TOC (Pao - Engineering Analysis)

EngineeringAnalysisInteractive Methods and Programswith FORTRAN, QuickBASIC, MATLAB,and MathematicaY. C. PaoCRC PressBoca Raton London New York Washington, D.C.© 2001 by CRC Press LLCAcquiring Editor:Project Editor:Cover design:Cindy Renee CarelliAlbert W. Starkweather, Jr.Dawn BoydLibrary of Congress Cataloging-in-Publication DataCatalog record is available from the Library of CongressThis book contains information obtained from authentic and highly regarded sources. Reprintedmaterial is quoted with permission, and sources are indicated. A wide variety of references are listed.Reasonable efforts have been made to publish reliable data and information, but the author and thepublisher cannot assume responsibility for the validity of all materials or for the consequences of their use.Neither this book nor any part may be reproduced or transmitted in any form or by any means,electronic or mechanical, including photocopying, microfilming, and recording, or by any informationstorage or retrieval system, without prior permission in writing from the publisher.The consent of CRC Press LLC does not extend to copying for general distribution, for promotion,for creating new works, or for resale.

Specific permission must be obtained in writing from CRC PressLLC for such copying.Direct all inquiries to CRC Press LLC, 2000 Corporate Blvd., N.W., Boca Raton, Florida 33431.Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and areonly used for identification and explanation, without intent to infringe.Mathematica® is developed by Wolfram Research, Inc., Champaign, IL.Windows® is developed by Microsoft Corp., Redmond, WA.© 1999 by CRC Press LLCNo claim to original U.S. Government worksInternational Standard Book Number 0-8493-2016-XPrinted in the United States of America 1 2 3 4 5 6 7 8 9 0Printed on acid-free paper© 2001 by CRC Press LLCFiles Available from CRC PressFORTRAN, QuickBASIC, MATLAB, and Mathematic files, which contain thesource and executable programs associated with this book are available from CRCPress’ website — http://www.crcpress.com.Before downloading, prepare two 3.5-inch, high-density disks — one for thefiles and one for a backup.

Also create a temporary directory named <interactive>on your hard drive, which will expedite downloading. To download these files, type:http://www.crcpress.com/us/ElectronicProducts/downandup.asp. When prompted, enter2016 under name and crcpress under password. Then store the files in the<interactive> folder. If you encounter a problem, call 1-800-CRC-PRES (272-7737).The dowloaded files may be copied to a 3.5-inch disk. The temporary <interactive>folder then may be deleted. Don’t forget to make a backup copy of your 3.5-inch disk.There are four subdirectories <FORTRAN>, <QB>, <mFiles>, and <Mathtica> which contain the FORTRAN source and executable programs, QuickBASICsource and executable programs, m files of MATLAB, and input and output statements of for the Mathematica operations depicted in this textbook, respectively:1.

<FORTRAN> has the following files:Bairstow.FOREditFOR.EXEFindRoot.FORGauss.FORLeastSqG.FORNuIntgra.FORRelaxatn.FORCharacEquationFOREigenVec.FORFOR1.EXEGauJor.FORLINK.EXEOdeBvpFD.FORRungeKut.FORCubeSpln.FOREigenvIt.FORFOR2.EXELagrangI.FORMatxInvD.FOROdeBvpRK.FORVolume.FORDiffTabl.FORExactFit.FORFORTRAN.LIBLeastSq1.FORNewRaphG.FORParabPDE.FORWavePDE.FOREDITFOR.EXE is provided for re-editing the *.FOR source programs such asBairstow.FOR, CubeSpln.FOR, etc. (refer to the FORTRAN programs index) toinclude supplementary subprograms describing the problem which need to be solvedinteractively.

To re-edit, insert the 3.5-inch disk into Drive A and when the a:\ promptshows, type cd fortran to switch to the <FORTRAN> subdirectory. For example,to solve a polynomial by the Bairstow’s method one needs to define the polynomial,for which the roots are to be computed. To reedit Bairstow.FOR, the user entersa:\editfor Bairstow.for to add new FORTRAN statements or change them.

Noticethat both upper and lower case characters are acceptable. While creating a newversion of Bairstow.FOR, the old version will be saved in Bairstow.BAK.To create an object file, FOR1 filename such as Bairstow.FOR and FOR2 needto be implemented. A BAISTOW.OBJ will then be generated. For linking with theFORTRAN library functions, FORTRAN.LIB, one enters, for example, LINKBairstow to create an executable file Bairstow.EXE.

To run, the user simply typesBairstow after the prompt A:\ and then answers questions interactively.© 2001 by CRC Press LLC2. <QuickBASIC> has the following files:Select.BASBairstow.EXEEigenStb.EXEExactFit.EXELeastSq1.EXEOdeBvpFD.EXERelaxatn.EXEBairstow.QBEigenStb.QBExactFit.QBLagrangI.QBMatxMtpy.QBOdeBvpRK.QBVolume.QBSelect.EXEBRUN40.EXEEigenVec.EXEFindRoot.EXELeastSqG.EXEOdeBvpRK.EXERungeKut.EXECharacEq.QBEigenVec.QBFindRoot.QBLeastSq1.QBNewRaphG.QBParabPDE.QBWavePDE.QBCharacEq.EXEEigenVib.EXEGauss.EXEMatxInvD.EXEParabPDE.EXEVolume.EXECubeSpln.QBEigenVib.QBGauJor.QBLeastSqG.QBNuIntgra.QBRelaxatn.QBCubeSpln.EXEEigenvIt.EXELagrangI.EXENuIntgra.EXEQB.EXEDiffTabl.QBEigenvIt.QBGauss.QBMatxAlgb.QBOdeBvpFD.QBRungeKut.QBTo commence QuickBASIC, when a:\ is prompted on screen, the user entersQB.

QB.EXE and BRUN40.EXE therefore are included in <QB>. The programSelect enables user to select the available QuickBASIC program in this textbook.After user responds with C:\Select, the screen shows a menu as shown in Figure 1and user then follow the screen help-messages to run a desired program.3. <mFiles> is a subdirectory associated with MATLAB and has the followingfiles:BVPF.mF.mFuncZ.mintegrnd.mParabPDE.mWavePDE.mDerivatF.mFindRoot.mFuncZnew.mLagrangI.mRelaxatn.mDiffTabl.mFP.mFunF.mLeastSqG.mVolume.mEigenvIt.mFunctns.mGauJor.mNewRaphG.mWarping.mWhen the 3.5-inch disk containing all of these m files is in Drive A, any of thesefiles can be accessed by enclosing the filename inside a pair of parentheses asillustrated in Section 3.2 where F.m and FP.m are required for FindRoot.m and inSection 5.2 where an integrand function integrnd.m is defined for numerical integration.

If all files have been added into MATLAB library m files, then no referenceto the Drive A is necessary and the pair of parentheses can also be dropped.4. <Mathtica> is a subdirectory associated with Mathematica and has the files of:Bairstow.MTKExactFit.MTKGauss.MTKLeastSqG.MTKOdeBvpFD.MTKRungeKut.MTK© 2001 by CRC Press LLCCubeSpln.MTKFindRoot.MTKGauJor.MTKMatxAlgb.MTKOdeBvpRK.MTKVolume.MTKDiffTabl.MTKFUNCTNS.MTKLagrangI.MTKNewRaphG.MTKParabPDE.MTKWavePDE.MTKEigenVec.MTKEigenvIt.MTKLeastSq1.MTKNuIntgra.MTKRexalatn.MTKAny of the above programs can be executed by Mathematica via mouse operation. First, by clicking the File option and when the pull-down menu appears, selectOpen and then enter the filename such as a:\Mathtica\MatxAlgb.MTK (assumingthe 3.5-inch disk containing <Mathtica> is in Drive A) and press the Enter key.When all lines of this file is displayed on screen, move cursor to any input line suchas In[1]: A = {{1,2},{3,4}}; MatrixForm[A] and hit the Enter key.

Mathematicawill respond by repeating those lines for Out[1]. Hence, user can reproduce all ofthe output lines by sequentially running the input lines [1] through [9]. However, ifuser first run In[1] and then In[3], Mathematica cannot perform the addition of [A]because [B] is not defined. If after having run In[1], user selects In[5], or, In[6],Mathematica then has no problem of giving out results.FIGURE 1. The Select screen.© 2001 by CRC Press LLCDedicationThis book is dedicated to Prof. E.

J. Marmo,who offered a congenial work-environment for the authorto grow in the computer-aided engineering field.© 2001 by CRC Press LLCPreface and AcknowledgmentsWriting textbooks on topics in the field of Computer Aided Engineering (CAE)indeed has been a very satisfying experience. First, I had the pleasure of being acoauthor with Prof. Thomas C.

Smith of the book Introduction to Digital ComputerPlotting by Gordon & Breach in 1973. The book Elements of Computer-AidedDesign and Manufacturing, CAD/CAM, was published in 1982 by John Wiley &Sons. The book A First Course in Finite Element Analysis published by Allyn &Bacon followed in 1986, and Engineering Drafting and Solid Modeling with SilverScreen, published by CRC Press, appeared in 1993.Having taught the subjects of computer methods for engineering analysis since1966, I finally have the courage to organize this textbook out of a large volume ofclassroom notes collected over the past 31 years.The rapid growth of computer technology is difficult for any one to keep pace,and to make revision of textbooks in the CAE field. However, the computationalmethods developed by the pioneers, such as Euler, Gauss, Lagrange, Newton, andRunge, continue to serve us incredibly effective.

These computational algorithmsremain classic, only are now executed with modern computer technology.As far as the programming languages are concerned, FORTRAN has beendominating the scientific fields for many decades. BASIC considered by many tobe too plain and cumbersome while C is considered by others to be too sophisticated;both, however, are gaining popularity and increasingly replacing FORTRAN in thecomputational community. This is particularly true when QuickBASIC was introduced by Microsoft.MATLAB and Mathematica developed by the MathWorks, Inc. and WolframResearch, Inc., respectively both contain a vast collection of files (similar to FORTRAN’s library functions) which can perform the often-encountered computationalproblems.

For implementation, the MATLAB and Mathematica instructions to beinteractively entered through keyboard are extremely simple. And, it also providesvery easy-to-use graphic output. When students find it too easy to use, they oftenbecome uninterested in learning what are the methods involved. This text is preparedwith FORTRAN, QuickBASIC, MATLAB and Mathematica, and more importantly gives the algorithms involved in the methods.