi-rigidity of beam-to-column joints as well as material inelasticity and geometric nonlinearity.The calculation formulas of elastic-plastic contact constitutive model of the MDEM that can consider semi-rigid connection are deduced.A virtual spring element with two particles but without actual mass and length is used to simulate the semi-rigid behaviors of beam-column joints.The spring element quantifies the semi-rigidity of beam-column joints in a linearly distributed manner to the stiffness of the contact elements adjacent to these joints,and then the modified formula of the contact elements is derived through the energy equivalence principle.Furthermore,the nonlinear cyclic behavior of the beam-to-column connection is captured by the independent hardening model.The applicability and accuracy of the procedure proposed are verified by various classic numerical examples,and several mechanical behaviors of semi-rigid steel frames are systematically investigated such as geometric nonlinearity,snap-through buckling,material nonlinearity,dynamic response,and fracture.Through theoretical derivation,many classic numerical examples,large-scale shaking table test verification and program compiling,it is shown that the Member Discrete Element Method possess strong accuracy,versatility,and stability.In this dissertation,many nonlinear and discontinuous mechanics problems in the research field of structures composed of members are quantitatively simulated and analyzed,which improves and promotes the formation of the theoretical system of the MDEM.And the MDEM provides powerful technical supports and means for complex mechanical behavior study of structures composed of members.Meanwhile,The MDEM as a novel numerical analysis method,still has a lot of room for improvement and development to push it to actual engineering applications or designers.Finally,the main innovations of this dissertation are summarized as follows:(1)The tangential spring of contact constitutive model in the Member Discrete Element Method(MDEM)is redefined,and the calculation formula of contact stiffness coefficient corresponding to every direction for the axial force rod element,the plane beam element and the space beam element is deduced strictly.Then,the calculational theories of the MDME are systematized.(2)The Refined Plastic-hinge Method of the MDEM is presented,which can approximately consider the plastic development of a member.The elastoplastic theory of the MDME is further complemented.(3)Shaking table test verification of quantitative and accurate simulation of the whole collapse process of the dome under multi-support excitation is carried out.The Member Discrete Element Method(MDEM)is modified for three aspects: the algorithm itself,multi-support seismic input and computational efficiency,and then the MDEM for strong seismic collapse analysis of the test model under multi-support excitation is proposed.The results are helpful for the promotion and application of the MEDM in the progressive collapse simulation of structures.(4)A novel and effective algorithm based on the Member Discrete Element Method(MDEM)is presented for dynamic analysis of space steel frames with semi-rigid connections,which incorporates nonlinear semi-rigidity of beam-to-column joints as well as material inelasticity and geometric nonlinearity.The approach proposed is simple and feasible for simulating semi-rigid connections,because the zero-length spring element in the MDME is not directly involved in the calculation and the modified stiffness coefficient of the contact element can be directly used into in the next time step.The results further reflect the advantages of the MDEM processing strong nonlinear and discontinuous issues.