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- W2055329815 abstract "A hierarchical formulation for a three-node axisymmetric shell element based on p-version for linear elastic axisymmetric stress analysis is presented. The element displacement field can be of arbitrary polynomial orders pξ and pη in the longitudinal (ξ) and the transverse (η) directions of the element. The element approximation functions and the corresponding nodal variables are derived by first constructing the one-dimensional hierarchical approximation functions of order pξ and pη and the corresponding nodal variables operators in the ξ and η directions and then taking their products (also known as tensor products). The element displacement approximation is hierarchical, i.e. the approximation functions and the nodal variables corresponding to the polynomial orders pξ and pη are a subset of those corresponding to the polynomial orders (pξ + 1) and (pη + 1). Since the displacement approximation is hierarchical, the resulting element stiffness matrix and the equivalent nodal load vectors are hierarchical also. The formulation ensures C0 continuity. The element properties are derived using the principal of virtual work and the hierarchical element approximation. In developing the element properties all four components of the stress (σθ, σr,τrz, σz) and strain (εθ, εr, γrz, εz) are retained, i.e. the stress normal to the middle surface of the element is not neglected (an assumption commonly used in developing axisymmetric shell elements) in the present formulation. The element formulation also permits non-differentiable geometries (sharp corners). The stress concentrations at such locations can be calculated accurately due to the presence of a complete state of stress (and strain) and a non-differentiable geometry feature. Numerical examples are presented to demonstrate the accuracy, efficiency, modeling convenience and overall superiority of the present formulation as well as its applications to pressure vessel stress analysis. The results obtained from the present formulation are also compared with those available in the literature as well as with the analytical solutions. The numerical results from the h-models using isoparametric axisymmetric solid elements are also presented for comparison purposes" @default.
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- W2055329815 date "1991-01-01" @default.
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- W2055329815 title "p-version hierarchical axisymmetric shell element" @default.
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- W2055329815 doi "https://doi.org/10.1016/0045-7949(91)90024-g" @default.
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