Coupled DEM/FEM Method And Its Application In Collapse Simulation Of Reticulated Shells

Large-span spatial reticulated structures have been widely applied in civil engineering, with the advantages of low cost, beautiful shape and large span. However, the collapse mechanism of such structures under severe earthquakes becomes an important issue and is on studying further. Collapse is a multi-physics mechanic process with large deformation, large rotation, material nonlinearity and member fracture, resulting in a big challenge for existing numerical method for the simulation of the strong nonlinear behavior. In this thesis, single-layer reticulated shells are taken as the main research objects to explore the collapse mechanism. Based on member discrete element method (DEM), both the whole collapse process simulation and the failure mechanism analyze can be realized by investigating the key problems involved in collapse analysis through theoretical derivation and numerical calculation.Collapse is essentially a complex mechanical process that the material undergoing from continuous to discontinuous dynamic transformation, and covers the continuum and non-continuum mechanics two areas. Commonly used finite element methods are not able to simulate the whole collapse process. Based on particle DEM considering the physical concept, a new DEM method is proposed for member structures and the application is extended to 2-D and 3-D member structures. Firstly, the basic concepts and principles of DEM method of 2-D/3-D member structures are established and detailed derivation of formulas together with solution procedure of the method are described. Meanwhile, the calculated and modified formulas of the mass and the moment of inertia of the particle are presented and the strategies of DEM method solving static problem is discussed. Besides, the calculation of damping force and the selection of timestep are also discussed. Compared with other numerical methods, the proposed method has more advantages and uniqueness in the analysis of member structures, which provides a basic method for the collapse simulation of large-span spatial reticulated structures.Based on the member DEM, research ideas and calculation process in dealing with geometric nonlinear problems together with a procedure of geometric nonlinear large deformation analysis are given. The applicability and accuracy of the static and dynamic geometric nonlinear analysis program are verified through several numerical examples, which also reflect the characteristics combined static and dynamic analysis processes of the proposed method. Besides, according to its application in spatial frame under seismic action and single-layer reticulated shells subjected to impact loads, the dynamic nonlinear analysis results indicated that this method can well solve plane or space member structures with large deformation problems. Compared with the finite element method (FEM), the DEM takes dynamic and geometric nonlinear analysis under consideration automatically during solving the equations of motion with no need to distinguish small or large deformation. Therefore, the member DEM is reliable in dealing with large deformation problems, especially for the analysis of structures with strong nonlinearity.Based on geometric nonlinear analysis, the framework of elastic-plastic analysis by DEM is further developed, the difference between DEM method and the traditional FEM used to elastic-plastic analysis is further compared and discussed. Plastic hinge model and fiber model considering plasticity development are established and detailed derivation of internal incremental force formula and solution procedure of the method are addressed. A program of elastic-plastic analysis is coded. With several numerical examples including plane and space member structures, the results agree well with the solutions solved by other numerical methods and the accuracy and applicability of the static and dynamic elastic-plastic analysis are demonstrated. Without assembling stiffness matrixes and iterations solving geometric and material nonlinear problems, DEM avoids the calculation convergence and has more advantages than FEM.DEM method is suitable for the simulation of nonlinearity, large deformation and fracture problems, while there are some shortcoming such as large calculation and long time consuming. However, due to the large number of nodes and elements in large-span space reticulated structure, DEM method is difficult to get real applications in engineering individually. In this paper, a coupled DEM/FEM model is proposed, by which large deformation region is simulated using DEM while elastic small deformation region is simulated using FEM. Firstly, according to the virtual work equation and variational principle, the equations of coupled model system are derived. Based on penalty function method, the formula of interface coupled force is derived and a program is written. By two typical examples:large deformation analysis of cantilever beam and transient dynamic nonlinear analysis of reticulated shells under impact loads, numerical results and computational efficiency of three different computational models, including pure FEM, pure DEM and coupled DEM/FEM model are compared. The results show that the coupled DEM/FEM model applied to large-span spatial reticulated structures can save the computation time and improve the efficiency because of less calculation amount than pure DEM. Further, the coupled DEM/FEM model applied to solve strong nonlinear problem has good performance of stability while the pure FEM easily leads convergence difficulty. Then, the coupled DEM/FEM model is applied to collapse numerical simulation of single-layer reticulated shells. Compared with the results of shaking table test of model 1 of single-layer spherical shells, it is observed that the numerical simulation agree well with the experimental phenomenon and process and reveal the collapse mechanism of reticulated shells through the plastic development of members. The presented coupled DEM/FEM model provides a new calculation method for collapse failure analysis of large and complex structures.Finally, based on the fiber model, the definition of fiber (distributed spring) failure criterion is proposed and the algorithm considering structural member fracture during collapse process is developed. According to two examples including the fracture of cantilever beam and steel frame under blast loads, the rationality and applicability of DEM used to simulate the collapse failure of structures are verified. Then, the coupled DEM/FEM model is applied to collapse numerical simulation of single-layer reticulated shells. It is observed that the numerical simulation agree well with the experimental phenomenon and process. In fact, when DEM is used to simulate the member fracture, section cracking and particle separation from each other are natural processes, which can successfully achieve a transition from the initial intact continuum state to a non-continuous body after fracture without amendments. Compared with FEM method, DEM is more advantageous because there is no mesh distortion, re-meshing and iterative convergence.A method, which provides a numerical method to study complex behavior analysis and collapse mechanics for space lattice structures, is developed in this study to simulate the whole collapse process of reticulated shells, including elastic, elastoplastic and fracture. Meanwhile, this paper promotes an extension of the discontinuous discrete element method for continuous space lattice structure, expanding the application of discrete element method in structural engineering and provides a new approach for the nonlinear response analysis of structure under extreme loads.