Numerical Simulation On Static And Dynamic Response Of Simple Structures Based On Discrete Element Method

The Discrete Element Method (DEM) is one kind of numerical analysis method which is often used to simulate mechanical behaviors of discontinuous medium. The basic idea of this method is to divide the studying area into discrete elements that displace independently from one another, and permit contact between elements in disregard of the deformation compatibility condition and continuity condition. Without integrating stiffness matrix of structure, the DEM chooses the dynamic relaxation method to calculate motion state of each element, and avoid the divergent result arising from the singularity of the stiffness matrix. By improving discrete element contact model in this paper, the DEM was extended to analyze the transition from a continuum to a non-continuum. Simultaneously, methods for determining parameters of the DEM model and its influence on the calculated results were discussed in detail. Finally, based on the improved DEM model, the whole collapse process of structures was simulated numerically, including linear elasticity, geometric and material nonlinearity, fracture, contact etc. The main contents and conclusions are as follows:(1) The discrete element model was established for continuous medium on the basis of the parallel-bond model and the contact-bond model. Through the relationship between force and displacement of beam end, the contact stiffness coefficients of two-dimensional discrete elements were deduced to accommodate a variety of cross sections. Reasonable parameters of the DEM model were obtained from a systematic research on element shapes and quantities, arrangement types, contact models, the treatment of boundary conditions, equivalent loads, time step and damping coefficient. The DEM model was extended to three-dimensional space by improving particle flow model, the contact stiffness coefficients of which were derived from the relationship between force and displacement of beam end. By introducing the equivalent mass and the equivalent stiffness, element mass and moment of inertia were modified correspondingly to ensure correctness and effectiveness during the analysis process.(2) The static/dynamic large-deflection response and material nonlinearity of different structures were simulated by the DEM. The yield condition of generalized stress (internal force) was proposed according to the Mises yield criterion, and then the DEM method of elastic-plastic contact constitutive relationships was established. The DEM plastic contact stiffness under simple internal force conditions was presented by using the plastic hinge model and the plastic-development model, and The DEM plastic contact stiffness matrix under complex internal force conditions was deduced from the orthogonality of the yield surface. Several numerical examples were presented to demonstrate the feasibility of the improved DEM model for nonlinear problems of continuous medium.(3) Based on the fracture model of structural member and the element impact model which were proposed in this paper, the calculation procedures were compiled to detect contacts between elements, update connections and calculate impact forces. The whole collapse process of a K6 single-layer reticulated spherical shell through a shaking table test and the blast demolition of a frame structure were simulated and investigated using the research results in this paper, thus the correctness of contact detection program and the feasibility of DEM could be verified in the analysis of structural complicated behaviors from a continuum to a non-continuum.(4) The 2-D and 3-D DEM calculating programs were written in Fortran language in this paper, and the algorithms of elastic-plastic analysis, element fracture, contact detection as well as contact force calculation were written as corresponding subprograms which would be called when needed. By simulating the mechanical behaviors of different structural forms (including simple mechanisms, frames, trusses and reticulated shells etc.), the applicability of DEM was verified during the analysis process with the static and dynamic response of simple structures, large elastic-plastic deformation process, fracture and contact etc.