ON THE SIMULATION OF WAVE PROPAGATION PROBLEMS IN NONREGULAR STRUCTURES WITH FINITE ELEMENT PROGRAMS

Abstract

Seismic analysis is used to test a material against random vibrations, shock, and impact. Each of these incidences may act on the natural frequency of the material which, in turn, may cause resonance and subsequent failure. The propagation of disturbances in the various media like solid, liquid, and gas share many common features and have differences too. Present work considers propagation of waves in solids. The physical basis for the propagation of a disturbance ultimately lies in the interaction of the discrete atoms of the solid. In solid mechanics, the medium is regarded as continuous, so that properties such as density or elastic constants are considered to be continuous functions representing averages of microscopic quantities. But it is helpful to first consider a model composed of discrete elements consisting of a series of interconnected masses and springs, without which some problem cannot be solved. If a disturbance is imparted to a mass particle, it is transmitted to the next mass by the intervening spring. In this manner the disturbance is soon transmitted to a remote point, although any given particle of the system will have moved only a small amount. The role of the mass and stiffness parameters in affecting the speed of propagation is such that if the stiffness of the connecting springs is increased or the particle masses decreased, or both, the speed of propagation would increase. Weaker springs and/or larger masses would slow the propagation velocity. Similar phenomenon occurs in the case of continuous media. In the problem of wave propagation for structure under impact load, the simulation of wave propagation with FE programs is strongly depending on the discretization with elements and other structural simulation techniques available in FE programs. This method of product design and testing is far superior to the manufacturing costs which may happen if each sample was actually built and tested. In static analysis often joints, constraints and local rigid bodies as well as simple contact algorithms are used. In dynamics such simulation techniques, though very effective in statics, may affect the solution quality considerably. Such simulation has been carried out using FE program LS-DYNA and the results are validated using analytical solution of wave propagation in solids. The results reveal strength and weakness of various modeling procedures in simple as well as in complex non-regular structures.