A finite element approximation for the analysis of thin shells

Clough, Ray W.; Johnson, Chloe

doi:10.1016/0020-7683(68)90032-2

Cited by 95 publications

(16 citation statements)

References 2 publications

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“…Figure 1 shows a plate combined with an eccentric stiffener in a manner whereby plane sections are assumed to remain plane and hence no additional variables are required beyond those necessary for the membranelbending analysis of the plate. 2*7 Because of the assumption that plane sections remain plane, U = u + z e (1) where u is the axial displacement at depth z, U is the axial displacement at the centre of the plate (or more generally, at the chosen reference plane), and i 3 is the rotation of the normal.…”

Section: Eccentric Stiffener Elementsmentioning

confidence: 99%

The eccentricity issue in the design of plate and shell elements

Crisfield

1991

Commun. appl. numer. methods

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Section: Eccentric Stiffener Elementsmentioning

confidence: 99%

The eccentricity issue in the design of plate and shell elements

Crisfield

1991

Commun. appl. numer. methods

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“…The sensitivity analysis is performed by the application of a finite difference method. For the analysis of the shell elements, a combination of a plate element and a membrane element was used, according to Clough and Johnson (1968). The Constant Strain Triangle (CST) membrane element and the Discrete Kirchhoff Theory (DKT) plate element were selected, because they show good results when paired with a moderately large number of elements, and they have an explicit formulation with a low computation cost when used in the optimization problem.…”

Section: Thickness Optimizationmentioning

confidence: 99%

Optimization of shells modeled using NURBS subjected to a dynamic loading condition

2020

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This study presents an optimization method for the thickness of shell elements subjected to dynamic loads. Structural analyses were carried out using the finite element method. The analyzed domains were modeled using NURBS, and meshes were generated using a transformation of the parametric domain into the geometric domain via a geometric function. The shell element considered is a combination of a CST membrane element and a DKT plate element, forming an element with 15 degrees of freedom. The Newmark method with constant acceleration was applied to solve the equation of motion. The optimization approach was considered in two different ways: with uniform and variable thickness throughout the shell element. Due to the nonlinear constraints of the problem, the Sequential Quadratic Programming (SQP) method was employed. SQP routines are available in MATLAB, in which this study was performed. Useful examples were detailed in this study to demonstrate the applicability of the optimization method to real structures, such as the Igrejinha da Pampulha, a church located in Belo Horizonte, Brazil, whose modeling was performed.

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“…Although the concept of the use of such elements in the analysis was suggested as early as 1961 by Greene et al [4] the success of such analysis was hampered by the lack of a good stiffness matrix for triangular plate elements in bending [5][6][7][8]. Although the concept of the use of such elements in the analysis was suggested as early as 1961 by Greene et al [4] the success of such analysis was hampered by the lack of a good stiffness matrix for triangular plate elements in bending [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%