p-Version finite elements and applications in structural impact and damage detection

Abstract

A part of the main work of the present research is the vibration analysis of beams, membranes, plates, two-dimensional and three-dimensional problems. New versatile Fourier p- elements using trigonometric functions as shape functions are developed for these structures to eliminate the ill-conditioning problems. Legendre orthogonal polynomials are also used for some elements. The results show that the convergence to the natural modes is faster than the conventional finite elements with the same number of degrees of freedom. The analysis includes geometric nonlinearity. An elasto-plastic impact model abandoning the Hertzian contact law is presented for structural collision protection. The impact force and responses of the impactor-absorber-structure system can be predicted accurately using the proposed pelements. An experiment of a three-dimensional column-plate structure attaching elasto-plastic and elastic absorbers is carried out to verify the model. A cost effective Cellular Reinforced Concrete Block (CRCB) is design to smooth the impact force and absorb the impact energy. Quasi-static tests show that the block has excellent energy absorbing characteristic. An experiment of a scaled frame model and a simulation of the ship collision of a T structure used to resist the Qiantang tide are carried out. Due to the plastic deformation of blocks, the impact force transmitted to the structure and responses of the structure are considerably reduced. Based on the wavelet transform, a two-stage damage detection method is developed. Two experiments of a cantilever beam and a cantilever plate attached with springs are carried out. Burning off the string connecting spring attached to the structure excites the high-frequency oscillations in the system, which results in a spike or impulse in the discrete wavelet transformed signal to recognize the damage at the moment it occurs. In the second stage, the shift of frequencies and damping ratios is identified by the continuous wavelet transform to ensure that the spike is indeed resulted from the damage but not noises. The random decrement technique is performed to the original signal to obtain the free decaying responses, and then the continuous wavelet transform is applied to identify the system parameters. The pelements are used for parametric study in the first stage of health monitoring. The results show that the two-stage method is successful for damage detection.

Date of Award	15 Jul 2005
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Yee Tak Andrew LEUNG (Supervisor)