The analysis of rigid-viscoplastic plane structures subjected to large impulsive loading - Griffin, Paul Dominic (Department of Civil Engineering, 2023)
This thesis is concerned with the analysis of plane ductile beams and frames which are subjected to large impulsive loading. The elastic response is ignored, and the material is considered as rigidviscoplastic in order to take rate effects into account. Computational advantage is obtained by modelling this behaviour by a homogeneous viscous constitutive relation, as the rigid phase is absent. As opposed to the standard displacement method finite element formulation where interpolation functions describing the velocity field across elements are given, a formulation is used in which nodal velocities, moments and element axial forces are carried as parameters. Three methods of analysis are presented; firstly, the mode approximation technique is described, where the actual behaviour of the structure is approximated in closed form by the product of a mode shape and a function of time. A new algorithm for the determination of the mode shape is presented. The mode technique is then extended to include geometric effects by means of the instantaneous mode solution technique. Secondly, a method is given whereby at each instant the accelerations (by the Tamuzh principle) and the rates of change of moment (by virtual velocities formulation) are found, and velocities and moments are integrated forward independently to obtain a solution. Finally, a direct method of analysis is described, where nodal forces conjugate to a given velocity field are calculated (by the principle of virtual velocities), and hence from the equations of motion, accelerations are determined. An implicit forward integration scheme is employed to advance the solution in time. Illustrative examples are presented which show that these techniques give very good and computationally efficient predictions of the displaced shape of the structures under consideration, even when displacements are in the order of the dimensions of the structure.