Energy principles in structural mechanics Contents General principles Elastic systems Linear elastic systems Applications Bibliography Navigation menu

Structural analysisCalculus of variations


stressesstrainsdeformationsdisplacementsexternal effectssolid mechanicspartial differential equations




Energy principles in structural mechanics express the relationships between stresses, strains or deformations, displacements, material properties, and external effects in the form of energy or work done by internal and external forces. Since energy is a scalar quantity, these relationships provide convenient and alternative means for formulating the governing equations of deformable bodies in solid mechanics. They can also be used for obtaining approximate solutions of fairly complex systems, bypassing the difficult task of solving the set of governing partial differential equations.




Contents





  • 1 General principles


  • 2 Elastic systems


  • 3 Linear elastic systems


  • 4 Applications


  • 5 Bibliography




General principles



  • Virtual work principle
    • Principle of virtual displacements

    • Principle of virtual forces
      • Unit dummy force method


  • Modified variational principles


Elastic systems


  • Minimum total potential energy principle

  • Principle of stationary total complementary potential energy


  • Castigliano's first theorem (for forces)


Linear elastic systems



  • Castigliano's second theorem (for displacements)

  • Betti's reciprocal theorem

  • Müller-Breslau's principle


Applications


  • Governing equations by variational principles

  • Approximate solution methods

  • Finite element method in structural mechanics


Bibliography


  • Charlton, T.M.; Energy Principles in Theory of Structures, Oxford University Press, 1973. .mw-parser-output cite.citationfont-style:inherit.mw-parser-output .citation qquotes:"""""""'""'".mw-parser-output .citation .cs1-lock-free abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center.mw-parser-output .citation .cs1-lock-subscription abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registrationcolor:#555.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration spanborder-bottom:1px dotted;cursor:help.mw-parser-output .cs1-ws-icon abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center.mw-parser-output code.cs1-codecolor:inherit;background:inherit;border:inherit;padding:inherit.mw-parser-output .cs1-hidden-errordisplay:none;font-size:100%.mw-parser-output .cs1-visible-errorfont-size:100%.mw-parser-output .cs1-maintdisplay:none;color:#33aa33;margin-left:0.3em.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-formatfont-size:95%.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-leftpadding-left:0.2em.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-rightpadding-right:0.2em
    ISBN 0-19-714102-1

  • Dym, C. L. and I. H. Shames; Solid Mechanics: A Variational Approach, McGraw-Hill, 1973.

  • Hu, H. Variational Principles of Theory of Elasticity With Applications; Taylor & Francis, 1984.
    ISBN 0-677-31330-6

  • Langhaar, H. L.; Energy Methods in Applied Mechanics, Krieger, 1989.

  • Moiseiwitsch, B. L.; Variational Principles, John Wiley and Sons, 1966.
    ISBN 0-470-61280-0

  • Mura, T.; Variational Methods in Mechanics, Oxford University Press, 1992.
    ISBN 0-19-506830-0


  • Reddy, J.N.; Energy Principles and Variational Methods in Applied Mechanics, John Wiley, 2002.
    ISBN 0-471-17985-X

  • Shames, I. H. and Dym, C. L.; Energy and Finite Element Methods in Structural Mechanics, Taylor & Francis, 1995,
    ISBN 0-89116-942-3

  • Tauchert, T.R.; Energy Principles in Structural Mechanics, McGraw-Hill, 1974.
    ISBN 0-07-062925-0

  • Washizu, K.; Variational Methods in Elasticity and Plasticity, Pergamon Pr, 1982.
    ISBN 0-08-026723-8

  • Wunderlich, W.; Mechanics of Structures: Variational and Computational Methods, CRC, 2002.
    ISBN 0-8493-0700-7


-

Popular posts from this blog

Thal And Out Agency railway station See also References External links Navigation menuOfficial Web Site of Pakistan RailwaysArchivedOfficial Web Site of Pakistan Railwayseeexpanding ite

Image
Golra Sharif KutbalFatehjangGaganChauntraKahal Basal Junction DomelNammalChura Sharif HaltLangar Jand Junction Khushalgarh Faqir Hussain ShaheedTilkanSeni GambatBabari BandaCadet College Kohat Kohat Cantonment Kohat Tehsil Nasrat Khel Chikarkot Ustarzai Raisan Ibrahimzai Hangu Doaba Darsmand Thal Aab-e-gumAhmedwalAlam RegAlozaiAzadBadinzaiBakhtiarabad DomkiBeleli Bostan Junction Chaman ChurmianDalbandinDamboliDera Allah YarDera Murad JamaliDingraDozanGalangurGatGulistanHirokKan MehtarzaiKhanaiKhan Muhammad ChahKila SaifullahKishingiKoh-e-TaftanKolpurKuchlakMachMangoliMirjavehMushkafMuslimbaghNok KundiNushkiNuttallPadag RoadPerakPehro KunriPanirPeshiQilla Abdullah Quetta Sar-i-AbSheikh MandahSheikh Wasil Sibi Junction Spezand Junction Shela BaghTozghiWali KhanYakmachYaru Zhob IslamabadGolra Sharif Junction Attock City Junction Attock KhurdBahawalpurChiniotDandot RSFaisalabadGujar KhanGujratJalloJhang SadarJhelum Khanewal Junction KhanpurKhewra Lahore Junction Lahore CantonmentLiaquat Pu...
Read more

How to get text form Clipboard with JavaScript in Firefox 56?How to validate an email address in JavaScript?How do JavaScript closures work?How do I remove a property from a JavaScript object?How do you get a timestamp in JavaScript?How do I copy to the clipboard in JavaScript?How do I include a JavaScript file in another JavaScript file?Get the current URL with JavaScript?How to replace all occurrences of a string in JavaScriptHow to check whether a string contains a substring in JavaScript?How do I remove a particular element from an array in JavaScript?

Image
Can an x86 CPU running in real mode be considered to be basically an 8086 CPU? Why does this relative pronoun not take the case of the noun it is referring to? Email Account under attack (really) - anything I can do? Why do we use polarized capacitors? N.B. ligature in Latex Is Social Media Science Fiction? how to create a data type and make it available in all Databases? Need help identifying/translating a plaque in Tangier, Morocco How to make payment on the internet without leaving a money trail? What do you call something that goes against the spirit of the law, but is legal when interpreting the law to the letter? How can the DM most effectively choose 1 out of an odd number of players to be targeted by an attack or effect? cryptic clue: mammal sounds like relative consumer (8) Infinite past with a beginning? How do you conduct xenoanthropology after first contact? Is there an example of two elementary particles colliding to result in a single elementar...
Read more

List of MPs elected to the English parliament in 1640 (April) Contents List of constituencies and members See also Notes References Navigation menueNational Archives – The Glynde Place ArchivesCobbett's Parliamentary history of England, from the Norman Conquest in 1066 to the year 1803'Aldermen in Parliament', The Aldermen of the City of London: Temp. Henry III – 1912onepage&q&f&#61, false 229

Image
Parliaments of Charles I of England1640 in England1640 in politicsLists of Members of the Parliament of England (pre-1707)English MPs 1640 (April) King Charles IShort ParliamentLong Parliament Parliaments of England 1604–1705 Parliament Date Blessed Parliament 1604 Addled Parliament 1614 3rd Parliament of King James I 1621 Happy Parliament 1624 Useless Parliament 1625 2nd Parliament of King Charles I 1626 3rd Parliament of King Charles I 1628 Short Parliament 1640 Apr Long Parliament (1) 1640 Nov Oxford Parliament 1644 Long Parliament (2) 1645 Rump Parliament (1) 1648 Barebone's Parliament 1653 First Protectorate Parliament 1654 Second Protectorate Parliament 1656 Third Protectorate Parliament 1659 Rump Parliament (2) 1659 Long Parliament (3) 1660 Convention Parliament 1660 Cavalier Parliament 1661 Habeas Corpus Parliament 1679 Exclusion Bill Parliament 1680 Oxford Parliament 1681 Loyal Parliament 1685 Convention Parliament 1689...
Read more