A reduction scheme for problems of structural dynamics

Hughes, Thomas J.R.; Hilber, Hans M.; Taylor, Robert L.

doi:10.1016/0020-7683(76)90040-8

Cited by 22 publications

(15 citation statements)

References 6 publications

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“…We use a uniform mesh of quadratic 3-node FEs with mass lumping. In this case d = 1 and p = 2, so that (24) becomes [1,16]. The 'jump' in the curve at n = N /2 is due to the transition from the 'acoustic branch' to the 'optical branch', which is completely spurious.…”

Section: Givolimentioning

confidence: 95%

On the number of reliable finite‐element eigenmodes

Givoli¹

2008

Commun. Numer. Meth. Engng.

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SUMMARYThe finite-element (FE) approximation of linear elliptic eigenvalue problems is considered. An analysis based on a number of known estimates leads to the simple formula M =r 0 d/(2 p) N relating the total number of degrees of freedom N , the maximum relative error level desired for the eigenvalues, and the number of 'reliable' modes M. (Here d is the spatial dimension and p is the polynomial degree of the FE space.) Moreover, a rough estimate for the numerical value of the constant r 0 for a given application is found. This result supports a well-known rule of thumb.

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Section: Givolimentioning

confidence: 95%

On the number of reliable finite‐element eigenmodes

Givoli¹

2008

Commun. Numer. Meth. Engng.

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“…One might exercise caution with this interpretation because of the limitations of a representation such as (20). An alternative single wave representation of (19) is possible:…”

Section: Triquadratic Rectangular 27-node Elementsmentioning

confidence: 98%

Finite element dispersion analysis for the three‐dimensional second‐order scalar wave equation

Abboud

Pinsky

1992

Numerical Meth Engineering

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SUMMARYThe dispersive properties of finite element semidiscretizations of the three-dimensional second-order scalar wave equation are examined for both plane and spherical waves. This analysis throws light on the performance and limitations of the finite element approximation over the entire spectrum of wavenumbers and provides guidance for optimal mesh discretization as well as mass representation. The 8-node trilinear element, 20-node serendipity element, 27-node triquadratic element and the linear and quadratic spherically symmetric elements are considered.

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“…Indeed, v s and H> 5 are independent quantities as far as the state and costate equations are concerned (see Ref. 19). Nevertheless, one can also artifically require that (v 5 )/ r -(v r )/ s = 0 and (w s ) /r -(w r )/ 5 = 0 (r,s = 1,2, ...,AW; r^s).…”

Section: *<= T(y? T a S Y S +Y; T B 5 Y 5 )-mentioning

confidence: 99%

“…The independent representation of the displacement and the velocity for distributed conservative systems is discussed in detail in Ref. 19. Here, the columns of (t> sd and 4> sv are chosen as substructure admissible vectors for the displacement u s and the velocity v 5 , respectively.…”

Section: Selection Of Substructure Trial Vectorsmentioning

confidence: 99%

Substructure synthesis and its iterative improvement for large nonconservative vibratory systems

Hale

1984

AIAA Journal

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A general synthesis method is developed for the dynamic analysis of nonconservative vibratory systems composed of substructures. The idea of the synthesis is to represent each substructure by a reduced-order model and to couple the substructure models together to act as the whole system. For general nonconservative systems, a state space formulation is adopted for each substructure. Reduced-order substructure models are obtained by approximating each state vector as a linear combination of a small number of real trial vectors. The accuracy with which the synthesized model represents the whole system depends on the choices of trial vectors and the number of vectors used. A procedure is developed for increasing the accuracy by iteratively generating improved substructure trial state vectors.

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A reduction scheme for problems of structural dynamics

Cited by 22 publications

References 6 publications

On the number of reliable finite‐element eigenmodes

On the number of reliable finite‐element eigenmodes

Finite element dispersion analysis for the three‐dimensional second‐order scalar wave equation

Substructure synthesis and its iterative improvement for large nonconservative vibratory systems

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