Book contents
- Frontmatter
- Contents
- GUIDED EXPLORATIONS OF THE MECHANICS OF SOLIDS AND STRUCTURES
- Introduction
- 1 QED the Computer Laboratory
- 2 Static Analysis
- 3 Vibration of Structures
- 4 Wave Propagation
- 5 Nonlinear Structural Mechanics
- 6 Stability of the Equilibrium
- 7 Constructing Simple Analytical Models
- References
- Index
5 - Nonlinear Structural Mechanics
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- GUIDED EXPLORATIONS OF THE MECHANICS OF SOLIDS AND STRUCTURES
- Introduction
- 1 QED the Computer Laboratory
- 2 Static Analysis
- 3 Vibration of Structures
- 4 Wave Propagation
- 5 Nonlinear Structural Mechanics
- 6 Stability of the Equilibrium
- 7 Constructing Simple Analytical Models
- References
- Index
Summary
There are two main sources of nonlinearities in the mechanics of solids and structures. The first is geometric in nature and arises from large deflections, large rotations, and large strains. The second arises from the material behavior and is typified by elastic-plastic and rubberlike materials. Contact problems are also nonlinear even when the contacting bodies themselves remain linear elastic. Figure 5.1 is an example of a long, thin cantilevered plate undergoing large deflections and rotations because of an end moment.
The explorations in this chapter look at aspects of each of these nonlinear behaviors. The first exploration considers the concept of stress and strain under large deformation conditions because they need to be refined relative to the ideas explored in Chapter 2. The second and third explorations consider nonlinear material (constitutive) behavior in the form of elastic-plastic and rubber elasticity, respectively. The presence of a nonlinearity can affect the fundamental behavior of phenomena; the fourth exploration shows the rich, complex behaviors of nonlinear vibrating systems. Within a nonlinear context, applied loads affect the stresses, which in turn affect the stiffness and thus the deformations; this in turn affects the stresses, leading to a complicated connection between the applied loads and the responses. The fifth exploration uses vibrations under gravity to illustrate this point. The final exploration considers the contact that is due to impact of various shaped bodies and the resulting contact force histories.
- Type
- Chapter
- Information
- Guided Explorations of the Mechanics of Solids and Structures , pp. 226 - 296Publisher: Cambridge University PressPrint publication year: 2009