國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Virtual work and shape change in sol...

Fremond, Michel.

Virtual work and shape change in solid mechanics

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Virtual work and shape change in solid mechanicsby Michel Fremond.
作者:	Fremond, Michel.
出版者:	Cham :Springer International Publishing :2017.
面頁冊數:	xvii, 371 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Virtual work.
電子資源:	http://dx.doi.org/10.1007/978-3-319-40682-4
ISBN:	9783319406824$q(electronic bk.)

Virtual work and shape change in solid mechanics
Fremond, Michel.

Virtual work and shape change in solid mechanics[electronic resource] /by Michel Fremond. - Cham :Springer International Publishing :2017. - xvii, 371 p. :ill., digital ;24 cm. - Springer series in solid and structural mechanics,v.72195-3511 ;. - Springer series in solid and structural mechanics ;v.2..

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 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 on virtual velocities, which are velocities we may think of. The virtual work of the internal forces accounts for the changes in shape. Engineering provides innumerable examples of shape changes, i.e., deformations, and of velocities of deformation. This book presents examples of usual and unusual shape changes, providing with the Principle of Virtual Work various and sometimes new equations of motion for smooth and non-smooth (i.e., with collisions) motions: 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, beams with third gradient theory, collisions, and fracturing of solids. The final example of shape change focuses on the motion of solids with large deformations. The stretch matrix and the rotation matrix of the polar decomposition are chosen to describe the shape change. Observation shows that a third gradient theory is needed to sustain the usual external loads. The new equations of motion are complemented with constitutive laws. Assuming a viscoelastic behavior, a mathematically coherent new predictive theory of motion is derived. The results are extended to motion with smooth and non-smooth self-contact, collision with an obstacle, incompressibility, and plasticity. Extreme behaviors are sufficiently numerous to consider the parti pris that a material may flatten into a surface (e.g., flattening of a structure by a power hammer) or a curve (e.g., transformation of an ingot into a wire in an extruder) Flattening is an example of the importance of the spatial variation of the rotation matrix when investigating the motion of a solid.

ISBN: 9783319406824$q(electronic bk.)

Standard No.: 10.1007/978-3-319-40682-4doiSubjects--Topical Terms:

745908
Virtual work.

LC Class. No.: QA831

Dewey Class. No.: 531.23

Virtual work and shape change in solid mechanics
LDR:04527nmm a2200337 a 4500 001 504912
003 DE-He213
005 20160924090847.0
006 m d
007 cr nn 008maaau
008 171030s2017 gw s 0 eng d
020 $a 9783319406824$q(electronic bk.)
020 $a 9783319406817$q(paper)
024 7 $a 10.1007/978-3-319-40682-4 $2 doi
035 $a 978-3-319-40682-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA831
072 7 $a TG $2 bicssc
072 7 $a TEC009070 $2 bisacsh
072 7 $a TEC021000 $2 bisacsh
082 0 4 $a 531.23 $2 23
090 $a QA831 $b .F872 2017
100 1 $a Fremond, Michel. $3 256361
245 1 0 $a Virtual work and shape change in solid mechanics $h [electronic resource] / $c by Michel Fremond.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2017.
300 $a xvii, 371 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer series in solid and structural mechanics, $x 2195-3511 ; $v v.7
505 0 $a 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.
520 $a 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 on virtual velocities, which are velocities we may think of. The virtual work of the internal forces accounts for the changes in shape. Engineering provides innumerable examples of shape changes, i.e., deformations, and of velocities of deformation. This book presents examples of usual and unusual shape changes, providing with the Principle of Virtual Work various and sometimes new equations of motion for smooth and non-smooth (i.e., with collisions) motions: 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, beams with third gradient theory, collisions, and fracturing of solids. The final example of shape change focuses on the motion of solids with large deformations. The stretch matrix and the rotation matrix of the polar decomposition are chosen to describe the shape change. Observation shows that a third gradient theory is needed to sustain the usual external loads. The new equations of motion are complemented with constitutive laws. Assuming a viscoelastic behavior, a mathematically coherent new predictive theory of motion is derived. The results are extended to motion with smooth and non-smooth self-contact, collision with an obstacle, incompressibility, and plasticity. Extreme behaviors are sufficiently numerous to consider the parti pris that a material may flatten into a surface (e.g., flattening of a structure by a power hammer) or a curve (e.g., transformation of an ingot into a wire in an extruder) Flattening is an example of the importance of the spatial variation of the rotation matrix when investigating the motion of a solid.
650 0 $a Virtual work. $3 745908
650 0 $a Mechanics. $3 200022
650 0 $a Motion. $3 191673
650 1 4 $a Engineering. $3 210888
650 2 4 $a Continuum Mechanics and Mechanics of Materials. $3 273691
650 2 4 $a Classical Mechanics. $3 769955
650 2 4 $a Structural Mechanics. $3 274624
650 2 4 $a Engineering Design. $3 273752
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Springer series in solid and structural mechanics ; $v v.2. $3 675300
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-40682-4
950 $a Engineering (Springer-11647)