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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.
List of contents
1. Statistical Evaluation for Data Quality.- 1.1 Statistical Methods and Numerical Methods.- 1.2 The Quality of Recorded Data.- 1.3 Probability and the Binomial Distribution.- 1.4 Application to Experimental Data.- 2. Least-Squares Methods.- 2.1 The Concept of "Least-Squares".- 2.2 Curve Fitting.- 2.3 The General Application of Linear Least-Squares Solutions.- 2.4 A Procedure for General Application.- 2.5 Factors Affecting the Accuracy of Least-Squares Solutions.- 2.6 Application to "Full Field" Stress Analysis Problems.- 2.7 The Well Posed Problem.- 2.8 Nonlinear Least-Squares Approximations.- 3. The Smoothed Spline.- 3.1 Piecewise Approximation.- 3.2 The Smoothed Spline.- 3.3 Specifying Second Derivatives for the Ends of the Spline.- 3.4 Example Application; Scattered Light Photoelasticity.- 3.5 Example Problem; Deformation and Strain Analysis of Extrusion.- 4. Fourier Transform Methods.- 4.1 The Nature of Repetitive Events.- 4.2 Fourier Series and the Discrete Fourier Transform.- 4.3 The Fast Fourier Transform.- 4.4 Additional Considerations for Experimental Mechanics.- 5. Digital Filters.- 5.1 Filtering of Experimental Data.- 5.2 A Filter for Continuous Data.- 5.3 Application to Discrete Data.- 5.4 The Cutoff Frequency.- 5.5 The Difference Equation; Solution for Filtered Data.- 5.6 Filter Application Examples; Transducer Data.- 5.7 Higher Order Filters; the Third Order Butterworth Filter.- 5.8 A High Pass Filter.- 6. Differentiation and Integration.- 6.1 Differentiation, Integration, and Discrete Experimental Data.- 6.2 Local Approximation Functions to Compute Derivatives.- 6.3 Integration; the Computation of Area.- 6.4 Example Problems for Differentiation and Integration.- Appendix; Computer Programs.
Summary
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.
