Skip to main content
SpringerLink
Log in

Solutions

  • Chapter
  • First Online:
Book cover Tensor Algebra and Tensor Analysis for Engineers

Part of the book series: Mathematical Engineering ((MATHENGIN))

  • 4951 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Başar Y, Krätzig WB (1985) Mechanik der Flächentragwerke. Vieweg Verlag, Braunschweig

    Google Scholar 

  2. Boehler JP (1977) Z Angew Math Mech 57:323–327

    Google Scholar 

  3. de Boer R (1982) Vektor- und Tensorrechnung für Ingenieure. Springer, Berlin/Heidelberg/ New York

    Google Scholar 

  4. Boulanger Ph, Hayes M (1993) Bivectors and waves in mechanics and optics. Chapman and Hall, London

    Google Scholar 

  5. Bronstein IN, Semendyayev KA, Musiol G, Muehlig H (2004) Handbook of mathematics. Springer, Berlin/Heidelberg/New York

    Google Scholar 

  6. Brousse P (1988) Optimization in mechanics: problems and methods. Elsevier, Amsterdam

    Google Scholar 

  7. Carlson DE, Hoger A (1986) J Elast 16:221–224

    Google Scholar 

  8. Chen Y, Wheeler L (1993) J Elast 32:175–182

    Google Scholar 

  9. Cheng H, Gupta KC (1989) J Appl Mech 56:139–145

    Google Scholar 

  10. Chrystal G (1980) Algebra. An elementary text-book. Part I. Chelsea, New York

    Google Scholar 

  11. Dui G, Chen Y-C (2004) J Elast 76:107–112

    Google Scholar 

  12. Friedberg SH, Insel AJ, Spence LE (2003) Linear algebra. Pearson, Upper Saddle River

    Google Scholar 

  13. Gantmacher FR (1959) The theory of matrices. Chelsea, New York

    Google Scholar 

  14. Guo ZH (1984) J Elast 14:263–267

    Google Scholar 

  15. Halmos PR (1958) Finite-dimensional vector spaces. Van Nostrand, New York

    Google Scholar 

  16. Hill R (1968) J Mech Phys Solids 16:229–242

    Google Scholar 

  17. Hill R (1978) Adv Appl Mech 18:1–75

    Google Scholar 

  18. Hoger A, Carlson DE (1984) J Elast 14:329–336

    Google Scholar 

  19. Itskov M (2002) Z Angew Math Mech 82:535–544

    Google Scholar 

  20. Itskov M (2003) Comput Meth Appl Mech Engrg 192:3985–3999

    Google Scholar 

  21. Itskov M (2003) Proc R Soc Lond A 459:1449–1457

    Google Scholar 

  22. Itskov M (2004) Mech Res Commun 31:507–517

    Google Scholar 

  23. Itskov M, Aksel N (2002) Int J Solids Struct 39:5963–5978

    Google Scholar 

  24. Kaplan W (2003) Advanced calculus. Addison Wesley, Boston

    Google Scholar 

  25. Kato T (1966) Perturbation theory for linear operators. Springer, New York

    Google Scholar 

  26. Kreyszig E (1991) Differential geometry. Dover, New York

    Google Scholar 

  27. Lax PD (1997) Linear algebra. Wiley, New York

    Google Scholar 

  28. Lew JS (1966) Z Angew Math Phys 17:650–653

    Google Scholar 

  29. Lubliner J (1990) Plasticity theory. Macmillan, New York

    Google Scholar 

  30. Ogden RW (1984) Non-Linear elastic deformations. Ellis Horwood, Chichester

    Google Scholar 

  31. Ortiz M, Radovitzky RA, Repetto EA (2001) Int J Numer Methods Eng 52:1431–1441

    Google Scholar 

  32. Papadopoulos P, Lu J (2001) Comput Methods Appl Mech Eng 190:4889–4910

    Google Scholar 

  33. Pennisi S, Trovato M (1987) Int J Eng Sci 25:1059–1065

    Google Scholar 

  34. Rinehart RF (1955) Am Math Mon 62:395–414

    Google Scholar 

  35. Rivlin RS (1955) J Ration Mech Anal 4:681–702

    Google Scholar 

  36. Rivlin RS, Ericksen JL (1955) J Ration Mech Anal 4:323–425

    Google Scholar 

  37. Rivlin RS, Smith GF (1975) Rendiconti di Matematica Serie VI 8:345–353

    Google Scholar 

  38. Rosati L (1999) J Elast 56:213–230

    Google Scholar 

  39. Sansour C, Kollmann FG (1998) Comput Mech 21:512–525

    Google Scholar 

  40. Seth BR (1964) Generalized strain measures with applications to physical problems. In: Reiner M, Abir D (eds) Second-order effects in elasticity, plasticity and fluid dynamics. Academic, Jerusalem

    Google Scholar 

  41. Smith GF (1971) Int J Eng Sci 9:899–916

    Google Scholar 

  42. Sokolnikoff IS (1964) Tensor analysis. Theory and applications to geometry and mechanics of continua. Wiley, New York

    Google Scholar 

  43. Spencer AJM (1984) Constitutive theory for strongly anisotropic solids. In: Spencer AJM (ed) Continuum theory of the mechanics of fibre-reinforced composites. Springer, Wien/New York

    Google Scholar 

  44. Steigmann DJ (2002) Math Mech Solids 7:393–404

    Google Scholar 

  45. Ting TCT (1985) J Elast 15:319–323

    Google Scholar 

  46. Truesdell C, Noll W (1965) The nonlinear field theories of mechanics. In: Flügge S (ed) Handbuch der Physik, vol III/3. Springer, Berlin

    Google Scholar 

  47. Wheeler L (1990) J Elast 24:129–133

    Google Scholar 

  48. Xiao H (1995) Int J Solids Struct 32:3327–3340

    Google Scholar 

  49. Xiao H, Bruhns OT, Meyers ATM (1998) J Elast 52:1–41

    Google Scholar 

  50. Zhang JM, Rychlewski J (1990) Arch Mech 42:267–277

    Google Scholar 

Further Reading

  1. Abraham R, Marsden JE, Ratiu T (1988) Manifolds, tensor analysis and applications. Springer, Berlin/Heidelberg/New York

    Google Scholar 

  2. Akivis MA, Goldberg VV (2003) Tensor calculus with applications. World Scientific, Singapore

    Google Scholar 

  3. Anton H, Rorres C (2000) Elementary linear algebra: application version. Wiley, New York

    Google Scholar 

  4. Başar Y, Weichert D (2000) Nonlinear continuum mechanics of solids. Fundamental mathematical and physical concepts. Springer, Berlin/Heidelberg/New York

    Google Scholar 

  5. Bertram A (2005) Elasticity and plasticity of large deformations. An introduction. Springer, Berlin/Heidelberg/New York

    Google Scholar 

  6. Betten J (1987) Tensorrechnung für Ingenieure. Teubner-Verlag, Stuttgart

    Google Scholar 

  7. Bishop RL, Goldberg SI (1968) Tensor analysis on manifolds. Macmillan, New York

    Google Scholar 

  8. Borisenko AI, Tarapov IE (1968) Vector and tensor analysis with applications. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  9. Bowen RM, Wang C-C (1976) Introduction to vectors and tensors. Plenum, New York

    Google Scholar 

  10. Brillouin L (1964) Tensors in mechanics and elasticity. Academic, New York

    Google Scholar 

  11. Chadwick P (1976) Continuum mechanics. Concise theory and problems. George Allen and Unwin, London

    Google Scholar 

  12. Dimitrienko Yu I (2002) Tensor analysis and nonlinear tensor functions. Kluwer, Dordrecht

    Google Scholar 

  13. Flügge W (1972) Tensor analysis and continuum mechanics. Springer, Berlin/Heidelberg/ New York

    Google Scholar 

  14. Golub GH, van Loan CF (1996) Matrix computations. The Johns Hopkins University Press, Baltimore

    Google Scholar 

  15. Gurtin ME (1981) An introduction to continuum mechanics. Academic, New York

    Google Scholar 

  16. Lebedev LP, Cloud MJ (2003) Tensor analysis. World Scientific, Singapore

    Google Scholar 

  17. Lütkepohl H (1996) Handbook of matrices. Wiley, Chichester

    Google Scholar 

  18. Narasimhan MNL (1993) Principles of continuum mechanics. Wiley, New York

    Google Scholar 

  19. Noll W (1987) Finite-dimensional spaces. Martinus Nijhoff, Dordrecht

    Google Scholar 

  20. Renton JD (2002) Applied elasticity: matrix and tensor analysis of elastic continua. Horwood, Chichester

    Google Scholar 

  21. Ruíz-Tolosa JR, Castillo (2005) From vectors to tensors. Springer, Berlin/Heidelberg/ New York

    Google Scholar 

  22. Schade H (1997) Tensoranalysis. Walter der Gruyter, Berlin/New York

    Google Scholar 

  23. Schey HM (2005) Div, grad, curl and all that: an informal text on vector calculus. W.W. Norton, New York

    Google Scholar 

  24. Schouten JA (1990) Tensor analysis for physicists. Dover, New York

    Google Scholar 

  25. Šilhavý M (1997) The mechanics and thermodynamics of continuous media. Springer, Berlin/Heidelberg/New York

    Google Scholar 

  26. Simmonds JG (1997) A brief on tensor analysis. Springer, Berlin/Heidelberg/New York

    Google Scholar 

  27. Talpaert YR (2002) Tensor analysis and continuum mechanics. Kluwer, Dordrecht

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Continuum Mechanics, RWTH Aachen University, Eilfschornsteinstr. 18, D 52062, Aachen, Germany

    Prof. Dr.-Ing. Mikhail Itskov

Authors
  1. Prof. Dr.-Ing. Mikhail Itskov
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Itskov, M. (2013). Solutions. In: Tensor Algebra and Tensor Analysis for Engineers. Mathematical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30879-6_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-30879-6_9

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30878-9

  • Online ISBN: 978-3-642-30879-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation