A discrete element procedure for thin-shell instability analysis.

Gallagher, Richard H.; Gellatly, R. A.; Mallett, R. H.; Padlog, Joseph

doi:10.2514/3.3919

Cited by 48 publications

(8 citation statements)

References 3 publications

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“…The initial treatment of the finite element buckling analysis appeared in the literature prior to the formal naming of the finite element method (Gallagher et al, 1967); this earliest reference identified the approach as being based on the discrete element procedure. In light of the foregoing, and based on a survey of the literature, it appears that in the most commonly held definition of the classical formulation for finite element buckling analysis, the following problem is solved (Cook et al, 2002;Holzer et al, 1990;Chang and Chen, 1986;Brendel and Ramm, 1980):…”

Section: Classical Formulationmentioning

confidence: 99%

Stability Analysis by the Finite Element Method

Ziemian¹

2010

Guide to Stability Design Criteria for Metal Structures

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Section: Classical Formulationmentioning

confidence: 99%

Stability Analysis by the Finite Element Method

Ziemian¹

2010

Guide to Stability Design Criteria for Metal Structures

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“…In a report in 1966, Gallagher [358] was among the earliest researchers to develop a 24 degree of freedom, doubly curved, thin shell "nite element. In a paper in 1967, Gallagher et al [359] used #at plate "nite elements to model thin spherical cap to predict the buckling load. The work in References [356}359] would appear rather primitive from the current point of view.…”

Section: Dedication*a Summary Of Professor Gallagher's Work On Shellmentioning

confidence: 99%

A survey of recent shell finite elements

Yang

Saigal

Masud

et al. 2000

Int. J. Numer. Meth. Engng.

264

126

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Since the mid-1960s when the forms of curved shell "nite elements were originated, including those pioneered by Professor Gallagher, the published literature on the subject has grown extensively. The "rst two present authors and Liaw presented a survey of such literature in 1990 in this journal. Professor Gallagher maintained an active interest in this subject during his entire academic career, publishing milestone research works and providing periodic reviews of the literature. In this paper, we endeavor to summarize the important literature on shell "nite elements over the past 15 years. It is hoped that this will be a be"tting tribute to the pioneering achievements and sustained legacy of our beloved Professor Gallagher in the area of shell "nite elements. This survey includes: the degenerated shell approach; stress-resultant-based formulations and Cosserat surface approach; reduced integration with stabilization; incompatible modes approach; enhanced strain formulations; 3-D elasticity elements; drilling d.o.f. elements; co-rotational approach; and higher-order theories for composites.

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“…. (11) and they are related to the stresses o through the Hooke's law generalised for thermal effect a=vte + y T a r (12) where * and * T are matrices of elastic constants, a is the coefficient of thermal expansion, and T is the temperature increase. The subsequent analysis requires the determination of the strain energy % from the expression…”

Section: X^xx ^Yy Andzz Andxy ^ Tjz ^Zx\ • ' \^Jmentioning

confidence: 99%

Discrete-Element Methods for Stability Analysis of Complex Structures

Przemieniecki

1968

Aeronaut. j.

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The matrix methods of structural analysis developed specifically for use on modern digital computers have now become universally accepted in structural design. These methods provide a means for rapid and accurate stress and deflection analysis of complex structures under static and dynamic loading conditions and they can also be used very effectively for the stability analysis. In the conventional stability analysis two possible approaches are normally used; either the differential equations describing the structural deflections are formulated and the lowest eigenvalue representing the buckling load condition is found for a given set of boundary conditions, or alternatively, if the differential equations are too difficult to prescribe, approximate deflection shapes are used in the strain energy expression for large deflections which is subsequently minimised, leading to the stability determinant whose lowest root represents the instability condition. When designing complex structures the conventional methods of finding buckling load conditions are extremely difficult to apply, and therefore in such cases we have to rely on the matrix methods of stability analysis.

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A discrete element procedure for thin-shell instability analysis.

Cited by 48 publications

References 3 publications

Stability Analysis by the Finite Element Method

Stability Analysis by the Finite Element Method

A survey of recent shell finite elements

Discrete-Element Methods for Stability Analysis of Complex Structures

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