Computational Statics Revision Course

Review of Engineering Mathematics -- Rods and Trusses -- Euler-Bernoulli Beams and Frames -- Timoshenko Beams -- Symmetry.;This revision and work book offers a very specific concept for learning the finite element method applying it to problems from statics of: It skips all the classical derivations and focusses only the essential final results. Based on these `essentials', fully solved example problems are presented. To facilitate the initial learning process, the authors compiled 10 recommended steps for a linear finite element solution procedure (`hand calculation') and all the solved examples follow this simple scheme. These 10 recommended steps help engineering students to master the finite ele ment method and guide through fundamental standard problems, although there are neither 10 recommended steps for real-life engineering problems nor 10 standard problems that cover all possible problems that a young engineer may face during his first years of professional work. This revision course accompanies the textbook "Computational Statics and Dyn amics: An Introduction Based on the Finite Element Method" by the same authors. Preface 6 Acknowledgement 8 Contents 9 Symbols and Abbreviations 11 1 Review of Engineering Mathematics 15 1.1 Solution of Linear Systems of Equations 15 1.1.1 Revision of Theory 16 1.1.2 Worked Examples 18 1.2 Analytical Integration 22 1.3 Numerical Integration 23 1.3.1 Revision of Theory 23 1.3.2 Worked Examples 24 1.4 Supplementary Problems 28 2 Rods and Trusses 30 2.1 Fundamentals and Analytical Treatment 30 2.2 Rod Elements 33 2.2.1 Revision of Theory 33 2.2.2 Worked Examples 38 2.3 Truss Structures 51 2.3.1 Revision of Theory 51 2.3.2 Worked Examples 52 2.4 Supplementary Problems 71 3 Euler--Bernoulli Beams and Frames 76 3.1 Fundamentals and Analytical Treatment 76 3.1.1 Euler--Bernoulli Beams 76 3.1.2 Generalized Beams 80 3.2 Beam Elements 83 3.2.1 Revision of Theory 83 3.2.2 Worked Examples 87 3.3 Generalized Beam Elements 101 3.3.1 Revision of Theory 101 3.3.2 Worked Examples 102 3.4 Rotation of Elements---Plane Frame Structures 118 3.4.1 Revision of Theory: Rotation of Beam Elements 118 3.4.2 Revision of Theory: Rotation of Generalized Beam Elements 119 3.4.3 Worked Examples 125 3.5 Supplementary Problems 151 4 Timoshenko Beams 158 4.1 Fundamentals and Analytical Treatment 158 4.2 Beam Elements 162 4.2.1 Revision of Theory 162 4.2.2 Worked Examples 164 4.3 Supplementary Problems 177 5 Symmetry 180 5.1 Placement of Nodes 180 5.2 Using Symmetry 182 5.3 Examples 184 5.4 Supplementary Problems 189 Appendix A Answers to Supplementary Problems 192 Appendix References 216 Index 218 Annotation This revision and work book offers a very specific concept for learning the finite element method applying it to problems from statics of: It skips all the classical derivations and focusses only the essential final results. Based on these èssentials', fully solved example problems are presented. To facilitate the initial learning process, the authors compiled 10 recommended steps for a linear finite element solution procedure (h̀and calculation') and all the solved examples follow this simple scheme. These 10 recommended steps help engineering students to master the finite element method and guide through fundamental standard problems, although there are neither 10 recommended steps for real-life engineering problems nor 10 standard problems that cover all possible problems that a young engineer may face during his first years of professional work. This revision course accompanies the textbook "Computational Statics and Dynamics: An Introduction Based on the Finite Element Method" by the same authors Front Matter ....Pages i-xvi Review of Engineering Mathematics (Zia Javanbakht, Andreas Öchsner)....Pages 1-15 Rods and Trusses (Zia Javanbakht, Andreas Öchsner)....Pages 17-62 Euler–Bernoulli Beams and Frames (Zia Javanbakht, Andreas Öchsner)....Pages 63-144 Timoshenko Beams (Zia Javanbakht, Andreas Öchsner)....Pages 145-166 Symmetry (Zia Javanbakht, Andreas Öchsner)....Pages 167-178 Back Matter ....Pages 179-206