The MITC9 shell element in plate bending: mathematical analysis of a simplified case

Bathe, Klaus-Jürgen; Brezzi, Franco; Marini, L.
June 2011
Computational Mechanics;Jun2011, Vol. 47 Issue 6, p617
Academic Journal
We consider the 9-node shell element referred to as the MITC9 shell element in plate bending solutions and present a simplified mathematical analysis. The element uses bi-quadratic interpolations of the rotations and transverse displacement, and the 'rotated Raviart-Thomas' interpolations for the transverse shear stresses. A rigorous mathematical analysis of the element is still lacking, even for the simplified case of plate solutions (that is, flat shells), although the numerical evidence suggests a good and reliable behavior. Here we start such an analysis by considering a very simple particular case; namely, a rectangular plate, clamped all around the boundary, and solved with a uniform decomposition. Moreover, we consider only the so-called limit case, corresponding to the limit equations that are obtained for the thickness t going to zero. While the mathematical analysis of the limit case is simpler, such analysis, in general, gives an excellent indication of whether shear locking is present in the real case t > 0. We detail that the element in the setting considered shows indeed optimal behavior.


Related Articles

  • Efficient higher-order shear deformation theories for bending and free vibration analyses of functionally graded plates. Thai, Huu-Tai; Choi, Dong-Ho // Archive of Applied Mechanics;Dec2013, Vol. 83 Issue 12, p1755 

    In this paper, various efficient higher-order shear deformation theories are presented for bending and free vibration analyses of functionally graded plates. The displacement fields of the present theories are chosen based on cubic, sinusoidal, hyperbolic, and exponential variations in the...

  • A NOTE ON THE NONCONFORMING FINITE ELEMENTS FOR ELLIPTIC PROBLEMS. Boran Gao; Shuo Zhang; Ming Wang // Journal of Computational Mathematics;Mar2011, Vol. 29 Issue 2, p215 

    In this paper, a class of rectangular finite elements for 2m-th-oder elliptic boundary value problems in n-dimension (m, n ≥ 1) is proposed in a canonical fashion, which includes the (2m - 1)-th Hermite interpolation element (n = 1), the n-linear finite element (m = 1) and the Adini...

  • Thermoelastoplastic Bending of Complexly Reinforced Plates. Nemirovskii, Yu.; Yankovskii, A. // Mechanics of Composite Materials;Nov2005, Vol. 41 Issue 6, p477 

    A problem on the transverse-longitudinal bending of reinforced plates of variable thickness under a thermal-force loading is formulated. A qualitative analysis of the problem is carried out, and a way of its linearization is indicated. Calculations of isotropic and metal composite plates...

  • On convergence of affine thin plate bending element. Flajs, Rado; Saje, Miran // World Academy of Science, Engineering & Technology;2012, Issue 68, p1983 

    In the present paper the displacement-based nonconforming quadrilateral affine thin plate bending finite element ARPQ4 is presented, derived directly from non-conforming quadrilateral thin plate bending finite element RPQ4 proposed by Wanji and Cheung [19]. It is found, however, that element...

  • A relook at Reissner's theory of plates in bending. Vijayakumar, K. // Archive of Applied Mechanics;Nov2011, Vol. 81 Issue 11, p1717 

    Shear deformation and higher order theories of plates in bending are (generally) based on plate element equilibrium equations derived either through variational principles or other methods. They involve coupling of flexure with torsion (torsion-type) problem and if applied vertical load is along...

  • Steady-state creep of bent reinforced metal-composite plates with consideration of their reduced resistance to transverse shear 2. Analysis of calculated results. Yankovskii, A. // Journal of Applied Mechanics & Technical Physics;Jul2014, Vol. 55 Issue 4, p701 

    Deformation of annular plates with different structures of helical reinforcement is studied. It is demonstrated that the use of the classical theory for calculating steady-state creep for thick reinforced plates subjected to bending leads to underprediction of the compliance of thin-walled...


    The shear deformation laminate theory is very useful for the calculation of the sandwich composites. Sandwich can be defined as a special laminate with three layers and therefore can be modeled using shear deformation laminate theory by neglecting of membrane and bending deformations in the core...

  • Bending of a fiber-reinforced viscoelastic composite plate resting on elastic foundations. Zenkour, Ashraf; Allam, M.; Sobhy, M. // Archive of Applied Mechanics;Jan2011, Vol. 81 Issue 1, p77 

    Composite structures on an elastic foundation are being widely used in engineering applications. Bending response of inhomogeneous viscoelastic plate as a composite structure on a two-parameter (Pasternak's type) elastic foundation is investigated. The formulations are based on sinusoidal shear...

  • Bending to shear ratio approach for beam design. Soltis, Lawrence A.; Rammer, Douglas R. // Forest Products Journal;Jan1997, Vol. 47 Issue 1, p104 

    Describes a design procedure based on lower bound theory of experimental shear and bending strength. Lack of correlation between bending and shear strength for the glued-laminated and solid-sawn timbers; Influence of bending and shear properties on the strength of the beams; Comparison of...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics