A simultaneous iteration algorithm for symmetric eigenvalue problems

Corr, R. B.; Jennings, A.

doi:10.1002/nme.1620100313

Cited by 149 publications

(31 citation statements)

References 7 publications

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“…When using the new stiffness matrix from equation (16), the eigenvalue problem in equation (2) can be resolved. Hence, the new gap vector can be obtained.…”

Section: Modification Of Fictitious Force Vectormentioning

confidence: 99%

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Buckling analysis of delaminated laminates with consideration of contact in buckling mode

1999

Int. J. Numer. Meth. Engng.

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SUMMARYThis paper concerns the buckling load analysis of laminates with a pre-existing delamination, using the finite element method based on the Mindlin plate theory. To deal with the contact problem in the buckling mode, an effective algorithm is presented. In this method, an iterative updating process based on the first-order sensitivity analysis and the quadratic programming technique is proposed to compute the fictitious forces in contacting areas at first. These fictitious forces are then transferred into the stiffness parameters of some artificial springs. The original stiffness matrix of system can be modified, using these artificial springs. Finally, the penetration between two delaminated layers in the buckling mode can be prevented effectively. Numerical examples show that this method is very efficient to solve the contact problem in eigenvalue analysis from the viewpoint of its accuracy, stability and convergence speed. The effects of contact and delamination size on the buckling load analysis are also investigated.

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“…When using the new stiffness matrix from equation (16), the eigenvalue problem in equation (2) can be resolved. Hence, the new gap vector can be obtained.…”

Section: Modification Of Fictitious Force Vectormentioning

confidence: 99%

“…7. Update the fictitious force vector and the stiffness matrix of system from equations (11) and (16), then go back to step 1.…”

Section: Iteration Strategymentioning

confidence: 99%

Buckling analysis of delaminated laminates with consideration of contact in buckling mode

1999

Int. J. Numer. Meth. Engng.

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“…For all these cases, the excitation frequency parameter Ω = 100ωa √ (ρ c /E 11 ) obtained are presented in Figures 4-12. The figures (4)(5)(6)(7)(8)(9)(10)(11)(12) show the locations of the tips (i.e., β = 0.0) of the whole dynamic stability regions, which also shows the difference between the stability and instability regions It is observed from the results shown in the figures (4-12) that for higher values of α and β the uniform trend is disturbed in some cases. …”

Section: Sandwich Plate Under Bi-axial In-plane Partial Edge Loadingmentioning

confidence: 98%

“…Eq. (14) is solved by the simultaneous iteration technique proposed by Corr and Jennings [6]. The above eigenvalue solution give the value of Ω, which are the bounding frequencies of the instability regions for the given values of α and β.…”

Section: Formulationmentioning

confidence: 99%

Dynamic instability of imperfect laminated sandwich plates with in-plane partial edge load

Chakrabarti

Sheikh

2010

Lat. Am. j. solids struct.

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Dynamic instability of laminated sandwich plates having inter-laminar imperfections with in-plane partial edge loading is studied for the first time using an efficient finite element plate model. The plate model is based on a refined higher order shear deformation plate theory, where the transverse shear stresses are continuous at the layer interfaces with stress free conditions at plate top and bottom surfaces. A linear spring-layer model is used to model the inter-laminar imperfection by considering in-plane displacement jumps at the interfaces. Interestingly the plate model having all these refined features requires unknowns at the reference plane only. However, this theory requires C1 continuity of transverse displacement (w) i.e., w and its derivatives should be continuous at the common edges between two elements, which is difficult to satisfy arbitrarily in any existing finite element. To deal with this, a new triangular element developed by the authors is used in the present paper.

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“…The eigenvalues is solved by the simultaneous iteration technique proposed by Corr and Jennings (1976).…”

Section: Governing Equations and Proposed Finite Elementmentioning

confidence: 99%

Dynamical Analysis of Stiffened Plates under Patch Loading

Srivastava¹,

Pandey

Kumar

2013

International Journal of Applied Mechanics and Engineering

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The vibration characteristics of stiffened plates with cutouts subjected to in-plane partial edge loadings at one end at the plate boundaries are studied using the finite element method. Buckling loads and vibration frequencies are determined for different cutout ratios and extent of partial edge loading at one end. In the structural modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. The main elegance of the formulation lies in the treatment of the stiffeners. The stiffeners can be placed anywhere within the plate element, and need not be placed on the nodal lines. The vibration characteristics are discussed and the results are compared with those available in the literature. Numerical results are presented for a range of cutout to plate size from 0 to 0.8.

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A simultaneous iteration algorithm for symmetric eigenvalue problems

Cited by 149 publications

References 7 publications

Buckling analysis of delaminated laminates with consideration of contact in buckling mode

Buckling analysis of delaminated laminates with consideration of contact in buckling mode

Dynamic instability of imperfect laminated sandwich plates with in-plane partial edge load

Dynamical Analysis of Stiffened Plates under Patch Loading

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