A formulation of the nonlinear discrete Kirchhoff quadrilateral shell element with finite rotations and enhanced strains. (English) Zbl 1186.74104

Summary: This paper presents a new formulation of a nonlinear discrete Kirchhoff quadrilateral shell element applicable to the analysis of geometrically nonlinear structures undergoing finite rotations. The shell director is directly interpolated, and the exact linearization of the discrete form of the equilibrium equations is derived in closed form. The consistent tangent stiffness matrix is symmetric, and is given explicitly. Two or three rotational variables are used at each node. To improve the in-plane deformation, enhanced incompatible modes are introduced. The formulation is then illustrated by a comprehensive set of numerical experiments selected from the literature.


74S05 Finite element methods applied to problems in solid mechanics
74K25 Shells
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