Numerical Methods for Experimental Mechanics

ISBN-13: 9780792374039 / Angielski / Twarda / 2001 / 297 str.

D. G. Berghaus; Donald Berghaus

Opis

The purpose of this book is to place a resource in the hands of experimental mechanics researchers to enable them to understand and to obtain a working familiarity with certain of the numerical methods particularly useful to the field. The book is organized to permit readers to study the methods and to observe their application in experimental problems. It is also intended to encourage readers to directly apply the methods to the same problems or to similar problems of their choosing. To this end, computer programs are available electronically, together with data, for easy application. Program listings are given in the appendix. There are four chapters which make up the central coverage of the text. The first of these deals with least-square methods of problem solution, both for curve fitting and for general solution of overdetermined problems. Nonlinear least-squares methods are included. Secondly, splines; specifically smoothed splines, are covered, including specification of boundary conditions for the latter. Use for differentiation is emphasized with attention to control of possible excesses in smoothing. Transform methods are the third major area covered; both the Discrete Fourier Transform and the Fast Fourier Transform. Their combined use is described for appropriate problems. Finally, digital filters are included, principally the Butterworth low pass filter. Coverage also includes different filter orders, high pass filters and the two-pass filter technique. The author has had experience with the four areas covered and with all ofthe example problems described in the text.

Spis treści

Preface. 1. Statistical Evaluation for Data Quality. 2. Least-Squares Methods: The concept of 'least-squares'. Coverage of curve fitting, and general application of least squares. Care with posing least-squares problems and solutions. Application to 'full field' stress analysis. Nonlinear least-squares approximations. Application to study of mechanical material properties. 3. The Smoothed Spline: Piecewise approximation; spline functions. The smoothed spline; specifying boundary second derivatives. Applications to photoelasticity and to deformation and strain analysis of extrusion. 4. Fourier Transform Methods: Fourier series and the discrete Fourier transform. The Fast Fourier transform, combined use of DFT and FF. Application to electromechanical transducer signals and to gait analysis. 5. Digital Filters: Filtering of continuous and then discrete experimental data. The cutoff frequency. The difference equation and the solution for filtered data. Single pass and two-pass filters; higher order filters; a high pass filter. Filter applications to transducer data. 6. Differentiation and Integration: Differentiation, integration, and discrete experimental data. Local approximation functions to compute derivatives. Integration using Newton-Cotes formulas. Example applications using transducer data. Appendix: Computer programs for all methods described. Available electronically Compiled programs, data to reproduce results in book, or for use with reader's data.