C 0 finite element discretization of Kirchhoff’s equations of thin plate bending. (English) Zbl 0636.73061
Summary: An alternative formulation of Kirchhoff’s equations is given which is amenable to a standard C 0 finite element discretization. In this formulation, the potential energy of the plate is formulated entirely in terms of rotations, whereas the deflections are the outcome of a subsidiary problem. The nature of the resulting equations is such that C 0 interpolation can be used on both rotations and deflections. In particular, general classes of triangular and quadrilateral isoparametric elements can be used in conjunction with the method. Unlike other finite element methods which are based on three-dimensional or Mindlin formulations, the present approach deals directly with Kirchhoff’s equations of thin plate bending. Excellent accuracy is observed in standard numerical tests using both distorted and undistorted mesh patterns.
Keywords:
C(sup 0) element discretization; potential energy; terms of rotations; deflections; triangular; quadrilateral isoparametric elements; Kirchhoff’s equations; thin plate bendingReferences:
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