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p ‐Version plate and curved shell element for geometrically non‐linear analysis
Author(s) -
Sorem Robert M.,
Surana Karan S.
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620330809
Subject(s) - lagrange polynomial , mathematics , element (criminal law) , interpolation (computer graphics) , mathematical analysis , geometry , shell (structure) , finite element method , displacement (psychology) , virtual work , polynomial , structural engineering , physics , classical mechanics , motion (physics) , psychology , materials science , law , composite material , psychotherapist , engineering , political science
This paper presents a p ‐version geometrically non‐linear formulation based on the total Lagrangian approach for a nine node three dimensional curved shell element. The element geometry is defined by the coordinates of the nodes located on its middle surface and nodal vectors describing the bottom and top surfaces of the element. The element displacement approximation can be of arbitrary and different polynomial orders in the plane of the element and in the transverse direction. The element approximation functions and the corresponding nodal variables are derived from the Lagrange family of interpolation functions. The resulting approximation functions and the nodal variables are hierarchical and the element displacement approximation ensures C ° continuity. The element properties are established using the principle of virtual work and the hierarchical element approximation. In formulating the properties of the element complete three dimensional stresses and strains are considered, hence the element is equally effective for very thin as well as extremely thick shells and plates. Incremental equations of equilibrium are derived and solved using the standard Newton–Raphson method. The total load is divided into increments, and for each increment of load, equilibrium iterations are performed until each component of the residuals is within a preset tolerance. Numerical examples are presented to show the accuracy, efficiency and advantages of the present formulation. The results obtained from the present formulation are compared with those available in the literature.