映射半解析边界元法解瞬态弹性动力问题的有关问题

提出了映射半解析边界元法解百轴对称瞬态弹性动力问题时存在解析方向不能正确反映波的传播现象的问题，产生该问题的原因和如何解决该问题的建议。     

A system model to predict the results of ultrasonic scattering experiments

A system model is presented for the computation of ultrasonic scattering experiments. It includes a two-dimensional transducer model, whose diffraction field is given as an elastic plane wave spectral decomposition. An electromechanical reciprocity theorem is used to calculate the voltage at the terminal of the receiver. As a flaw-model, we use a strip-like crack, whose scattered field is calculated by the elastodynamic Huygens principle including mode conversion effects. Results in the time domain are presented for LLT- and 45° -tandem inspection situations and compared with measurements. Agreement between the model predictions and experimental results is typical to within 2 dB for average scan amplitudes.     

Numerical evaluation of elastodynamic energy fracture parameters in 2-D heterogeneous media

The elastodynamic energy fracture parameters for a stationary crack in 2-D heterogeneous media are evaluated with a presented generalized Domain Integral Method (DIM). The method, incorporated with the finite element solutions, is demonstrated to be patch-independent in a generalized sense. In the context of dynamic response, the near-tip region is always involved in the calculation. The method is used for determination of the associated Energy Release Rate (ERR) for the cases when the crack tip is away from the material interface, with the formulation valid for both small and large elastic deformations. Numerical results for such problems appear to be very insensitive to the crack-tip finite element models. As to the instances when the tip terminates normally at the material interface, the ERR is not feasible for use as a fracture criterion. The generalized DIM is then applied for calculation of the alternative elastodynamic energy parameter J/R^λ₀. The exponential order λ, with regard to the strength of stress singularity, is also properly evaluated in the calculation. No particular singular finite element is required throughout the study. © 1998 John Wiley & Sons, Ltd.     

A coupled numerical scheme of dual reciprocity BEM with DQM for the transient elastodynamic problems

The two‐dimensional transient elastodynamic problems are solved numerically by using the coupling of the dual reciprocity boundary element method (DRBEM) in spatial domain with the differential quadrature method (DQM) in time domain. The DRBEM with the fundamental solution of the Laplace equation transforms the domain integrals into the boundary integrals that contain the first‐ and the second‐order time derivative terms. Thus, the application of DRBEM to elastodynamic problems results in a system of second‐order ordinary differential equations in time. This system is then discretized by the polynomial‐based DQM with respect to time, which gives a system of linear algebraic equations after the imposition of both the boundary and the initial conditions. Therefore, the solution is obtained at any required time level at one stroke without the use of an iterative scheme and without the need of very small step size in time direction. The numerical results are visualized in terms of graphics. Copyright © 2008 John Wiley & Sons, Ltd.     

Improvement of numerical modeling in the solution of static and transient dynamic problems using finite element method based on spherical Hankel shape functions

In this paper, finite element method is reformulated using new shape functions to approximate the state variables (ie, displacement field and its derivatives) and inhomogeneous term (ie, inertia term) of Navier's differential equation. These shape functions and corresponding elements are called spherical Hankel hereafter. It is possible for these elements to satisfy the polynomial and the first and second kind of Bessel function fields simultaneously, while the classic Lagrange elements can only satisfy polynomial ones. These shape functions are so robust that with least degrees of freedom, much better results can be achieved in comparison with classic Lagrange ones. It is interesting that no Runge phenomenon exists in the interpolation of proposed shape functions when going to higher degrees of freedom, while it may occur in classic Lagrange ones. Moreover, the spherical Hankel shape functions have a significant robustness in the approximation of folded surfaces. Five numerical examples related to the usage of suggested shape functions in finite element method in solving problems are studied, and their results are compared with those obtained from classic Lagrange shape functions and analytical solutions (if available) to show the efficiency and accuracy of the present method.     

The solution of elastostatic and dynamic problems using the boundary element method based on spherical Hankel element framework

In this paper, new spherical Hankel shape functions are used to reformulate boundary element method for 2‐dimensional elastostatic and elastodynamic problems. To this end, the dual reciprocity boundary element method is reconsidered by using new spherical Hankel shape functions to approximate the state variables (displacements and tractions) of Navier's differential equation. Using enrichment of a class of radial basis functions (RBFs), called spherical Hankel RBFs hereafter, the interpolation functions of a Hankel boundary element framework has been derived. For this purpose, polynomial terms are added to the functional expansion that only uses spherical Hankel RBF in the approximation. In addition to polynomial function fields, the participation of spherical Bessel function fields has also increased robustness and efficiency in the interpolation. It is very interesting that there is no Runge phenomenon in equispaced Hankel macroelements, unlike equispaced classic Lagrange ones. Several numerical examples are provided to demonstrate the effectiveness, robustness and accuracy of the proposed Hankel shape functions and in comparison with the classic Lagrange ones, they show much more accurate and stable results.     

Probe model implementation in the null field approach to crack scattering

A model of a compressional ultrasonic transducer is implemented into a T-matrix method-based solution to a crack scattering problem. The probe can act both as a receiver and as a transmitter, and it is modeled as an acoustic piston-like source. A previous solution by the null field approach is applied and is here used to model a crack that is partly closed due to an external background pressure. Numerical calculations of the signal response when the crack is penny-shaped are performed and compared with results from a program based on the Geometrical Theory of Diffraction, and the agreement is generally found to be very good.     

Ill-posed and well-posed problems in inverse elastodynamic scattering for nondestructive evaluation

The practical significance of ill-posedness in a data reduction problem is reviewed. Inverse elastodynamic scattering is shown to be ill-posed in general, although suitably restricted problems may be well-posed. These results underscore the need to analyze carefully the errors of data reduction problems in NDE, and to focus attention on final results of an NDE exercise, rather than on intermediate steps.     

A system model for the ultrasonic inspection of smooth planar cracks

This paper describes a system model for the ultrasonic inspection of smooth planar cracks in ferritic steel, using pulse-echo probes. The model predicts the echo amplitudes and ranges as functions of the probe position. It is applied to problems of procedure design, assessment, and technical justification on power station plant. The model is implemented as a suite of versatile and user-friendly computer codes, suitable for use by practical NDT engineers, and is supported by a comprehensive user manual. The paper describes the principles of the model and gives examples of its application to power plant problems. Illustrations are also given of the extensive validation which the model has undergone through comparison with experiment.     

A Galerkin boundary element formulation with dual reciprocity for elastodynamics

In this paper, a Galerkin boundary integral equation method for two‐dimensional elastodynamic problems is presented. The formulation makes use of a static fundamental solution to weight the dynamic equilibrium equations. Following the Galerkin approach, the equations are weighted again with the interpolation functions used in the discretization of the unknowns. For the numerical integration, a regularization process is followed to deal with the integrands containing strong singularities. The implementation of the dual reciprocity method to transfer the domain integrals to the boundary is also presented in the context of the Galerkin formulation. Finally, the Hubolt integration scheme was used for the time‐marching process. Several numerical examples are presented to demonstrate the accuracy of the method. Copyright © 2000 John Wiley & Sons, Ltd.