Abstract
Mathematical basis for the existence and stability of numerical solutions of multifield finite element methods has been studied by many authors [1 – 4]. For problems in elasticity it is well recognized that such stability problem is associated with the zero energy deformation modes. For example, for the formulation of hybrid elements a procedure has been proposed for the selection of assumed stresses to suppress such modes [5]. Examples in Reference [5] are plane stress, 3-D solid and axisymmetric solid elements. Reference [4] applies the same approach and includes an example of plate bending element with transverse shear effect. These examples are all concerning problems that involve homogeneous solids and also require only C 0 continuity conditions for the assumed displacements. The present paper is to extend this appoach to two problems of different nature. The first one is the Kirchhoff plate bending problem for which the displacements are required to be C 1 continuous. The second one is an element which contains two layers of different materials with assumed stresses that satisfy the interface equilibrium conditions.
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Pian, T.H.H. (1991). Remarks on Selection of Stresses to Suppress Zero Energy Deformation Modes in Hybrid Element Formulations. In: Oñate, E., Periaux, J., Samuelsson, A. (eds) The finite element method in the 1990’s. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10326-5_15
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DOI: https://doi.org/10.1007/978-3-662-10326-5_15
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