Adaptively Coupled DEM/FEM Algorithm And Its Application In Complex Behavior Simulation Of Member Structures

Member structures are widely used in practical engineering,such as frame structure,large-span space structure.The complex behaviors of this type of structure mainly include: geometric nonlinear behavior,material nonlinear behavior,dynamic behavior,buckling behavior,semi-rigid joint behavior,contact collision behavior,fracture behavior,and composite behavior composed of the above behaviors,for example local damage or overall collapse failure.The existing numerical analysis methods represented by finite element method are essentially a continuum mechanics method.When solving the above-mentioned structural mechanical behavior,the process is cumbersome and complicated,the calculation efficiency is low,and the collapse behavior of the structure cannot be described simply and effectively.Therefore,a series of quantitative simulation calculation methods for the mechanical behavior of the member structures are proposed by using the member discrete element method as the analysis tool.Necessary supplements and improvements are made to the research contents of contact element type,structural buckling,semi-rigid connection of beam-column joints,coupled discrete element method(DEM)/finite element method(FEM)algorithm,contact collision and fracture,which further promote the development and application of the member discrete element theory system.The existing research results have only established one type of contact element,namely beam contact element,which cannot effectively simulate truss structures behavior.Therefore,a new type of contact element — hinged contact element is established in this thesis.In order to obtain the spring coefficient of the hinged contact element,the discrete element method and the structural mechanics method are used to analyze the hinged contact element under the condition of known end displacement respectively,and the equation is established and solved by the equalizing the internal forces obtained through this two method.At the same time,the above method is also used to re-derive the constitutive of the beam contact element,and the spring stiffness coefficients of the contact element with and without shear deformation are given respectively.The value is the same as the result deduced by using strain energy theory,but this method proposed in thesis is simpler and more intuitive,and directly establishes a quantitative relationship between the structural analysis of discontinuous media and continuum media.On this basis,the basic concept and calculation formula of the spatial member discrete element method are introduced and deduced,which provides theoretical support for the study of complex mechanical behavior of structures.The arc length method is introduced into the member discrete element method,and a discrete element explicit arc length method is established to track the whole process of structural buckling behavior.The dynamic damping technique is used to simplify the solution process of the particle motion equation.The solution strategy and implementation process combined the arc-length method with the discrete element method are described in detail.For material nonlinear problems,two elastic-plastic analysis methods,the plastic hinge method and the plastic zone method,are established.Compared with the elastic analysis,the elastic-plastic analysis except to use the yield equation to judge the stress state of the element and use the elastic-plastic constitutive to calculate the internal force increment,the other solution process are unchanged.Therefore,it can be developed into an independent module,which can be called when needed.Numerical examples show that the discrete element explicit arc length method can effectively track the whole process of structural elastic and elastic-plastic buckling behavior,and has better performance than the traditional finite element arc length method.A simple and effective discrete element analysis model is proposed to study the static and dynamic behavior of semi-rigidly connected steel frames.In the model,a virtual zero-length,multi-degree-of-freedom spring element is used at the end of the rods to simulate the semi-rigid connection behavior.The key problems of the analysis model,such as modeling process,determining the physical information of the virtual particles formed by the connection of the zero-length spring element,calculating the stiffness of the zero-length spring element under different connection conditions,are examined in detail.The proposed numerical approach is subsequently verified by many classical examples.Different from that in the traditional finite element method,the dummy zero-length spring element in DEM has no length,but has mass,and is regarded as the basic analysis element,directly participating in the calculation process.The response of spring element represents the semi-rigid connection behavior which has more explicit physical meaning.At the same time,the simulation of rigid connection,hinged connection and semi-rigid connection can be realized by changing the stiffness of zero length spring element,and the algorithm is more complete.The member discrete element method is extended to the analysis of the collision behavior of the structure,and the collision response between the members is simulated by correcting the particle motion trajectory.A global rough detection algorithm for space member structure is established by using the theory of geometric vector analysis and the concept of space sub-field.In the process of local accurate detection,a "point-line" contact model and a "line-line" contact model are established respectively according to the contact modes that may occur between the space members.Then the concept of "virtual contact point pair" is introduced into the critical contact constraint,and the calculation formulas of the contact force are deduced.The correctness and effectiveness of the algorithm are quantitatively verified through the simulation and analysis of typical numerical examples.The results show that the global rough detection algorithm can effectively narrow the contact search range and quickly obtain potential contact pairs,improving computational efficiency.The "point-line" contact model and the "line-line" contact model can make timely and effective judgments on whether a potential contact pair has real contact behavior,and accurately calculate the normal repulsion force and tangential friction force.Meanwhile,there is energy dissipation in the process of contact-impact.In the DEM/FEM direct coupling algorithm,the finite element domain and discrete element domain need to be specified in advance,while the large deformation region of large complex structures can not be accurately predicted in advance,and the coupling interface position remains unchanged throughout the analysis process.The range of discrete element domain cannot be "adaptive" adjusted according to the size of the structural response.Therefore,an adaptively coupled DEM/FEM algorithm is proposed.The key problems of the algorithm,such as meeting consistency requirements,determining the adaptive criterion,transferring information between the DEM and FEM and dynamic coupled interface processing,are examined in detail.The calculation and analysis process of the adaptively coupled algorithm is established,and the correctness of the algorithm is verified by examples.In the algorithm,the identification of large deformation regions is an automatic process,and the DEM and FEM calculation domains can be changed interactively in every load step in real time according to the structural response.When the response of an arbitrary element in the FEM domain exceeds the predetermined adaptive criterion,the element will be moved to the DEM domain and analyzed using the DEM.Similarly,when the response of an arbitrary element in the DEM domain is smaller than the predetermined adaptive criterion,the element will be moved to the FEM domain and analyzed using the FEM.The transition of elements between the two domains achieves the objective of using the DEM for large deformation regions and the FEM for small deformation regions.Finally,the problem of component fracture in structural collapse failure is studied.Two fracture simulation algorithms for components are established by combining the plastic hinge method and the plastic zone method with the microscopic ductile fracture damage model.When the macroscopic plastic hinge method is combined with the microscopic ductile fracture damage model,it is necessary to use the obtained macroscopic internal force of the section to calculate the stress at the most unfavorable points on the edge of the contact section through the material mechanics and section geometry characteristics.Then the ductile fracture damage model is called,and the minimum fracture strain is taken as the ultimate fracture strain of the entire section.While the plastic zone method is used for elasto-plastic analysis,the stress state of each small area can be directly obtained,so the combined analysis of the plastic zone method and the ductile fracture model is a natural process.When using the adaptively coupled DEM/FEM algorithm to simulate the collapse and failure of the structure,it is only necessary to implant the fracture subroutine as a module into the DEM calculation program,and the FEM does not change.By simulating the collapse failure of two single-layer spherical reticulated shell shaking table test models under the action of earthquake,the results show that the structural response and collapse failure process obtained by numerical simulation are very consistent with the experimental process and experimental phenomenon.Therefore,the DEM/FEM adaptive coupling algorithm provides a new calculation method for the whole process analysis of structural collapse and failure and has strong stability.Main innovations:(1)The constitutive model of hinged-fixed contact element for truss structure,and the zero length spring element for semi-rigid connection analysis are established,which expand the application range of the member discrete element method.(2)The member discrete element explicit arc length method is established by combining the bar discrete element method with the arc length method,which provides a new numerical calculation method for the whole process tracking of structural buckling.(3)An adaptively coupled DEM/FEM algorithm is established,which can automatically identify the large deformation area of the structure and use DEM analysis for it and FEM analysis for other small deformation areas according to the structure response without the analyst specifying their respective calculation domain range according to their own experience.(4)The "point-line" contact model and the "line-line" contact model are established to simulate the contact and collision behavior between members;By combining the plastic hinge method and plastic zone method with the micro ductile fracture model,two fracture simulation algorithms are established to effectively simulate the member fracture behaviors.