Chapter 3. Approximate Theories for Thin Elastic Bodies
3.1. One-dimensional Bodies 77
3.1.1. Bar's and string's axial deformation 77
3.1.2. Linear Euler-Bernoulli beam theory 78
3.1.3. Timoshenko beam 80
3.1.4. Nonlinear Euler-Bernoulli beam theory 81
3.2. Linear Theories for Two-dimensional Bodies 82
3.2.1. Kirchhoff-Love plate theory 82
3.2.2. Shells 86
3.2.3. Mindlin-Reissner plate theory 87
3.3. High-order Plate Theories and Laminated Structures 90
3.4. Nonlinear von-Karman Plate and Weakly-Curved Shell 92
3.4.1. Von-Karman Plate 92
3.4.2. Weakly-curved (shallow) shell 93
3.5. Bifurcation and Stability 93