Holdings: Analytical methods in anisotropic elasticity

Analytical methods in anisotropic elasticity: with symbolic computational tools

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Bibliographic Details
Main Authors:	Rand, Omri (Author), Rovenski, Vladimir 1953- (Author)
Format:	Book
Language:	English
Published:	Boston [u.a.] Birkhäuser 2005
Subjects:	Elasticidade Mathematisches Modell Elasticity Anisotropy Anisotropy > Mathematical models Inhomogeneous materials Inhomogener Festkörper Elastizitätstheorie Anisotroper Stoff Elastizität Anisotropie Mathematische Methode
Online Access:	Inhaltsverzeichnis
Item Description:	Includes bibliographical references (p. [429]-446) and index
Physical Description:	xviii, 451 p. ill. 1 CD-ROM (12 cm)
ISBN:	0817642722

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adam_text	x Preface General Style Clarification Notes: Contents Preface vii 1 Fundamentals of Anisotropie Elasticity and Analytical Methodologies 1 1.1 Deformation Measures and Strain ........................ 1 1.1.1 Displacements in Cartesian Coordinates ................. 2 1.1.2 Strain in Cartesian Coordinates ..................... 3 1.1.3 Strain in Orthogonal Curvilinear Coordinates .............. 6 1.1.4 Physical Interpretation of Strain Components .............. 7 1.2 Displacement by Strain Integration ........................ 9 1.2.1 Compatibility Equations ......................... 9 1.2.2 Continuous Approach .......................... 11 1.2.3 Level Approach .............................. 12 1.3 Stress Measures .................................. 14 1.3.1 Definition of Stress ............................ 15 1.3.2 Equilibrium Equations .......................... 17 1.3.3 Stress Tensor Transformation due to Coordinate System Rotation ... 19 1.3.4 Strain Tensor Transformation due to Coordinate System Rotation ... 28 1.4 Energy Theorems ................................. 28 1.4.1 The Theorem of Minimum Potential Energy ............... 28 1.4.2 The Theorem of Minimum Complementary Energy ........... 29 1.4.3 Theorem of Reciprocity ......................... 30 1.4.4 Castigliano s Theorems .......................... 31 1.5 Euler s Equations ................................. 31 1.5.1 Functional Based on Functions of One Variable ............. 32 1.5.2 Variational Problems with Constraints .................. 34 1.5.3 Functional Based on Function of Several Variables ........... 36 1.6 Analytical Methodologies ............................. 38 1.6.1 The Fundamental Problems of Elasticity ................. 39 1.6.2 Fundamental Ingredients of Analytical Solutions ............ 39 xii Contents 1.6.3 St. Venanťs Semi-Inverse Method of Solution .............. 41 1.6.4 Variational Analysis of Energy Based Functionals ............41 1.6.5 Typical Solution Trails .......................... 1.7 Appendix: Coordinate Systems .......................... 1.7.1 Transformation Between Coordinate Systems .............. 47 1.7.2 Curvilinear Coordinate Systems .....................49 2 Anisotropie Materials 2.1 The Generalized Hook s Law ........................... 54 2.2 General Anisotropie Materials .......................... 2.3 Monoclinic Materials ............................... 2.4 Orthotropic Materials ............................... 56 2.5 Tetragonal Materials ............................... 2.6 Transversely Isotropie (Hexagonal) Materials .................. 59 2.7 Cubic Materials .................................. 61 2.8 Isotropie Materials ................................ 61 2.9 Engineering Notation of Composites ....................... 62 2.10 Positive-Definite Stress-Strain Law ........................ 63 2.11 Typical Material Characteristics ......................... 65 2.12 Compliance Matrix Transformation ....................... 66 2.13 Stiffness Matrix Transformation ......................... 69 2.14 Compliance and Stiffness Matrix Transformation to Curvilinear Coordinates . . 70 2.15 Principal Directions of Anisotropy ........................ 70 2.16 Planes of Elastic Symmetry ............................ 74 2.17 Non-Cartesian Anisotropy ............................ 76 3 Plane Deformation Analysis 79 3.1 Plane Domain Definition and Contour Parametrization .............80 3.1.1 Plane Domain Topology ......................... 80 3.1.2 Contour Parametrization and Directional Cosines ............ 81 3.1.3 Parametrization by Conformai Mapping .................83 3.1.4 Parametrization by Piecewise Linear Functions ............. 85 3.2 Plane-Strain and Plane-Stress ...........................86 3.2.1 Plane-Strain ................................87 3.2.2 Plane-Stress ................................90 3.2.3 Illustrative Examples of Prescribed Airy s Function ...........92 3.2.4 The Influence of Body Forces ......................93 3.2.5 Boundary and Single-Value Conditions .................94 3.2.6 Plane Stress/Strain Analysis in a Non-Homogeneous Domain .....100 3.3 Plane-Shear ................ 200 3.3.1 Analysis by Stress Function .......................101 3.3.2 Analysis by Warping Function ......................104 3.3.3 Generic Dirichlet/Neumann BVPs on a Homogeneous Domain .....105 3.3.4 Simplification of Generalized Laplace s and Boundary Operators. ... 107 3.3.5 Plane-Shear Analysis of Non-Homogeneous Domain 108 3.4 Coupled-Plane BVP ............... ...... .qş 3.5 Analysis of Plates .............................. ]0 3.5.1 The Classical Laminated Plate Theory .......... ....... HO 3.5.2 Bending of Anisotropie Plates . ............. 117 3.6 Appendix: Differential Operators . . ................... j 20 Contents xiii 3.6.1 Generalized Laplace s Operators.....................120 3.6.2 Biharmonic Operators ..........................121 3.6.3 Third-Order and Sixth-Order Differential Operators ...........123 3.6.4 Generalized Normal Derivative Operators ................123 3.6.5 Ellipticity of the Differential Operators .................124 4 Solution Methodologies 125 4.1 Unified Formulation of Two-Dimensional В VPs .................126 4.2 Particular Polynomial Solutions .........................128 4.2.1 The Biharmonic BVP ...........................129 4.2.2 The Dirichlet/Neumann BVPs ......................130 4.2.3 The Coupled-Plane BVP .........................131 4.3 Homogeneous BVPs Polynomial Solutions ...................132 4.3.1 Prescribing the Boundary Functions ...................133 4.3.2 Prescribing the Field Equations .....................134 4.3.3 Exact and Conditional Polynomial Solutions ..............135 4.3.4 Approximate Polynomial Solutions ...................141 4.4 The Method of Complex Potentials ........................149 4.4.1 n-Coupled Dirichlet BVP .........................150 4.4.2 Application of Complex Potentials to the Dirichlet BVP ........152 4.4.3 Application of Complex Potentials to the Biharmonic В VP....... 157 4.4.4 Application of Complex Potentials to a Coupled-Plane В VP ......159 4.4.5 Fourier Series Based Solution of a Coupled-Plane BVP .........161 4.5 Three-Dimensional Prescribed Solutions .....................169 4.5.1 Equilibrium Equations in Terms of Displacements ...........169 4.5.2 Fourier Series Based Solutions in an Isotropie Parallelepiped ......171 4.5.3 Direct Solution in Terms of Displacements for Three-Dimensional Bod¬ ies .....................................173 4.6 Closed Form Solutions in Circular and Annular Isotropie Domains .......177 4.6.1 Harmonic and Biharmonic Functions in Polar Coordinates .......177 4.6.2 The Dirichlet BVP in a Circle ......................178 4.6.3 The Neumann BVP in a Circle ......................178 4.6.4 The Dirichlet BVP in a Circular Ring ..................179 4.6.5 The Neumann BVP in a Circular Ring ..................179 4.6.6 The Biharmonic BVP in a Circle .....................180 4.6.7 The Biharmonic BVP in a Circular Ring .................181 5 Foundations of Anisotropie Beam Analysis 183 5.1 Notation and Definitions .............................184 5.1.1 Geometrical Degrees of Freedom ....................184 5.1.2 Tip and Distributed Loading .......................187 5.1.3 Boundary Conditions ...........................188 5.2 Elastic Coupling in General Anisotropie Beams .................192 5.2.1 Coupling at the Material Level ......................192 5.2.2 Coupling at the Structural Level .....................193 5.3 Simplified Beam Models .............................198 5.3.1 Beam-Plate Models ............................199 5.3.2 Analysis by Cross-Section Stiffness Matrix ...............205 5.3.3 The Influence of the In-Plane Deformation ...............207 5.3.4 Strength-of-Materials Isotropie Beam Analysis ............211 xiv Contents ......212 5.4 Literature ............................. 6 Beams of General Anisotropy ^15 6.1 Stress and Strain ................................. 6.1.1 Stress Resultants ............................. 21/ 6.1.2 Compatibility Conditions ......................... 219 6.1.3 Axial Strain Integration ..........................220 6 1.4 Stress Functions and the Coupled-Plane В VP.............. 221 994. 6.2 Displacements and Rotations ........................... ZZ4 6.2.1 Continuous Expressions .........................225 6.2.2 Level Expressions ............................226 6.2.3 Axis Deformation .............................227 6.2.4 Root Warping Integration .........................229 6.3 Recurrence Solution Scheme ...........................230 6.3.1 Solution Steps ..............................230 6.3.2 Expressions for the High Solution Levels ................232 6.4 Applications ....................................234 6.4.1 Tip Moments and Axial Force ......................234 6.4.2 Tip Bending Forces ............................238 6.4.3 Axially Uniform Distributed Loading ..................242 6.4.4 Additional Examples ...........................245 6.5 Appendix: Integral Identities ...........................246 7 Homogeneous, Uncoupled Monoclinic Beams 249 7.1 Background ....................................250 7.2 Tip Loads .....................................250 7.2.1 Torsionai Moment ............................251 7.2.2 Tip Bending Forces ............................259 7.2.3 Summarizing the Tip Loading Effects ..................263 7.3 Axially Distributed Loads .............................265 7.3.1 Solution Methodology ..........................265 7.3.2 Solution Hypothesis ...........................266 7.3.3 The Harmonic Stress Functions .....................267 7.3.4 The Biharmonic and Longitudinal Stress Functions ...........268 7.3.5 Verification of Solution Hypothesis ...................268 7.3.6 Solution Procedure ............................269 7.3.7 Detailed Solution Expressions ......................270 7.4 Applications ......................... 275 7.5 Beams of Cylindrical Anisotropy .........................281 7.5.1 Geometrical Aspects ........................ 283 7.5.2 Torsion of a Beam of Cylindrical Anisotropy ..............284 7.5.3 Extension and Bending of a Beam of Cylindrical Anisotropy ......285 8 Non-Homogeneous Plane and Beam Analysis 297 8.1 Plane (Two-Dimensional) BVPs ............... 298 8.1.1 The Neumann BVP ....... .......... 20й 8.1.2 TheDirichletBVP ............................299 8.1.3 The Biharmonic BVP ....... -,,™ 8.1.4 Coupled-Plane BVP . . . . . . . . ..[]...............302 8.1.5 n-CoupledDirichletBVP ......................... 302 Contents xv 8.2 Uncoupled Beams Under Tip Loads .......................304 8.2.1 General Aspects and Interlaminar Conditions ..............304 8.2.2 The Auxiliary Problems of Plane Deformation .............305 8.2.3 Tip Axial Force ..............................308 8.2.4 Tip Bending Moments ..........................310 8.2.5 Tip Bending Forces ............................311 8.2.6 Torsionai Moment ............................314 8.2.7 Summarizing the Tip Loading Effects ..................319 8.2.8 Fulfilling the Tip Conditions .......................321 8.2.9 Principal Axis of Extension and Principal Planes of Bending ......322 8.2.10 Shear Center ...............................323 8.2.11 Solution Procedure ............................323 8.3 Uncoupled Beam Under Axially Distributed Loads ...............324 8.3.1 The Solution Hypothesis .........................324 8.3.2 The Strain Components .........................325 8.3.3 Displacements and Rotations .......................326 8.3.4 The Biharmonic Stress Functions ....................326 8.3.5 The Harmonic and Longitudinal Stress Functions ............326 8.3.6 The Auxiliary Functions .........................327 8.3.7 The Loading Constants ..........................327 8.3.8 Verification of Solution Hypothesis ...................328 8.3.9 Solution Procedure ............................329 8.4 Applications ....................................329 9 Solid Coupled Monoclinic Beams 335 9.1 Background ....................................335 9.1.1 Cross-Section Warping ..........................335 9.1.2 Approximate Analytical Solutions ....................336 9.1.3 Coupling Effects in Symmetric and Antisymmetric Solid Beams . . . .336 9.2 An Approximate Analytical Model ........................338 9.2.1 Reduced Stress-Strain Relationships ...................339 9.2.2 Equilibrium Equations ..........................341 9.2.3 Analytical Solutions ...........................344 9.3 An Exact Multilevel Approach ..........................353 9.3.1 Displacements and Stress-Strain Relationships .............354 9.3.2 Definition of Solution Levels .......................355 9.3.3 Examples .................................361 10 Thin-Walled Coupled Monoclinic Beams 369 10.1 Background ....................................369 10.2 Multiply Connected Domain ...........................370 10.2.1 The Elastic Coupling Effects .......................370 10.2.2 An Approximate Analytical Model ...................371 10.3 Simply Connected Domain ............................380 10.3.1 The Transverse and Axial Loads Effect .................381 10.3.2 The Torsionai Moment Effect ......................389 11 Program Descriptions 401 P.I Programs for Chapter 1..............................402 P. 1.1 Strain Tensor in Space ..........................402 xvi Contents 402 P. 1.2 Strain Tensor in the Plane ........................ P.I. 3 Compatibility Equations in Space .................... P. 1.4 Compatibility Equations in the Plane ..................4Ü P. 1.5 Displacements by Strain Integration in Space ..............403 P. 1.6 Displacements by Strain Integration in the Plane ............ 403 P.I. 7 Equilibrium Equations in Space ..................... 403 P. 1.8 Equilibrium Equations in the Plane ................... 404 P. 1.9 Stress/Strain Tensor Transformation due to Coordinate System Rotation 404 P.I. 10 Application of Stress/Strain Tensor Transformation ...........404 P. 1.11 Stress/Strain Tensor Transformations from Cartesian to Curvilinear Coordinates ................................ 404 P.I. 12 Stress/Strain Visualization ........................405 P. 1.13 Euler s Equation for a Functional Based on a Function of One or Two Variables .................................405 P.I. 14 Elastica ..................................405 P.I. 15 Rotation Matrix in Space .........................405 P.I. 16 Curvilinear Coordinates in Space ....................405 P.I. 17 Curvilinear Coordinates in the Plane ...................406 P.2 Programs for Chapter 2..............................406 P.2. 1 Compliance and Stiffness Matrices Presentation .............406 P.2.2 Material Data by Compliance Matrix ..................406 P.2.3 Material Data by Stiffness Matrix ....................407 P.2. 4 Compliance Matrix Positiveness .....................407 P.2. 5 Generic Compliance Matrix Transformation due to Coordinate System Rotation ..................................407 P.2. 6 Application of the Compliance Matrix Transformation .........407 P.2. 7 Compliance Matrix Transformation due to Coordinate System Rotation 407 P.2. 8 Visualization of a Compliance Matrix Transformation .........408 P.2.9 Generic Stiffness Matrix Transformation due to Coordinate System Rotation ..................................408 P.2. 10 Stiffness Matrix Transformation due to Coordinate System Rotation . .408 P.2. 11 Application of the Stiffness Matrix Transformation ...........408 P.2. 12 Compliance Matrix Transformation from Cartesian to Curvilinear Co¬ ordinates .................................408 P.2. 13 Principal Directions of Anisotropy ....................409 P.3 Programs for Chapter 3..............................409 P.3.1 Illustrative Parametrizations .......................409 P.3.2 Regular Polygon Parametrization Using the Schwarz-Christoffel Integral 409 P.3.3 Generic Polygon Parametrization Using the Schwarz-Christoffel Integral 410 P.3. 4 Fourier Series Parametrization of a Polygon ...............410 P.3.5 Prescribed Polynomial Solution of the Biharmonic Equation ......410 P.3.6 Application of Prescribed Polynomial Solution of the Biharmonic Equ¬ ation ................................... 411 P.3. 7 Prescribed Polynomial Solution of Laplace s Equation .........411 P.3.8 Application of Prescribed Polynomial Solution of Laplace s Equation і 411 P.3.9 Affine Transformation ................ 412 P.3.10 Prescribed Polynomial Solution of Coupled-Plane Equations ......412 P.3. 11 Application of Prescribed Polynomial Solution of Coupled-Plane Equa¬ tions ...................... ľ H P.3. 12 Ellipticity of the Differential Operators .................412 Contents xvii P.4 Programs for Chapter 4..............................413 P.4. 1 Particular Polynomial Solution of the Biharmonic Equation in an Ellipse ..................................413 P.4. 2 Particular Polynomial Solution of the Biharmonic Equation ......414 P.4.3 Particular Polynomial Solution of Poisson s Equation ..........414 P.4.4 Particular Polynomial Solution of Poisson s Equation in an Ellipse . . . 414 P.4.5 Particular Polynomial Solution of Coupled-Plane Equations ......415 P.4. 6 Particular Polynomial Solution of Coupled-Plane Equations in an Ellipse ..................................415 P.4. 7 Prescribed Polynomial Boundary Functions ...............415 P.4. 8 Exact/Conditional Polynomial Solution of Dirichlet/Neumann Homo¬ geneous BVPs ..............................416 P.4.9 Symbolic Verification of the Neumann BVP Solution ..........416 P.4. 10 Exact/Conditional Polynomial Solution of Homogeneous Biharmonic BVPs ...................................416 P.4. 11 Symbolic Verification of the Biharmonic В VP Solution .........417 P.4. 12 Exact/Conditional Polynomial Solution of Homogeneous Coupled-Plane BVPs ...................................417 P.4. 13 Approximate Polynomial Solution of Homogeneous Dirichlet/Neumann BVPs ...................................417 P.4. 14 Approximate Polynomial Solution of Homogeneous Biharmonic BVPs 418 P.4. 15 Approximate Polynomial Solution of Homogeneous Coupled-Plane BVPs ...................................419 P.4.16 Rotating Plate: Application of the Biharmonic BVP Solution ......419 P.4. 17 Bending of Thin Plates: Application of the Biharmonic BVP Solution . 419 P.4. 18 Approximate Polynomial Solution of Homogeneous «-Coupled Dirich¬ let BVPs .................................420 P.4. 19 Fourier Series Solution of Homogeneous Dirichlet BVPs in a Rectangle 420 P.4. 20 Fourier Series Solution of Homogeneous Coupled-Plane BVPs in a Rectangle .................................421 P.4. 21 Equilibrium Equations in Terms of Displacements ...........421 P.4. 22 Prescribed Solutions in an Isotropie Parallelepiped ...........421 P.4.23 Fourier Series Solution of the Dirichlet/Neumann BVPs in an Isotropie Circle ...................................422 P.4.24 Fourier Series Solution of the Dirichlet/Neumann BVPs in an Isotropie Circular Ring ...............................422 P.4. 25 Fourier Series Solution of the Biharmonic BVP in an Isotropie Circle . 422 P.4.26 Fourier Series Solution of the Biharmonic BVP in an Isotropie Circular Ring ....................................423 P.5 Programs for Chapter 5..............................423 P.5.1 Elementary Strength-of-Materials Isotropie Beam Analysis .....423 P.6 Programs for Chapter 6..............................423 P.6.1 An Anisotropie Beam of Elliptical Cross-Section ............423 P.7 Programs for Chapter 7..............................424 P.7.1 Tip Loads Effect in a Monoclinic Beam .................424 P.7. 2 Auxiliary Harmonic Functions for Elliptical Monoclinic Cross-Sections 424 P.7.3 A Monoclinic Beam Under Axially Non-Uniform Distributed Loads (I) 424 P.7.4 A Monoclinic Beam Under Axially Non-Uniform Distributed Loads (II) 425 P.7.5 Solution for an Elliptical Monoclinic Beam Under Constant Longitu¬ dinal Loading ...............................425 xviii Contents P.7.6 Solution Implementation for an Elliptical Monoclinic Beam Under Con¬ stant Longitudinal Loading ........................425 P.8 Programs for Chapter 8..............................425 P.8.1 Auxiliary Harmonic Functions in a Non-Homogeneous Rectangle . . .425 P.8.2 Plane Deformation and the Auxiliary Biharmonic Problems ......426 P.8.3 Fourier Series Based Torsion Function in a Non-Homogeneous Or- thotropic Rectangle ............................426 P.8.4 A Non-Homogeneous Monoclinic Beam Under Tip Loads .......426 P.8. 5 A Non-Homogeneous Beam of Rectangular Cross-Section Under Tip Loads ...................................427 P.8.6 A Monoclinic Non-Homogeneous Beam Under Axially Distributed Non-Uniform Loads (I) ..........................427 P.8.7 A Monoclinic Non-Homogeneous Beam Under Axially Distributed Non-Uniform Loads (II) .........................427 References 429 Index 447
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author	Rand, Omri Rovenski, Vladimir 1953-
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id	DE-604.BV019833202
illustrated	Illustrated
indexdate	2024-07-09T20:07:10Z
institution	BVB
isbn	0817642722
language	English
lccn	2004054558
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-013158248
oclc_num	55990361
open_access_boolean
owner	DE-703 DE-706 DE-Aug4
owner_facet	DE-703 DE-706 DE-Aug4
physical	xviii, 451 p. ill. 1 CD-ROM (12 cm)
publishDate	2005
publishDateSearch	2005
publishDateSort	2005
publisher	Birkhäuser
record_format	marc
spelling	Rand, Omri Verfasser aut Analytical methods in anisotropic elasticity with symbolic computational tools Omri Rand, Vladimir Rovenski Boston [u.a.] Birkhäuser 2005 xviii, 451 p. ill. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. [429]-446) and index Elasticidade larpcal Mathematisches Modell Elasticity Anisotropy Anisotropy Mathematical models Inhomogeneous materials Inhomogener Festkörper (DE-588)4225741-4 gnd rswk-swf Elastizitätstheorie (DE-588)4123124-7 gnd rswk-swf Anisotroper Stoff (DE-588)4280461-9 gnd rswk-swf Elastizität (DE-588)4014159-7 gnd rswk-swf Anisotropie (DE-588)4002073-3 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Elastizität (DE-588)4014159-7 s Anisotropie (DE-588)4002073-3 s DE-604 Anisotroper Stoff (DE-588)4280461-9 s Inhomogener Festkörper (DE-588)4225741-4 s Mathematische Methode (DE-588)4155620-3 s 1\p DE-604 Elastizitätstheorie (DE-588)4123124-7 s 2\p DE-604 Rovenski, Vladimir 1953- Verfasser (DE-588)12012985X aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013158248&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Rand, Omri Rovenski, Vladimir 1953- Analytical methods in anisotropic elasticity with symbolic computational tools Elasticidade larpcal Mathematisches Modell Elasticity Anisotropy Anisotropy Mathematical models Inhomogeneous materials Inhomogener Festkörper (DE-588)4225741-4 gnd Elastizitätstheorie (DE-588)4123124-7 gnd Anisotroper Stoff (DE-588)4280461-9 gnd Elastizität (DE-588)4014159-7 gnd Anisotropie (DE-588)4002073-3 gnd Mathematische Methode (DE-588)4155620-3 gnd
subject_GND	(DE-588)4225741-4 (DE-588)4123124-7 (DE-588)4280461-9 (DE-588)4014159-7 (DE-588)4002073-3 (DE-588)4155620-3
title	Analytical methods in anisotropic elasticity with symbolic computational tools
title_auth	Analytical methods in anisotropic elasticity with symbolic computational tools
title_exact_search	Analytical methods in anisotropic elasticity with symbolic computational tools
title_full	Analytical methods in anisotropic elasticity with symbolic computational tools Omri Rand, Vladimir Rovenski
title_fullStr	Analytical methods in anisotropic elasticity with symbolic computational tools Omri Rand, Vladimir Rovenski
title_full_unstemmed	Analytical methods in anisotropic elasticity with symbolic computational tools Omri Rand, Vladimir Rovenski
title_short	Analytical methods in anisotropic elasticity
title_sort	analytical methods in anisotropic elasticity with symbolic computational tools
title_sub	with symbolic computational tools
topic	Elasticidade larpcal Mathematisches Modell Elasticity Anisotropy Anisotropy Mathematical models Inhomogeneous materials Inhomogener Festkörper (DE-588)4225741-4 gnd Elastizitätstheorie (DE-588)4123124-7 gnd Anisotroper Stoff (DE-588)4280461-9 gnd Elastizität (DE-588)4014159-7 gnd Anisotropie (DE-588)4002073-3 gnd Mathematische Methode (DE-588)4155620-3 gnd
topic_facet	Elasticidade Mathematisches Modell Elasticity Anisotropy Anisotropy Mathematical models Inhomogeneous materials Inhomogener Festkörper Elastizitätstheorie Anisotroper Stoff Elastizität Anisotropie Mathematische Methode
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013158248&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT randomri analyticalmethodsinanisotropicelasticitywithsymboliccomputationaltools AT rovenskivladimir analyticalmethodsinanisotropicelasticitywithsymboliccomputationaltools

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