Processing math: 100%
EI、Scopus 收录
中文核心期刊
Finite Element Of Elasticity With Couple-Stress Using The Analogy Between Plane Couple-Stress And Reissner/Mindlin Plate Bending[J]. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(3): 272-280. DOI: 10.6052/0459-1879-2004-3-2003-203
Citation: Finite Element Of Elasticity With Couple-Stress Using The Analogy Between Plane Couple-Stress And Reissner/Mindlin Plate Bending[J]. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(3): 272-280. DOI: 10.6052/0459-1879-2004-3-2003-203

Finite Element Of Elasticity With Couple-Stress Using The Analogy Between Plane Couple-Stress And Reissner/Mindlin Plate Bending

  • In order to include the effect of microstructure, thetheory of elasticity with couple stress considers couple stress which doesnot appear in the classical elasticity theory. However, there exists acrucial C1 continuity difficulty in the finite element formulation ofelasticity with couple stress.The analogy between plane elasticity with couple stress and Reissner/Mindlinplate bending provides an important way to avoid the C1 continuitydifficulty. According to the analogy, the C1 continuity difficulty canbe avoided naturally by the formulation in the space of stress functions,and the formulation can be analogous to the one of certain Reissner/Mindlinplate bending element in the space of transversal deflection and rotation.The unsettled problem is how to transform the finite element with stressfunctions as degree of freedom (DOF) into the one with usual planardisplacement and rotation as DOF. Using the analogy, the present workprovides an effective and rigorous method to deal with this problem. Thefinal finite element has two important characteristics. Firstly, theformulation in space of stress functions avoids C1 continuitydifficulty. Secondly, the discrete unknown DOF are usual displacement androtation.As an application of the present method, a finite element of plane couplestress with 12 DOF is transformed from the eight nodes serendipityReissner/Mindlin plate bending element. Numerical results of typicalproblems show that the present element has satisfactory precision andconvergence.
  • Related Articles

    [1]Xu Xiaojian, Deng Zichen. DISCUSSION ON BOUNDARY VALUE PROBLEMS OF A MINDLIN PLATE BASED ON THE SIMPLIFIED STRAIN GRADIENT ELASTICITY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(11): 3080-3087. DOI: 10.6052/0459-1879-22-310
    [2]Du Chaofan, Zheng Yanlong, Zhang Dingguo, Zhou Xiaoting. HIGH-ORDER RIGID-FLEXIBLE COUPLED DYNAMIC MODEL OF ROTATING MINDLIN PLATE BASED ON RADIAL POINT INTERPOLATION METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 119-133. DOI: 10.6052/0459-1879-21-362
    [3]Tian Rong. A GFEM WITH C1 CONTINUITY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 263-277. DOI: 10.6052/0459-1879-18-188
    [4]Gang Yan, Li Zhou. A simulation study on migration technique for damage imaging based on mindlin plate theory[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(3): 499-505. DOI: 10.6052/0459-1879-2010-3-2008-210
    [5]Bin Ji, Wanji Chen, Jie Zhao. Elastoplastic finite element analysis of shear band with couple stress theory[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(2): 192-199. DOI: 10.6052/0459-1879-2009-2-2007-416
    [6]Optimization method of hybrid element stress function for strain gradient theory based on Hellinger-Reissner principle[J]. Chinese Journal of Theoretical and Applied Mechanics, 2005, 37(3): 301-306. DOI: 10.6052/0459-1879-2005-3-2004-139
    [7]Scattering of flexural waves in mindlin's plates of soft ferromagnetic materials with a cutout[J]. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(5): 549-556. DOI: 10.6052/0459-1879-2004-5-2003-531
    [8]A NEW BOUNDARY ELEMENTMETHOD FOR REISSNER’S PLATE WITH NEW BOUNDARY VALUES[J]. Chinese Journal of Theoretical and Applied Mechanics, 1995, 27(5): 551-559. DOI: 10.6052/0459-1879-1995-5-1995-466
    [9]ON THE PROBLEM OF NONLINEAR REISSNER PLATE[J]. Chinese Journal of Theoretical and Applied Mechanics, 1990, 22(6): 748-752. DOI: 10.6052/0459-1879-1990-6-1995-1007
    [10]COMPLEX VARIABLE ANALYTIC METHOD FOR SOLVING REISSNERS PLATE BENDING PROBLEMS[J]. Chinese Journal of Theoretical and Applied Mechanics, 1990, 22(6): 689-699. DOI: 10.6052/0459-1879-1990-6-1995-1000

Catalog

    Article Metrics

    Article views (1951) PDF downloads (755) Cited by()
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return