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Large deflexion, geometrically non-linear finite element analysis of circular arches

Large deflexion, geometrically non-linear finite element analysis of circular arches
Large deflexion, geometrically non-linear finite element analysis of circular arches
This paper presents the results of an investigation into the geometrically nonlinear behaviour of circular arches. A curved element is used, based on satisfying the condition that the circumferential strain and change in curvature, rather than the displacements, should be simple independent functions of the co-ordinate axes. The analysis was carried out using the linearized incremental method based on the mid-increment stiffness in conjunction with the Newton-Raphson iterative technique. A comparison is first made between the results obtained with this element and those using a simple polynomial shape function. The behaviour of a range of arches is then considered and the results are compared and found to agree well with an analytical method. The results include the behaviour of deeper but still shallow arches which exhibit “looping” of the load-deflexion curve, and bifurcation of the equilibrium path into unsymmetric deflexions of the arch.

A computer program was developed to allow any of the generalized degrees of freedom which are designated for incrementation to be expressed as either forces, to avoid failure at the vertical tangent to the load deflexion curves, or as generalized displacements to avoid failure at the horizontal tangent. The program also allows the quantity subjected to incrementation to be changed as necessary to follow complex load-deflexion equilibrium paths.

0020-7403
37-47
Sabir, A.B.
a649ab78-e56f-41bd-88f0-b71f007d9456
Lock, A.C.
a0a98ea4-05c0-49ab-8807-26cd5e6cac89
Sabir, A.B.
a649ab78-e56f-41bd-88f0-b71f007d9456
Lock, A.C.
a0a98ea4-05c0-49ab-8807-26cd5e6cac89

Sabir, A.B. and Lock, A.C. (1973) Large deflexion, geometrically non-linear finite element analysis of circular arches. International Journal of Mechanical Sciences, 15 (1), 37-47. (doi:10.1016/0020-7403(73)90044-1).

Record type: Article

Abstract

This paper presents the results of an investigation into the geometrically nonlinear behaviour of circular arches. A curved element is used, based on satisfying the condition that the circumferential strain and change in curvature, rather than the displacements, should be simple independent functions of the co-ordinate axes. The analysis was carried out using the linearized incremental method based on the mid-increment stiffness in conjunction with the Newton-Raphson iterative technique. A comparison is first made between the results obtained with this element and those using a simple polynomial shape function. The behaviour of a range of arches is then considered and the results are compared and found to agree well with an analytical method. The results include the behaviour of deeper but still shallow arches which exhibit “looping” of the load-deflexion curve, and bifurcation of the equilibrium path into unsymmetric deflexions of the arch.

A computer program was developed to allow any of the generalized degrees of freedom which are designated for incrementation to be expressed as either forces, to avoid failure at the vertical tangent to the load deflexion curves, or as generalized displacements to avoid failure at the horizontal tangent. The program also allows the quantity subjected to incrementation to be changed as necessary to follow complex load-deflexion equilibrium paths.

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Published date: January 1973

Identifiers

Local EPrints ID: 74732
URI: https://eprints.soton.ac.uk/id/eprint/74732
ISSN: 0020-7403
PURE UUID: 5e24680b-769f-420f-a6bd-0f7a2487e1ff

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Date deposited: 11 Mar 2010
Last modified: 18 Jul 2017 23:45

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Contributors

Author: A.B. Sabir
Author: A.C. Lock

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