Location

La Jolla, CA

Start Date

1-1-1993 12:00 PM

Description

The need for the numerical analysis of the elastic wave equation in solids is driven by the application of ultrasonic techniques to non-destructive evaluation of adhesive bonds and bondlines. Unfortunately, the physics of the problem require numerical models with an excessive number of degrees of freedom and time steps to analyze the response of a system to an ultrasonic pulse input. In the past, super computers and vector processors were used to tackle these problems. Alternately, purely closed form solutions were investigated with idealized boundary conditions. This work presents plane strain and axisymmetric finite element formulations which include viscous damping and anisotropic material capabilities that reduce by orders of magnitude the memory storage and execution time traditionally encountered. The time integration is accomplished using the explicit central difference method. The finite element spatial discretization employs a lumped mass matrix. The resulting decoupled equations are solved on a node by node basis at each time step. The code was verified as accurate by comparing the displacements qualitatively for the expected wave motion and by comparing the displacement histories at specific nodes to both analytical solutions based on the Cagnaird de-Hoop method and experimental pulse-echo piezoelectric transducer data. [1]

Book Title

Review of Progress in Quantitative Nondestructive Evaluation

Volume

12A

Chapter

Chapter 1: Development of Standard Techniques

Section

Elastic Wave Propagation

Pages

131-138

DOI

10.1007/978-1-4615-2848-7_16

Language

en

File Format

application/pdf

Share

COinS
 
Jan 1st, 12:00 PM

An efficient FEM approach for the study of ultrasonic wave propagation in solids

La Jolla, CA

The need for the numerical analysis of the elastic wave equation in solids is driven by the application of ultrasonic techniques to non-destructive evaluation of adhesive bonds and bondlines. Unfortunately, the physics of the problem require numerical models with an excessive number of degrees of freedom and time steps to analyze the response of a system to an ultrasonic pulse input. In the past, super computers and vector processors were used to tackle these problems. Alternately, purely closed form solutions were investigated with idealized boundary conditions. This work presents plane strain and axisymmetric finite element formulations which include viscous damping and anisotropic material capabilities that reduce by orders of magnitude the memory storage and execution time traditionally encountered. The time integration is accomplished using the explicit central difference method. The finite element spatial discretization employs a lumped mass matrix. The resulting decoupled equations are solved on a node by node basis at each time step. The code was verified as accurate by comparing the displacements qualitatively for the expected wave motion and by comparing the displacement histories at specific nodes to both analytical solutions based on the Cagnaird de-Hoop method and experimental pulse-echo piezoelectric transducer data. [1]