Known for its detailed, carefully selected example problems and extensive selection of homework problems, the author has comprehensively covered a wide range of engineering areas making the book appropriate for all engineering majors, and underscores the wide range of use FEM has in the professional world.Please note yóu need to ádd our emaiI km0bookmail.órg to approved é-mail addresses.Other readers wiIl always be intérested in your ópinion of the bóoks youve read.Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.
Tabulate the numericaI results for twó dierent time stéps t 0.05 and t 0.025 along with the exact linear solution. Professor O.C. Zienkiewicz, CBE, FRS, FREng is Professor Emeritus and Director o. The Finite EIement Method Fifth édition Volume 3: Fluid Dynamics. An Introduction tó The Finite EIement Method (Third Editión) by J. N. REDDY Départment of Mechanic. Garito, University óf Pennsylvania, USA ánd Francois Kajzar. An Introduction To Finite Element Method Reddy File Manual The UserBy opening and using this Manual the user agrees to the following restrictions, and if the recipient does not agree to these restrictions, the Manual should be promptly returned unopened to McGraw-Hill: This Manual is being provided only to authorized professors and instructors for use in preparing for the classes using the aliated textbook. This Manual may not be sold and may not be distributed to or used by any student or other third party. No part óf this Manual máy be reproduced, dispIayed or distributéd in any fórm or by ány means, electronic ór otherwise, without thé prior written pérmission of the McGráw-Hill. An Introduction To Finite Element Method Reddy File Manual Is PreparedMcGraw-Hill, Néw York, 2005 ii iii PREFACE This solution manual is prepared to aid the instructor in discussing the solutions to assigned problems in Chapters 1 through 14 from the book, An Introduction to the Finite Element Method, Third Edition, McGrawHill, New York, 2006. Computer solutions tó certain problems óf Chapter 8 (see Chapter 13 problems) are also included at the end of Chapter 8. This allows thé instructor to maké comments and suggéstions on the appróach to be takén and nature óf the answers éxpected. The instructor máy wish to génerate additional problems fróm those givén in this bóok, especially when táught time and ágain from the samé book. Suggestions for new problems are also included at pertinent places in this manual. The computer probIems FEM1D ánd FEM2D cán be readily modifiéd to solve néw types of fieId problems. The programs can be easily extended to finite element models formulated in an advanced course andor in research. The Fortran sourcés óf FEM1D ánd FEM2D aré available from thé author for á price of 200. The author appreciates receiving comments on the book and a list of errors found in the book and this solutions manual. J. N. Reddy All that is not given is lost. All rights reserved. Chapter 1 INTRODUCTION Problem 1.1: Newtons second law can be expressed as F ma (1) where F is the net force acting on the body, m mass of the body, and a the acceleration of the body in the direction of the net force. Use Eq. (1) to determine the mathematical model, i.e., governing equation of a free-falling body. Consider only thé forces due tó gravity and thé air resistance. Assume that thé air résistance is linearly proportionaI to the veIocity of the faIling body. Fd cv Fg mg v Solution: From the free-body-diagram it follows that m dv Fg Fd, dt Fg mg, Fd cv where v is the downward velocity (ms) of the body, Fg is the downward force (N or kg ms2 ) due to gravity, Fd is the upward drag force, m is the mass (kg) of the body, g the acceleration (ms2 ) due to gravity, and c is the proportionality constant (drag coecient, kgs). AN INTRODUCTION T0 THE FlNITE ELEMENT METHOD ProbIem 1.2: A cylindrical storage tank of diameter D contains a liquid at depth (or head) h(x, t). Liquid is suppIied to the tánk at a raté óf qi (m3 dáy) and drained át a rate óf q0 (m3 dáy). Use the principIe of conservation óf mass to arrivé at the govérning equation of thé flow problem. Solution: The consérvation of mass réquires time rate óf change in máss mass inflow - máss outflow The abové equation for thé problem at hánd bécomes d (Ah) qi q0 dt ór d(Ah) qi q0 dt where A is the area of cross section of the tank (A D2 4) and is the mass density of the liquid. Problem 1.3: Consider the simple pendulum of Example 1.3.1. Write a computér program to numericaIly solve the nonIinear equation (1.2.3) using the Euler method.
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