東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Foundations of geometric continuum m...

Segev, Reuven.

FindBook

Google Book

Amazon

博客來

Foundations of geometric continuum mechanics = geometry and duality in continuum mechanics /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Foundations of geometric continuum mechanics/ by Reuven Segev.
其他題名:	geometry and duality in continuum mechanics /
作者:	Segev, Reuven.
出版者:	Cham :Springer International Publishing : : 2023.,
面頁冊數:	xvi, 411 p. :ill., digital ;24 cm.
內容註:	1. Introduction -- 2. Prelude: Finite Dimensional Systems -- Part I Algebraic Theory: Uniform Fluxes -- 3. Simplices in Affine Spaces and Their Boundaries -- 4. Uniform Fluxes in Affine Spaces -- 5. From Uniform Fluxes to Exterior Algebra -- Part II: Smooth Theory -- 6. Smooth Analysis on Manifolds: A Short Review -- 7. Interlude: Smooth Distributions of Defects -- 8. Smooth Fluxes -- 9. Frames, Body Points, and Spacetime Structure -- 10. Stresses -- 11. Smooth Electromagnetism on Manifolds -- 12. The Elasticity Problem -- 13. Symmetry and Dynamics -- Part III Non-Smooth, Global Theories -- 14. Banachable Space of Sections of Vector Bundles over Compact Manifolds -- 15. Manifolds of Sections and Embeddings -- 16. The General Framework for Global Analytic Stress Theory -- 17. Dual Spaces Corresponding to Spaces of Differentiable Sections of a Vector Bundle: Localization of Sections and Functionals -- 18. de Rham Currents -- 19. Interlude: Singular Distributions of Defects in Bodies -- 20. Vector-Valued Currents -- 21. The Representation of Forces by Stresses and Hyperstresses -- 22. Simple Forces and Stresses -- 23. Whitney's Geometric Integration Theory and Non-Smooth Bodies -- 24. Optimal Fields and Load Capacity of Bodies -- Index.
Contained By:	Springer Nature eBook
標題:	Continuum mechanics - Mathematics. -
電子資源:	https://doi.org/10.1007/978-3-031-35655-1
ISBN:	9783031356551

Foundations of geometric continuum mechanics = geometry and duality in continuum mechanics /
Segev, Reuven.

Foundations of geometric continuum mechanicsgeometry and duality in continuum mechanics /[electronic resource] :by Reuven Segev. - Cham :Springer International Publishing :2023. - xvi, 411 p. :ill., digital ;24 cm. - Advances in continuum mechanics,v. 492524-4647 ;. - Advances in continuum mechanics ;v. 49..

1. Introduction -- 2. Prelude: Finite Dimensional Systems -- Part I Algebraic Theory: Uniform Fluxes -- 3. Simplices in Affine Spaces and Their Boundaries -- 4. Uniform Fluxes in Affine Spaces -- 5. From Uniform Fluxes to Exterior Algebra -- Part II: Smooth Theory -- 6. Smooth Analysis on Manifolds: A Short Review -- 7. Interlude: Smooth Distributions of Defects -- 8. Smooth Fluxes -- 9. Frames, Body Points, and Spacetime Structure -- 10. Stresses -- 11. Smooth Electromagnetism on Manifolds -- 12. The Elasticity Problem -- 13. Symmetry and Dynamics -- Part III Non-Smooth, Global Theories -- 14. Banachable Space of Sections of Vector Bundles over Compact Manifolds -- 15. Manifolds of Sections and Embeddings -- 16. The General Framework for Global Analytic Stress Theory -- 17. Dual Spaces Corresponding to Spaces of Differentiable Sections of a Vector Bundle: Localization of Sections and Functionals -- 18. de Rham Currents -- 19. Interlude: Singular Distributions of Defects in Bodies -- 20. Vector-Valued Currents -- 21. The Representation of Forces by Stresses and Hyperstresses -- 22. Simple Forces and Stresses -- 23. Whitney's Geometric Integration Theory and Non-Smooth Bodies -- 24. Optimal Fields and Load Capacity of Bodies -- Index.

This monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the theory by scrutinizing the relationship between the physical aspects and the mathematical notions used in its formulation. The theory of uniform fluxes in affine spaces is covered first, followed by the smooth theory on differentiable manifolds, and ends with the non-smooth global theory. Because continuum mechanics provides the theoretical foundations for disciplines like fluid dynamics and stress analysis, the author's extension of the theory will enable researchers to better describe the mechanics of modern materials and biological tissues. The global approach to continuum mechanics also enables the formulation and solutions of practical optimization problems. Foundations of Geometric Continuum Mechanics will be an invaluable resource for researchers in the area, particularly mathematicians, physicists, and engineers interested in the foundational notions of continuum mechanics.

ISBN: 9783031356551

Standard No.: 10.1007/978-3-031-35655-1doiSubjects--Topical Terms:

1015241
Continuum mechanics
--Mathematics.

LC Class. No.: QA808.2

Dewey Class. No.: 531.7

Foundations of geometric continuum mechanics = geometry and duality in continuum mechanics /
LDR:03369nmm a2200337 a 4500 001 2335605
003 DE-He213
005 20231031030330.0
006 m d
007 cr nn 008maaau
008 240402s2023 sz s 0 eng d
020 $a 9783031356551 $q (electronic bk.)
020 $a 9783031356544 $q (paper)
024 7 $a 10.1007/978-3-031-35655-1 $2 doi
035 $a 978-3-031-35655-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA808.2
072 7 $a PBMP $2 bicssc
072 7 $a MAT012030 $2 bisacsh
072 7 $a PBMP $2 thema
082 0 4 $a 531.7 $2 23
090 $a QA808.2 $b .S454 2023
100 1 $a Segev, Reuven. $3 3524846
245 1 0 $a Foundations of geometric continuum mechanics $h [electronic resource] : $b geometry and duality in continuum mechanics / $c by Reuven Segev.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2023.
300 $a xvi, 411 p. : $b ill., digital ; $c 24 cm.
490 1 $a Advances in continuum mechanics, $x 2524-4647 ; $v v. 49
505 0 $a 1. Introduction -- 2. Prelude: Finite Dimensional Systems -- Part I Algebraic Theory: Uniform Fluxes -- 3. Simplices in Affine Spaces and Their Boundaries -- 4. Uniform Fluxes in Affine Spaces -- 5. From Uniform Fluxes to Exterior Algebra -- Part II: Smooth Theory -- 6. Smooth Analysis on Manifolds: A Short Review -- 7. Interlude: Smooth Distributions of Defects -- 8. Smooth Fluxes -- 9. Frames, Body Points, and Spacetime Structure -- 10. Stresses -- 11. Smooth Electromagnetism on Manifolds -- 12. The Elasticity Problem -- 13. Symmetry and Dynamics -- Part III Non-Smooth, Global Theories -- 14. Banachable Space of Sections of Vector Bundles over Compact Manifolds -- 15. Manifolds of Sections and Embeddings -- 16. The General Framework for Global Analytic Stress Theory -- 17. Dual Spaces Corresponding to Spaces of Differentiable Sections of a Vector Bundle: Localization of Sections and Functionals -- 18. de Rham Currents -- 19. Interlude: Singular Distributions of Defects in Bodies -- 20. Vector-Valued Currents -- 21. The Representation of Forces by Stresses and Hyperstresses -- 22. Simple Forces and Stresses -- 23. Whitney's Geometric Integration Theory and Non-Smooth Bodies -- 24. Optimal Fields and Load Capacity of Bodies -- Index.
520 $a This monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the theory by scrutinizing the relationship between the physical aspects and the mathematical notions used in its formulation. The theory of uniform fluxes in affine spaces is covered first, followed by the smooth theory on differentiable manifolds, and ends with the non-smooth global theory. Because continuum mechanics provides the theoretical foundations for disciplines like fluid dynamics and stress analysis, the author's extension of the theory will enable researchers to better describe the mechanics of modern materials and biological tissues. The global approach to continuum mechanics also enables the formulation and solutions of practical optimization problems. Foundations of Geometric Continuum Mechanics will be an invaluable resource for researchers in the area, particularly mathematicians, physicists, and engineers interested in the foundational notions of continuum mechanics.
650 0 $a Continuum mechanics $x Mathematics. $3 1015241
650 1 4 $a Differential Geometry. $3 891003
650 2 4 $a Continuum Mechanics. $3 3538810
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Advances in continuum mechanics ; $v v. 49. $3 3668154
856 4 0 $u https://doi.org/10.1007/978-3-031-35655-1
950 $a Mathematics and Statistics (SpringerNature-11649)