Virtual Work and Shape Change in Solid Mechanics

• Main Author: Frémond, Michel (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Series: Springer Series in Solid and Structural Mechanics, 7
• Subjects: Engineering.; Continuum mechanics.; Structural mechanics.; Engineering design.; Continuum Mechanics and Mechanics of Materials.; Classical Mechanics.; Structural Mechanics.; Engineering Design.

This book provides novel insights into two basic subjects in solid mechanics: virtual work and shape change. When we move a solid, the work we expend in moving it is used to modify both its shape and its velocity. This observation leads to the Principle of Virtual Work. Virtual work depends linearly...

Table of Contents:

• Introduction
• The System
• The Principle of Virtual Work
• What We See: the Velocities
• The Actions which are Applied to the System: the Work of the External Forces
• What We See: the Velocities of Deformation
• The Work to Change the Shape of the System
• The Work to Change the Velocities of the System
• The Principle of Virtual Work and the Equations of Motion
• Summary of the Abstract Setting to get the Equations of Motion
• Two Points on a Line
• Three Disks in a Plane
• Three Balls on a Plane
• A Deformable Solid
• Two Deformable Solids
• At a Distance Interactions: Continuum Reinforced by Fibers
• At a Distance Interactions: Continuum Reinforced by Beams
• At a Distance Interactions: Continuum Reinforced by Plates
• Damage of a Connection
• Damage of a Rod Glued on a Rigid Surface
• Damage of a Beam Glued on a Rigid Surface
• A Damageable Solid
• Two Damageable Solids
• Porous Solids
• Discontinuum Mechanics: Collisions and Fractures in Solids
• There is neither Flattening nor Self-contact or Contact with an Obstacle. Smooth Evolution
• There is neither Flattening nor Self-contact or Contact with an Obstacle. Non Smooth Evolution
• There is no Flattening. There is Self-contact and Contact with an Obstacle. Smooth Evolution
• There is no Flattening. There is Self-contact and Contact with an Obstacle. Non Smooth Evolution. Flattening. Smooth and Non Smooth Evolutions
• Conclusions.