Instability Analysis of Pressure-Loaded Thin Arches of Arbitrary Shape

1983 ◽  
Vol 50 (2) ◽  
pp. 315-320 ◽  
Author(s):  
T. Q. Ye ◽  
R. H. Gallagher
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Arbitrary Shape ◽  
Virtual Work ◽  
Large Displacement ◽  
Classical Solutions ◽  
Displacement Analysis ◽  
Wide Range ◽  
Constant Direction ◽  
Circular Rings

The governing differential equations and the virtual work expressions for the large displacement analysis of thin arches of arbitrary shape, subjected to pressure loads, are derived. The virtual work expressions are employed as the basis for formulation of finite element stiffness equations. Classical solutions are obtained, from the differential equations, for the buckling of circular rings under uniform “follower” (hydrostatic) and “dead” (constant direction) pressure loadings. Finite element solutions are calculated for elliptical rings for a wide range of axis ratios.

Curvature Expressions for the Large Displacement Analysis of Planar Beam Motions

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Yinhuan Zheng ◽  
Ahmed A. Shabana ◽  
Dayu Zhang
Keyword(s):  
Differential Geometry ◽  
Finite Element ◽  
Beam Element ◽  
Elastic Force ◽  
Large Displacement ◽  
Displacement Analysis ◽  
The Third ◽  
Shear Deformable Beam ◽  
Approach Method ◽  
Shear Deformable

While several curvature expressions have been used in the literature, some of these expressions differ from basic geometry definitions and lead to kinematic coupling between bending and shear deformations. This paper uses three different elastic force formulations in order to examine the effect of the curvature definition in the large displacement analysis of beams. In the first elastic force formulation, a general continuum mechanics approach (method 1) based on the nonlinear strain–displacement relationship is used. The second approach (method 2) is based on a classical nonlinear beam theory, in which a curvature expression consistent with differential geometry and independent of the shear deformation is used. The third elastic force formulation (method 3) employs a curvature expression that depends on the shear angle. In order to examine numerically the effect of using different curvature definitions, three different planar beam elements are used. The first element (element I) is the fully parameterized absolute nodal coordinate formulation (ANCF) shear deformable beam element. The second element (element II) is an ANCF consistent rotation-based formulation (CRBF) shear deformable beam element obtained from element I by consistently replacing the position gradient vectors by rotation parameters. The third element (element III) is a low-order bilinear ANCF/CRBF finite element in which nonzero differential geometry-based curvature definition cannot be obtained because of the low order of interpolation. Numerical results are obtained using the three elastic force formulations and the three finite elements in order to shed light on the definition of bending and shear in the large displacement analysis of beams. The results obtained in this investigation show that the use of method 2, with a penalty formulation that restricts the excessive cross section deformation, can improve significantly the convergence of the ANCF finite element.

A finite element large displacement analysis of stiffened plates

1993 ◽  
Vol 47 (6) ◽  
pp. 987-993 ◽  
Author(s):  
D.Venugopal Rao ◽  
A.H. Sheikh ◽  
M. Mukhopadhyay
Keyword(s):  
Finite Element ◽  
Large Displacement ◽  
Stiffened Plates ◽  
Displacement Analysis
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