A theoretical and numerical comparison of elastic nonlinear finite element methods

Ebner, Alan M.; Ucciferro, Joseph J.

doi:10.1016/0045-7949(72)90055-7

Cited by 20 publications

(7 citation statements)

References 10 publications

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“…They nay be subjected to pressures which cause inelastic deformation, lite finite element method was chosen to model these structures because it is easily applied to complex geometries and has successfully modeled inelastic material behavior 23 " 28 and large deflections. 29…”

Section: Membran -A Finite Element Program To Predict Window Deflementioning

confidence: 99%

Thin windows for gaseous and liquid targets: An optimization procedure

Hassenzahl

Gray

1975

Cryogenics

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Many nuclear physics experiments require cryogenic or highpressure gas targets with thin windows. To obtain the best data, i.e. to reduce background signals, a target window would ideally have zero thickness and zero deflection. Since this is not possible a trade off is made among target geometry, window geometry, window material, and window thickness. Measurements of deflections of a variety of window materials and geometries were performed at room temperature and in liquid nitrogen to aid in designing windows in the future. A simple graphical method for predicting the rupture pressure for several typical window materials is described. The results of the deflection measurement are compared to a finite element computer program MEMBRAN which predicts window deflection and material stresses for a uniform applied pressure.

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Section: Membran -A Finite Element Program To Predict Window Deflementioning

confidence: 99%

Thin windows for gaseous and liquid targets: An optimization procedure

Hassenzahl

Gray

1975

Cryogenics

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“…Since these structures often undergo large deformations with small strains, the choice of the reference configurations is important for establishing the governing equations. For example, the conventional quadratic beam strain-displacement relations based on the total Lagrangian (TL) format have been found to be inadequate for large deformation beam problems [1][2][3][4]. Mattiasson et al [5] presented ways to alleviate this inadequacy.…”

Section: Introductionmentioning

confidence: 99%

Variable order secant matrix technique applied to the elastic postbuckling of arches

Jayachandran

White

2007

Commun. Numer. Meth. Engng.

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SUMMARYThis paper presents the implementation of Reissner's (J. Appl. Math. Phys. 1972; 23:795-804) straindisplacement relations for a planar beam using a variable order secant matrix (VOSM) technique. The secant matrices are formed using a Taylor expansion of the strain energy and hence the order of the secant and tangent matrices to be included in the nonlinear analysis can be varied depending upon the degree of nonlinearity involved in the problem. Nevertheless, a maximum of 24 matrices is sufficient to obtain predicted internal stress resultants to within 0.2% of the converged solution in all the problems tested. Using a three-noded isoparametric beam element, the accuracy of the VOSM method is demonstrated for the elastic postbuckling of arches.

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“…The design of failure-free installation procedures for submarine pipelines [1], dynamic analysis of marine pipes during operation [2], ight simulation of exible aircraft [3], and stability analysis of frame structures [4][5][6][7][8], are examples of such applications. The development of accurate and e cient computational procedures to accommodate large rotation capability of beams and frame structures has therefore become a subject of considerable interest among researchers.…”

Section: Introductionmentioning

confidence: 99%

A corotational finite element formulation for the analysis of planar beams

Urthaler

Reddy

2005

Commun. Numer. Meth. Engng.

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SUMMARYAn e cient and accurate locking-free corotational beam ÿnite element for the analysis of large displacements and small-strain problems is developed in this paper. Three di erent ÿnite element models based on three di erent beam theories, namely, the Euler-Bernoulli, Timoshenko, and simpliÿed Reddy theories are presented. In order to develop a single corotational ÿnite element that incorporates the kinematics of all three theories, the uniÿed linear ÿnite element model of beams developed by Reddy (Comm. Numer. Meth. Eng. 1997; 13:495-510) is included in the formulation. An incremental iterative technique based on the Newton-Raphson method is employed for the solution of the non-linear equilibrium equations. Numerical examples that demonstrate the e ciency and large rotation capability of the corotational formulation are presented. The element is validated by comparisons with exact and=or approximate solutions available in the literature. Very good agreement is found in all cases.

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A theoretical and numerical comparison of elastic nonlinear finite element methods

Cited by 20 publications

References 10 publications

Thin windows for gaseous and liquid targets: An optimization procedure

Thin windows for gaseous and liquid targets: An optimization procedure

Variable order secant matrix technique applied to the elastic postbuckling of arches

A corotational finite element formulation for the analysis of planar beams

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