Application of ritz vectors for dynamic analysis of large structures

Arnold, Rocky R.; Citerley, Richard L.; Chargin, M.; Galant, David

doi:10.1016/0045-7949(85)90123-3

Cited by 30 publications

(2 citation statements)

References 4 publications

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“…20 [Eqs. (8)(9)(10)(11)(12)], a full-order damping matrix for the reference structure is created and assumed xed as the structural stiffness is being changed. MD and MD with FM approximation results are compared to the full-order exact results, as well as statically full-order mode acceleration with three MD modes, reduced-order mode acceleration based on reduced-order adjoint, and, nally, reduced-order, second-order approximation of the MA method.…”

Section: Static Resultsmentioning

confidence: 99%

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Reduced-Order Design-Oriented Stress Analysis Using Combined Direct and Adjoint Solutions

Livne

Blando

2000

AIAA Journal

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A new method for extracting accurate stress information from reduced-order structural and aeroelastic models is presented. The method has second-order accuracy when approximate reduced-order direct and adjoint solutions (based on different reduced-order bases) are used simultaneously to obtain approximate stresses. The method is applicable to both static and dynamiclinear analysis. A review of four common methods for structural model order reduction [two variants of the mode displacement method (standard mode displacement and the ctitious mass method), the mode acceleration method, and the Ritz vector method] identi es sources of dif culty and causes of errors in stress behavior sensitivity calculations. Considerations used for selection of the reduced-order direct and adjoint bases are discussed. A series of static and dynamic test cases is used to assess accuracy of the new method in an analysis mode. Accuracy studies of sensitivity calculations follow. We hope to contribute to the eld of design-oriented structural dynamics in terms of both insight and practice.

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Section: Static Resultsmentioning

confidence: 99%

“…(14)] for displacement approximation,but for stress recoverythe full-orderstiffness matrix is used. Equation (11) is rewritten in the form…”

Section: Ma Methodsmentioning

confidence: 99%

Reduced-Order Design-Oriented Stress Analysis Using Combined Direct and Adjoint Solutions

Livne

Blando

2000

AIAA Journal

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Use of load‐dependent vectors for dynamic analysis of large space structures

Ricles¹,

Léger²

1993

Commun. Numer. Meth. Engng.

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SUMMARYStructural models of large space structures have a substantial number of degrees of freedom (DOF) and possess semi-positive-definite stiffness matrices. The paper presents an efficient co-ordinate reduction procedure for structural dynamic analysis of large space structures. The method is based on the superposition of load-dependent Ritz vectors, which are computed in block form using a shifted stiffness matrix. Comparative transient dynamic analyses are performed on a 2803 DOF model of the space station Freedom using the load-dependent method (LDM) and the mode-displacement method (MDM) based on the superposition of eigenvectors. It is shown that the LDM is able to provide convergence of displacements with a small number of vectors. The acceleration response is found to be more sensitive to vector truncation than the displacement response. Error norms based on the representation of the dynamic load by the vector basis are developed to provide an indication of the effect of vector truncation on the structural response.

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An Efficient Crankshaft Dynamic Analysis Using Substructuring With Ritz Vectors

Mourelatos¹

2000

Journal of Sound and Vibration

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Application of ritz vectors for dynamic analysis of large structures

Cited by 30 publications

References 4 publications

Reduced-Order Design-Oriented Stress Analysis Using Combined Direct and Adjoint Solutions

Reduced-Order Design-Oriented Stress Analysis Using Combined Direct and Adjoint Solutions

Use of load‐dependent vectors for dynamic analysis of large space structures

An Efficient Crankshaft Dynamic Analysis Using Substructuring With Ritz Vectors

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