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

Posting a File and Associated Data to a RESTful WebService preferably as JSON2019 Community Moderator ElectionREST URI convention - Singular or plural name of resource while creating itUploading both data and files in one form using Ajax?How do I upload a file with metadata using a REST web service?REST API - file (ie images) processing - best practicesSpring: JSON data and file in the same requestREST API Put large dataPosting a file and JSON data to Spring rest serviceRESTful Web Service Upload/Download Large Data With JSONREST API Design sending JSON data and a file to the api in same requestPost JSONArray to REST servicePUT vs. POST in RESTParsing values from a JSON file?JavaScript/jQuery to download file via POST with JSON dataHow do I upload a file with metadata using a REST web service?How to POST JSON data with Curl from Terminal/Commandline to Test Spring REST?Separate REST JSON API server and client?what's the correct way to send a file from REST web service to client?How do I write JSON data to a file?What is “406-Not Acceptable Response” in HTTP?REST API - file (ie images) processing - best practices

Image
Convert an array of objects to array of the objects' values Can a space-faring robot still function over a billion years? ESPP--any reason not to go all in? Create chunks from an array Has a sovereign Communist government ever run, and conceded loss, on a fair election? When to use the term transposed instead of modulation? How to chmod files that have a specific set of permissions Is this nominative case or accusative case? Are there other characters in the Star Wars universe who had damaged bodies and needed to wear an outfit like Darth Vader? What does "rhumatis" mean? How to write a chaotic neutral protagonist and prevent my readers from thinking they are evil? Can a Mimic (container form) actually hold loot? A bug in Excel? Conditional formatting for marking duplicates also highlights unique value What is Tony Stark injecting into himself in Iron Man 3? Iron deposits mined from under the city Why would the IRS ask for birth certificates ...
Read more

How can I change the color of pagination dots of UIPageControl?How to change UIPageControl dotsIs there a way to change page indicator dots colorCustomize dot with image of UIPageControl at index 0 of UIPageControlNo visible @interface for 'NSObject<PageControlDelegate>' declares the selector 'pageControlPageDidChange:'How to change the color of pagination dots in UIPageControl with a different color per pagepagecontrol indicator custom image instead of DefaultChanging the colour of UIPageControl dots in MonoTouchpagecontrol selectable page visibility color?Alternative way to load ViewControllers on a UIPageControlHow to set only layer.border-color for UIpage control dots in swiftHow can I develop for iPhone using a Windows development machine?How to change the name of an iOS app?UITableView - change section header coloruipagecontrol indicator(dot)issueCustom UIPageControl dots color not changingchange the interspace between UIPageControl dotsHow to change Status Bar text color in iOSHow can I change image tintColor in iOS and WatchKitUIPageControl dots with larger space in between each dotsHow to change the color of pagination dots in UIPageControl with a different color per page

Image
How do I implement a file system driver driver in Linux? Fly on a jet pack vs fly with a jet pack? Is possible to search in vim history? Translation of Scottish 16th century church stained glass Ridge Regression with Gradient Descent Converges to OLS estimates What linear sensor for a keyboard? Did US corporations pay demonstrators in the German demonstrations against article 13? Is it improper etiquette to ask your opponent what his/her rating is before the game? Why does Async/Await work properly when the loop is inside the async function and not the other way around? Why did the EU agree to delay the Brexit deadline? A Permanent Norse Presence in America Did arcade monitors have same pixel aspect ratio as TV sets? Can the Supreme Court overturn an impeachment? Drawing ramified coverings with tikz Greco-Roman egalitarianism Can someone explain how this makes sense electrically? Is it possible to use .desktop files to open local pdf files on specific pa...
Read more