Virtual Work and Shape Change in Solid Mechanics

Michel Frémond (Autor)

Buch | Hardcover

XVII, 371 Seiten

2016 | 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-40681-7 (ISBN)

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This book provides novel insights into two fundamental subjects in solid mechanics: virtual work and shape change. The author explains how the principle of virtual work represents a tool for analysis of the mechanical effects of the evolution of the shape of a system, how it can be applied to observations and experiments, and how it may be adapted to produce predictive theories of numerous phenomena. The book is divided into three parts. The first relates the principle of virtual work to what we observe with our eyes, the second demonstrates its flexibility on the basis of many examples, and the third applies the principle to predict the motion of solids with large deformations. Examples of both usual and unusual shape changes are presented, and equations of motion, some of which are entirely new, are derived for smooth and non-smooth motions associated with, for instance, systems of disks, systems of balls, classical and non-classical small deformation theories, systems involving volume and surface damage, systems with interactions at a distance (e.g., solids reinforced by fibers), systems involving porosity, collisions, and fracturing of solids.

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.

"This is a remarkable textbook on the mechanics of deformable solids pertaining to thermal intervention. ... The present work stands out for its phenomenological access to the subject in conjunction with the pertaining mathematical tools, the inductive art of tackling and exposing the arguments and for the elaboration of single tasks of general interest as well as of engineering relevance. The reader will find the text inspiring ... ." (Ioannis Doltsinis, Mathematical Reviews, March, 2019)

“This is a remarkable textbook on the mechanics of deformable solids pertaining to thermal intervention. … The present work stands out for its phenomenological access to the subject in conjunction with the pertaining mathematical tools, the inductive art of tackling and exposing the arguments and for the elaboration of single tasks of general interest as well as of engineering relevance. The reader will find the text inspiring … .” (Ioannis Doltsinis, Mathematical Reviews, March, 2019)

Erscheinungsdatum	14.10.2016
Reihe/Serie	Springer Series in Solid and Structural Mechanics
Zusatzinfo	XVII, 371 p. 17 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
	Technik ► Maschinenbau
Schlagworte	Beam Glued • Collision Engineering • Continuum Mechanics • Continuum Mechanics and Mechanics of Materials • Damageable Solids • Deformable Solids • Discontinuum Mechanics • Engineering • Engineering design • Equations of motion • Lagrangian mechanics • large deformations • Mechanics • Porous Solids • Rod Glued • solid mechanics • Structural Mechanics • Surface Damage
ISBN-10	3-319-40681-7 / 3319406817
ISBN-13	978-3-319-40681-7 / 9783319406817
Zustand	Neuware