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  Volume 5, Number 2, April 2020, pages 147-175

Two rectangular elements based on analytical functions
Mohammad Rezaiee-Pajand and Arash Karimipour

    To achieve appropriate stresses, two new rectangular elements are presented in this study. For reaching this aim, a complementary energy functional is used within an element for the analysis of plane problems. In this energy form, the Airy stress function will be used as a functional variable. Besides, some basic analytical solutions are found for the stress functions. These trial functions are matched with each element number of degrees of freedom, which leads to a number of equations with the anonymous constants. Subsequently, according to the principle of minimum complementary energy, the unknown constants can be expressed in terms of displacements. This system can be rewritten in terms of the nodal displacement. In this way, two new hybrid-rectangular triangular elements are formulated, which have 16 and 40 degrees of freedom. To validate the outcomes, extensive numerical studies are performed. All findings clearly demonstrate accuracies of structural displacements, as well as, stresses.
Key Words
    rectangular element; hybrid element; plane problem; finite element method; airy stress function
Department of Civil Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

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