1<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> 2<html xmlns="http://www.w3.org/1999/xhtml"> 3<head> 4<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> 5<title>Applied Mechanics of Solids (A.F. Bower) - Home Page</title> 6<link rel=stylesheet style="text/css" href="main_page_stylesheet_new.css" /> 7</head> 8 9 10 11<body> 12 13 14 15<div class="container"> 16<div class="header"><img src="Header.png" alt="Insert Logo Here" name="Insert_logo" width="815" height="95" border="0" align="left" id="Insert_logo" style="background: #F00; display:block;" /> 17 <!-- end .header --></div> 18 19<div id="cssmenu"> 20<ul> 21 <li class="active"><a href="http://solidmechanics.org/index.html"><span>Home</span></a></li> 22 <li class="active"><a href="http://solidmechanics.org/contents.php"><span>Contents</span></a></li> 23 <li class="has-sub"><a href="http://solidmechanics.org/contents.php"><span>Quick Navigation</span></a> 24 <ul> 25 <li class="has-sub"><a href="http://solidmechanics.org/Text/Chapter1_1/Chapter1_1.php"><span>1. Objectives and Applications</span></a> 26 </li> 27 <li class="has-sub"><a href="http://solidmechanics.org/Text/Chapter2_1/Chapter2_1.php"><span>2. Governing Equations</span></a> 28 <ul> 29 <li><a href="http://solidmechanics.org/Text/Chapter2_1/Chapter2_1.php"><span>2.1 Basic Assumptions</span></a></li> 30 <li><a href="http://solidmechanics.org/Text/Chapter2_2/Chapter2_2.php"><span>2.2 Deformation Measures</span></a></li> 31 <li><a href="http://solidmechanics.org/Text/Chapter2_3/Chapter2_3.php"><span>2.3 Internal Forces</span></a></li> 32 <li><a href="http://solidmechanics.org/Text/Chapter2_4/Chapter2_4.php"><span>2.4 Equations of Motion</span></a></li> 33 <li><a href="http://solidmechanics.org/Text/Chapter2_5/Chapter2_5.php"><span>2.5 Work and Virtual Work</span></a></li> 34 <li><a href="http://solidmechanics.org/Text/Chapter2_6/Chapter2_6.php"><span>2.6 Laws of Thermodynamics</span></a></li> 35 <li class="last"><a href="http://solidmechanics.org/Text/Chapter2_7/Chapter2_7.php"><span>2.7 Changes of Reference Frame</span></a></li> 36 </ul> 37 </li> 38 <li class="has-sub"><a href="http://solidmechanics.org/Text/Chapter3_1/Chapter3_1.php"><span>3. Constitutive Laws</span></a> 39 <ul> 40 <li><a href="http://solidmechanics.org/Text/Chapter3_1/Chapter3_1.php"><span>3.1 General Principles</span></a></li> 41 <li><a href="http://solidmechanics.org/Text/Chapter3_2/Chapter3_2.php"><span>3.2 Linear Elasticity</span></a></li> 42 <li><a href="http://solidmechanics.org/Text/Chapter3_3/Chapter3_3.php"><span>3.3 Hypoelasticity</span></a></li> 43 <li><a href="http://solidmechanics.org/Text/Chapter3_4/Chapter3_4.php"><span>3.4 Generalized Hookes Law</span></a></li> 44 <li><a href="http://solidmechanics.org/Text/Chapter3_5/Chapter3_5.php"><span>3.5 Hyperelasticity</span></a></li> 45 <li><a href="http://solidmechanics.org/Text/Chapter3_6/Chapter3_6.php"><span>3.6 Small Strain Viscoelasticity</span></a></li> 46 <li><a href="http://solidmechanics.org/Text/Chapter3_7/Chapter3_7.php"><span>3.7 Rate Independent Plasticity</span></a></li> 47 <li><a href="http://solidmechanics.org/Text/Chapter3_8/Chapter3_8.php"><span>3.8 Small Strain Viscoplasticity</span></a></li> 48 <li><a href="http://solidmechanics.org/Text/Chapter3_9/Chapter3_9.php"><span>3.9 Large Strain Viscoplasticity</span></a></li> 49 <li><a href="http://solidmechanics.org/Text/Chapter3_10/Chapter3_10.php"><span>3.10 Large Strain Viscoelasticity</span></a></li> 50 <li><a href="http://solidmechanics.org/Text/Chapter3_11/Chapter3_11.php"><span>3.11 Soils</span></a></li> 51 <li><a href="http://solidmechanics.org/Text/Chapter3_12/Chapter3_12.php"><span>3.12 Crystal Plasticity</span></a></li> 52 <li class="last"><a href="http://solidmechanics.org/Text/Chapter3_13/Chapter3_13.php"><span>3.13 Surfaces and Interfaces</span></a></li> 53 </ul> 54 </li> 55 <li class="has-sub"><a href="http://solidmechanics.org/Text/Chapter4_1/Chapter4_1.php"><span>4. Solutions to Simple Problems</span></a> 56 <ul> 57 <li><a href="http://solidmechanics.org/Text/Chapter4_1/Chapter4_1.php"><span>4.1 Axially/Spherically Symmetric elasticity</span></a></li> 58 <li><a href="http://solidmechanics.org/Text/Chapter4_2/Chapter4_2.php"><span>4.2 Axially/Spherically Symmetric Hyperelasticity</span></a></li> 59 <li><a href="http://solidmechanics.org/Text/Chapter4_3/Chapter4_3.php"><span>4.3 1-D Elastodynamics</span></a></li> 60 </ul> 61 </li> 62 <li class="has-sub"><a href="http://solidmechanics.org/Text/Chapter5_1/Chapter5_1.php"><span>5. Linear Elasticity</span></a> 63 <ul> 64 <li><a href="http://solidmechanics.org/Text/Chapter5_1/Chapter5_1.php"><span>5.1 General Principles</span></a></li> 65 <li>
65<a href="http://solidmechanics.org/Text/Chapter5_2/Chapter5_2.php"><span>5.2 Plane Problems: Airy Function Solutions</span></a></li> 66 <li><a href="http://solidmechanics.org/Text/Chapter5_3/Chapter5_3.php"><span>5.3 Plane Problems: Complex Variable Solutions</span></a></li> 67 <li><a href="http://solidmechanics.org/Text/Chapter5_4/Chapter5_4.php"><span>5.4 3D Static Problems</span></a></li> 68 <li><a href="http://solidmechanics.org/Text/Chapter5_5/Chapter5_5.php"><span>5.5 Solutions to Dynamic Problems</span></a></li> 69 <li><a href="http://solidmechanics.org/Text/Chapter5_6/Chapter5_6.php"><span>5.6 Energy Methods</span></a></li> 70 <li><a href="http://solidmechanics.org/Text/Chapter5_7/Chapter5_7.php"><span>5.7 The Reciprocal Theorem</span></a></li> 71 <li><a href="http://solidmechanics.org/Text/Chapter5_8/Chapter5_8.php"><span>5.8 Dislocations</span></a></li> 72 <li class="last"><a href="http://solidmechanics.org/Text/Chapter5_9/Chapter5_9.php"><span>5.9 Rayleigh-Ritz method (Vibrations)</span></a></li> 73 </ul> 74 </li> 75 <li class="has-sub"><a href="http://solidmechanics.org/Text/Chapter6_1/Chapter6_1.php"><span>6. Plasticity</span></a> 76 <ul> 77 <li><a href="http://solidmechanics.org/Text/Chapter6_1/Chapter6_1.php"><span>6.1 Slip-Line Fields</span></a></li> 78 <li class="last"><a href="http://solidmechanics.org/Text/Chapter6_2/Chapter6_2.php"><span>6.2 Bounding Theorems</span></a></li> 79 </ul> 80 </li> 81 <li class="has-sub"><a href="http://solidmechanics.org/Text/Chapter7_1/Chapter7_1.php"><span>7. Intro to Finite Elements</span></a> 82 <ul> 83 <li><a href="http://solidmechanics.org/Text/Chapter7_1/Chapter7_1.php"><span>7.1 Guide to FEA Software</span></a></li> 84 <li class="last"><a href="http://solidmechanics.org/Text/Chapter7_2/Chapter7_2.php"><span>7.2 Simple FEA Program</span></a></li> 85 </ul> 86 </li> 87 <li class="has-sub"><a href="http://solidmechanics.org/Text/Chapter8_1/Chapter8_1.php"><span>8. Theory of FEA</span></a> 88 <ul> 89 <li><a href="http://solidmechanics.org/Text/Chapter8_1/Chapter8_1.php"><span>8.1 Generalized Linear Elasticity</span></a></li> 90 <li><a href="http://solidmechanics.org/Text/Chapter8_2/Chapter8_2.php"><span>8.2 Dynamic Linear Elasticity</span></a></li> 91 <li><a href="http://solidmechanics.org/Text/Chapter8_3/Chapter8_3.php"><span>8.3 Nonlinear Hypoelastic Materials</span></a></li> 92 <li><a href="http://solidmechanics.org/Text/Chapter8_4/Chapter8_4.php"><span>8.4 Hyperelasticity</span></a></li> 93 <li><a href="http://solidmechanics.org/Text/Chapter8_5/Chapter8_5.php"><span>8.5 Viscoplasticity</span></a></li> 94 <li class="last"><a href="http://solidmechanics.org/Text/Chapter8_6/Chapter8_6.php"><span>8.6 Special Elements</span></a></li> 95 <li class="last"><a href="http://solidmechanics.org/Text/Chapter8_7/Chapter8_7.php"><span>8.7 Structural Elements</span></a></li> 96 <li class="last"><a href="http://solidmechanics.org/Text/Chapter8_8/Chapter8_8.php"><span>8.8 Constraints, Interfaces and Contact</span></a></li> 97 </ul> 98 </li> 99 <li class="has-sub"><a href="http://solidmechanics.org/Text/Chapter9_1/Chapter9_1.php"><span>9. Modeling Failure</span></a> 100 <ul> 101 <li><a href="http://solidmechanics.org/Text/Chapter9_1/Chapter9_1.php"><span>9.1 Summary of Failure Mechanisms</span></a></li> 102 <li><a href="http://solidmechanics.org/Text/Chapter9_2/Chapter9_2.php"><span>9.2 Stress/Strain Based Failure Criteria</span></a></li> 103 <li><a href="http://solidmechanics.org/Text/Chapter9_3/Chapter9_3.php"><span>9.3 Linear Elastic Fracture Mechanics</span></a></li> 104 <li><a href="http://solidmechanics.org/Text/Chapter9_4/Chapter9_4.php"><span>9.4 Energy Methods</span></a></li> 105 <li><a href="http://solidmechanics.org/Text/Chapter9_5/Chapter9_5.php"><span>9.5 Plastic Fracture Mechanics</span></a></li> 106 <li class="last"><a href="http://solidmechanics.org/Text/Chapter9_6/Chapter9_6.php"><span>9.6 Interface Fracture Mechanics</span></a></li> 107 </ul> 108 </li> 109 <li class="has-sub"><a href="http://solidmechanics.org/Text/Chapter10_1/Chapter10_1.php"><span>10. Rods, Plates and Shells</span></a> 110 <ul> 111 <li><a href="http://solidmechanics.org/Text/Chapter10_1/Chapter10_1.php"><span>10.1 Dyadic Notation</span></a></li> 112 <li><a href="http://solidmechanics.org/Text/Chapter10_2/Chapter10_2.php"><span>10.2 Rods: General Theory</span></a></li> 113 <li><a href="http://solidmechanics.org/Text/Chapter10_3/Chapter10_3.php"><span>10.3 Simplified Rods - Strings and Beams</span></a></li> 114 <li><a href="http://solidmechanics.org/Text/Chapter10_4/Chapter10_4.php"><span>10.4 Solutions for Rods</span></a></li> 115 <li><a href="http://solidmechanics.org/Text/Chapter10_5/Chapter10_5.php"><span>10.5 Shells : General Theory</span></a></li> 116 <li><a href="http://solidmechanics.org/Text/Chapter10_6/Chapter10_6.php"><span>10.6 Simplified Shells: Membranes and Plates</span></a></li> 117 <li class="last"><a href="http://solidmechanics.org/Text/Chapter10_7/Chapter10_7.php"><span>10.7 Solutions for Plates and Shells</span></a></li> 118 </ul> 119 </li> 120 <li class="has-sub"><a href="http://solidmechanics.org/Text/AppendixA/AppendixA.php"><span>Appendix A: Vectors & Matrices</span></a> 121 </li> 122 <li class="has-sub"><a href="http://solidmechanics.org/Text/AppendixB/AppendixB.php"><span>Appendix B: Intro to Tensors</span></a> 123 </li> 124 <li class="has-sub"><a href="http://solidmechanics.org/Text/AppendixC/AppendixC.php"><span>Appendix C: Index Notation</span></a> 125 </li> 126 <li class="has-sub"><a href="http://solidmechanics.org/Text/AppendixD/AppendixD.php"><span>Appendix D: Polar Coordinates</span></a> 127 </li> 128 <li class="has-sub"><a href="http://solidmechanics.org/Text/AppendixE/AppendixE.php"><span>Appendix E: Misc. Derivations</span></a> 129 </li> 130 </ul> 131 </li> 132 <li class="has-sub"><a href="http://solidmechanics.org/problems/problems.php" ><span>Problems</span></a> 133 </li> 134 <li class="last"><a href="http://solidmechanics.org/FEA.php"><span>FEA Codes</span></a></li> 135</ul> 136</div> 137 138 <div class="content"> 139 140 <table width="815" border="0"> 141 <tbody> 142 <tr> 143 <td width="210" > 144 <div class="sidebar1"" 145 <p> </p> 146 <p> </p> 147 <p> </p> 148 <form method="get" action="https://www.google.com/search"> 149 <div align="center"> 150 <input type="submit" value="Google Search" /> 151 <input type="text" name="q" size="21" maxlength="200" value="" /><br /> 152 <input type="checkbox" name="sitesearch" value="https://solidmechanics.org/" checked/>Only search this site 153 </div> 154 </form> 155 <p> </p> 156 157 <ul> 158 <li><a href="http://solidmechanics.org/contents.php">Table of Contents >></a></li> 159 <li><a href="http://solidmechanics.org/problems/problems.php" target="new">Example Problems >></a></li> 160 <li><a href="http://solidmechanics.org/FEA.php">Sample FEA codes >></a></li> 161 <li><a href="http://solidmechanics.org/references.php">Cited references >></a></li> 162 <li><a href="http://solidmechanics.org/author.php">About the author >></a></li> 163 <li><a href="https://www.amazon.com/Applied-Mechanics-Solids-Allan-Bower/dp/1041019955">Buy a print version >></a></li> 164 <li><a href="https://www.amazon.com/Solved-Problems-Applied-Mechanics-Solids/dp/1041237170/">Buy solved problems >></a></li> 165 </ul> 166 <p> </p> 167 <p> </p> 168 <p> </p> 169 170 171 <p> </p> 172<p> </p> 173 <p> </p> 174 <p> </p> 175 <p> </p> 176 <p> </p> 177 <p> </p> 178 <p> </p> 179 <p> </p> 180<h1> </h1> 181</div> 182 183 </td> 184 <td> 185 <h2 align="center"> </h2> 186 <p align="center"><img border="0" src="Logo.png" width="250" height="157" align="center" ></p> 187 <h1 align="center"> </h1> 188 <h1 align="center" style="font-size: 14pt; font-family: Arial, Helvetica, sans-serif;">Applied Mechanics of Solids </h1> 189 <h3 align="center">    Allan F. Bower      </h3> 190 <p> </p> 191 <p align="justify">This electronic text summarizes the physical laws, mathematical methods, and computer algorithms that are used to predict the response of materials and structures to mechanical or thermal loading.</p> 192 <p align="justify">Topics include: the mathematical descriptions of deformation and forces in solids; constitutive laws;
192 analytical techniques and solutions to linear elastic and elastic-plastic boundary value problems; the use and theory of finite element analysis; fracture mechanics; and the theory of deformable rods, plates and shells.</p> 193 <p align="justify">Over 500 practice problems are provided, as well as demonstration finite element codes in MATLAB. A pdf format copy of the problems (without solutions) may be downloaded <a href="http://solidmechanics.org/problems/Example_Problems_in_Mechanics_of_Solids.pdf" target="new">here</a>.</p> 194 195 196 <p align="justify">A print version of the text is available from <a href="https://www.amazon.com/Applied-Mechanics-Solids-Allan-Bower/dp/1041019955">Amazon</a>. The print edition does not include the problem sets, which are published (with solutions) in a separate companion volume "Solved Problems in Applied Mechanics of Solids", available from <a href="https://www.routledge.com/Solved-Problems-in-Applied-Mechanics-of-Solids/Bower/p/book/9781041237198">Routlege</a> or <a href="https://www.amazon.com/Solved-Problems-Applied-Mechanics-Solids/dp/1041237197/ref=zg_bsnr_g_14585_d_sccl_1/140-2111246-7689054?psc=1">Amazon</a>. This electronic web site will continue to be freely available.</p> 197 198 </td> 199 </tr> 200 </tbody> 201 </table> 202 203 <!-- end .content --></div> 204 205 <div class="footer"> 206 <p align="center" class="footer"><br /> 207 (c) A.F. Bower (2025)</p> 208 <!-- end .footer --></div> 209 <!-- end .container --></div> 210</body> 211</html>
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