Extended GDQ and related discrete element analysis methods for transient analyses of continuum mechanics problems

AbstractThe extended GDQ proposed by the author is used to develop solution algorithms for solving the discrete transient equation system of a continuum mechanics problem. It is a direct integration approach. Two integration methods are developed. They are time-element by time-element method and stages by stages method. These two time integration algorithms can be used to solve a generic discrete transient equation system of an originally discrete system or a discrete system resulting from the discretization of a transient system of continuum mechanics problems by using a certain discretization technique such as the DQEM, FEM, FDM, etc

Dynamic behavior of bridge structures under moving loads and masses using differential quadrature method

The current study is focused on the dynamic behavior of an idealized highway bridge structure subjected to moving heavy vehicular loads using simplified representative models such as Euler beams and Kirchhoff plates. The study also successfully implemented the application of a numerical procedure called Differential Quadrature Method (DQM) to solve transient dynamic systems using conventional and generalized DQ schemes. A semi-analytical (modal method) DQ procedure proved computationally very effective to study the vehicle-bridge dynamic system.Three types of models were used to represent the vehicle-bridge system i.e. moving force, moving mass and moving oscillator systems. The dynamic behavior of the vehicle-bridge system is discussed with reference to vehicle speed, damping characteristics of the bridge, vehicle to bridge frequency ratio, vehicle to bridge mass ratio for a single axle load system, including inter-load spacing for a two axle load system. The dynamic amplification factor (DAF), characterizing the dynamic behavior of a bridge structure, was found to increase with the speed of moving vehicles. The vehicle-bridge dynamic behavior is unclear in the low speed parameter range to sufficiently address the differences in the moving force, moving mass and moving oscillator models. For a single axle load system with speed parameters ranging above 0.1, the moving mass model appeared conservative with higher DAF's, the moving oscillator yielded reduced DAF's and the moving force model predicted DAF's in between the above models. However, for a two axle load system with speed parameters ranging above 0.1, a moving oscillator model predicted higher dynamic responses than a corresponding moving force model