DYNAMIC MICRO-STRUCTURAL FINITE-ELEMENT METHOD FOR GRANULAR STRUCTURES

A new numerical model, dynamic micro-structural finite element method (DMFEM), for granular structures comprising a number of particles is p resented. Particles are regarded as rigid and the contact points of tw o particles are assumed to be joined by pseudo springs to transmit for ces through their contacts. The stiffnesses of pseudo springs correspo nding to the macroscopic elastic constants, E and v, could be evaluate d according to the linear Hertz contact theory. DMFEM is the extension of the micro-structural finite element method (MFEM) proposed by C. S . Chang. The formulas of DMFEM are derived on the basis of the finite element technique and Hamilton's principle. By using the finite elemen t technique, the degrees of freedom of particles inside the structure can be transformed to the nodal degrees of freedom and the dimension o f equations of motion is thus reduced considerably. By means of Hamilt on's principle, the equations of motion for granular structures are de rived. It is shown that the stiffness matrix of the granular structure in DMFEM is related to the contact stiffnesses of granules and the ar rangement of the particles. The mass matrix is formulated in terms of the mass of particles and the moment of inertia of mass of particles. Examples of the vibration of granular structures that are regularly pa cked with equal size particles are introduced to illustrate the applic ability of the new numerical model.