A first order finite similitude approach to scaled aseismic structures

Davey, Keith; Darvizeh, Rooholamin; Atar, Muhammed

doi:10.1016/j.engstruct.2020.111739

Cited by 15 publications

(11 citation statements)

References 30 publications

(53 reference statements)

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“…In this way the finite similitude theory embraces the presence of scale effects as opposed to ignoring them as in the theory of dimensional analysis (see refs. [6,7,41,44]). The revealing of hidden dependencies can be readily achieved by the application of scale invariances, which are similitude rules that connect information across scaled experiments.…”

Section: Projected Structural Dynamics In Transport Formmentioning

confidence: 99%

“…The application details surrounding this identity termed zeroth-order finite similitude can be found in references [7,41,44]. The scaling parameters 0 2) are presented in Table 1 but also [6,41], so are not considered further here.…”

Section: Scale Invariancesmentioning

confidence: 99%

“…The issue is one of scale effects [4,5], where the behaviour of the scaled model fails to be representative of the full-scale system. This is certainly the situation prior to the arrival of finite similitude [6,7] but has the arrival of this theory significantly changed the situation? Questions about the usefulness of the new similitude identities remain and an objective of this work is to discover whether nonlinear systems can be assessed with this new approach.…”

Section: Introductionmentioning

confidence: 99%

“…To overcome these shortcomings with dimensional analysis a new theory has recently emerged called finite similitude [6,[40][41][42][43][44][45][46]. This approach is not underpinned by dimensionless forms but assumes that scaling can be viewed as an imagined process in which space itself is contracted or expanded.…”

Section: Introductionmentioning

confidence: 99%

“…The finite similitude theory although explained elsewhere [6,47] is re-examined in brief in Sec. 2 for the sake of readability, but also to bring into focus the limitations of the theory.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The scaling of nonlinear structural dynamic systems

Davey

Atar

Sadeghi

et al. 2021

International Journal of Mechanical Sciences

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Section: Projected Structural Dynamics In Transport Formmentioning

confidence: 99%

Section: Scale Invariancesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The finite similitude theory although explained elsewhere [6,47] is re-examined in brief in Sec. 2 for the sake of readability, but also to bring into focus the limitations of the theory.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The scaling of nonlinear structural dynamic systems

Davey

Atar

Sadeghi

et al. 2021

International Journal of Mechanical Sciences

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The theory of scaling

Davey

Sadeghi

Darvizeh

2023

Continuum Mech. Thermodyn.

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Scaled experimentation is an important approach for the investigation of complex systems but for centuries has been impeded by the want of a scaling theory that can accommodate scale effects. The present definition of a scale effect is founded on the violation of an invariance principle arising out of dimensional analysis, i.e. dimensionless equations do not change with scale. However, apart from all but the most rudimentary of systems, most dimensionless governing equations invariably do change with scale, thus providing a very severe constraint on the reach of scaled experimentation. This paper introduces the theory of scaling that in principle applies to all physics and quantifies either implicitly or explicitly all scale dependencies. It is shown here how the route offered by dimensional analysis is nothing more than a particular similitude condition among a countable infinite number of alternative possibilities provided by the new theory. The theory of scaling is founded on a metaphysical concept where space is scaled and the mathematical consequences of this are reflected in the governing equations in transport form. The theory is trialled for known problems in continuum mechanics, electromagnetism and heat transfer to illustrate the breath of the approach and additionally demonstrate the advantages offered by additional forms of similitude.

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Extended finite similitude and dimensional analysis for scaling

Davey,

Ochoa-Cabrero

2023

J Eng Math

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The theory of scaling called finite similitude does not involve dimensional analysis and is founded on a transport-equation approach that is applicable to all of classical physics. It features a countable infinite number of similitude rules and has recently been extended to other types of governing equations (e.g., differential, variational) by the introduction of a scaling space $$\Omega _{\beta }$$ Ω β , within which all physical quantities are deemed dependent on a single dimensional parameter $$\beta $$ β . The theory is presently limited to physical applications but the focus of this paper is its extension to other quantitative-based theories such as finance. This is achieved by connecting it to an extended form of dimensional analysis, where changes in any quantity can be associated with curves projected onto a dimensional Lie group. It is shown in the paper how differential similitude identities arising out of the finite similitude theory are universal in the sense they can be formed and applied to any quantitative-based theory. In order to illustrate its applicability outside physics the Black-Scholes equation for option valuation in finance is considered since this equation is recognised to be similar in form to an equation from thermal physics. It is demonstrated that the theory of finite similitude can be applied to the Black-Scholes equation and more widely can be used to assess observed size effects in portfolio performance.

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A first order finite similitude approach to scaled aseismic structures

Cited by 15 publications

References 30 publications

The scaling of nonlinear structural dynamic systems

The scaling of nonlinear structural dynamic systems

The theory of scaling

Extended finite similitude and dimensional analysis for scaling

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