Discrete-Element Methods for Stability Analysis of Complex Structures

Przemieniecki, J. S.

doi:10.1017/s0001924000085778

Cited by 21 publications

(4 citation statements)

References 5 publications

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“…To use a 2 x 2 Gauss rule, set WT(1) = WT(2) = 1.0, GP(2) = -GP(l) = J3/3, and let I1 and JJ run from 1 to 2. To obtain a subroutine based on Equation (12) rather than Equation (6), replace the bracketed statements in Appendix I by the statements of Appendix 11.…”

Section: Formulation Of Initial Stress Stiffness Matricesmentioning

confidence: 99%

“…where the shape functions within brackets are defined in Reference 10. These functions contain factors (1 k t) and (1 kq), which serve the same purpose as those in Equation (6). Equation (12) can represent the constant twist d'w/dxay but does not provide inter-element compatibility.…”

Section: (4)mentioning

confidence: 99%

“…There are eight different nodal 8's in Equation(6). These must be replaced by the eight nodalrotation d.0.f.…”

mentioning

confidence: 99%

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Finite element buckling analysis of homogeneous and sandwich plates

Cook

1975

Numerical Meth Engineering

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SUMMARYFinite element buckling analyses of plates are performed by means of quadrilateral elements having 12 degreesof-freedom. It is found that if the plate is capable of appreciable transverse shear deformation, initial-stress stiffness matrices that represent the lateral displacement by cubic polynomials do not yield convergence to correct results. An initial-stress stiffness that works satisfactorily for both homogeneous and sandwich plates is formulated. A Fortran listing of the associated subroutine is provided.

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Section: Formulation Of Initial Stress Stiffness Matricesmentioning

confidence: 99%

Section: (4)mentioning

confidence: 99%

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Finite element buckling analysis of homogeneous and sandwich plates

Cook

1975

Numerical Meth Engineering

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“…Although a general stiffness matrix for an element of open section thin-walled beam, was derived in 1965 by Marten [3], and then by Przemieniecki [4], Livesley [5] and many others, it appears that this matrix applies only to the beam for pure bending.…”

Section: Introductionmentioning

confidence: 99%

Transformation Matrix for Combined Loads Applied to Thin-Walled Structures

Alsheikh¹,

Rees²

2022

WJM

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This paper transforms combined loads, applied at an arbitrary point of a thin-walled open section beam, to the shear centre of the cross-section of the beam. Therein, a generalized transformation matrix for loads with respect to the shear centre is derived, this accounting for the bimoments that develop due to the way the combined loads are applied. This and the authors' earlier paper (World Journal of Mechanics 2021, 11, 205-236) provide a full solution to the theory of thin-walled, open-section structures bearing combined loading. The earlier work identified arbitrary loading with the section's area properties that are necessary to axial and shear stress calculations within the structure's thin walls. In the previous paper attention is paid to the relevant axes of loading and to the transformations of loading required between axes for stress calculations arising from tension/compression, bending, torsion and shear. The derivation of the general transformation matrix applies to all types of loadings including, axial tensile and compression forces, transverse shear, longitudinal bending. One application, representing all these load cases, is given of a simple channel cantilever with an eccentrically located end load.

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Vibration analysis of rotating cantilever plates

Dokainish

Rawtani

1971

Numerical Meth Engineering

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A finite element technique is used to determine the natural frequencies and the mode shapes of a cantilever plate mounted on the periphery of a rotating disc. The plane of the plate is assumed to make any arbitrary angle with the plane of rotation of the disc. The distributed centrifugal force is resolved into two components-one acting in the plane of the plate and the other normal to the plate. The stresses produced in the middle surface of the plate due to the in-plane forces are first determined. The increase in the bending stiffness of the plate elements due to these in-plane stresses is obtained in a manner similar to that used in the stability analysis of plates. The component of the distributed centrifugal force normal to the plate surface is added to the inertia force.From the results of computations carried out for various values of the aspect ratio, the speed of rotation, the disc radius and the setting angle, empirical formulae are derived giving the effect of these parameters on the natural frequencies. These empirical formulae are observed to be in agreement with the corresponding known formulae for rotating cantilever beams, when the aspect ratio is high.

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Discrete-Element Methods for Stability Analysis of Complex Structures

Cited by 21 publications

References 5 publications

Finite element buckling analysis of homogeneous and sandwich plates

Finite element buckling analysis of homogeneous and sandwich plates

Transformation Matrix for Combined Loads Applied to Thin-Walled Structures

Vibration analysis of rotating cantilever plates

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