Structural Mechanics with a Pen A Guide to Solve Finite Difference Problems by Öchsner, Andreas

This book is focused on the introduction of the finite difference method based on the classical one-dimensional structural members, i.e., rods/bars and beams. It is the goal to provide a first introduction to the manifold aspects of the finite difference method and to enable the reader to get a methodical understanding of important subject areas in structural mechanics. The reader learns to understand the assumptions and derivations of different structural members. Furthermore, she/he learns to critically evaluate possibilities and limitations of the finite difference method. Additional comprehensive mathematical descriptions, which solely result from advanced illustrations for two- or three-dimensional problems, are omitted. Hence, the mathematical description largely remains simple and clear.

• Introduces the ​finite difference method base on one-dimensional structural members, i.e. rods/bars and beams
• Offers methodical understanding of important subject areas in structural mechanics
• Explains the mathematical description simple and clear

Table of Contents

1 Idea and Derivation of the Method 1

1. 1 Supplementary Problems 9
   References 9
   2 Investigation of Rods in the Elastic Range 11
2. 1 The Basics of a Rod 11
3. 2 Constant Material and Geometry Parameters 13
4. 3 Varying Material and Geometry Parameters 18
5. 4 Solved Problems 26
6. 5 Supplementary Problems 33
   References 35
   3 Investigation of Euler–Bernoulli Beams in the Elastic Range 37
7. 1 The Basics of an Euler–Bernoulli Beam 37
8. 2 Constant Material and Geometry Parameters 41
9. 3 Varying Material and Geometry Parameters 43
10. 4 Solved Problems 45
11. 5 Supplementary Problems 80
    References 87
    4 Investigation of Timoshenko Beams in the Elastic Range 89
12. 1 The Basics of a Timoshenko Beam 89
13. 2 Approximation of the Differential Equations 94
14. 3 Supplementary Problems 99
    References 101
    5 Consideration of Euler–Bernoulli Beams with Plastic Material Behavior 103
15. 1 Basics of the Layered Approach 103
16. 2 Supplementary Problems 112
    References 113