Nonintrusive parametric solutions in structural dynamics

Cavaliere, Fabiola; Zlotnik, Sergio; Sevilla, Rubén; Larráyoz, Xabier; Dı́ez, Pedro

doi:10.1016/j.cma.2021.114336

Cited by 4 publications

(4 citation statements)

References 45 publications

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“…We note that we would have arrived exactly at the same set of equations if we had chosen to discretize the problem in time by the finite differences Crank-Nicolson scheme. More interestingly, we observe that (29) has exactly the same structure as (21) except for the fact that matrix M in (21) has been replaced by either M or M . We shall see in the following how this slight difference will affect the results within the PGD framework.…”

Section: Discrete Formulationmentioning

confidence: 75%

“…where we have multiplied the first row by m x . We observe that the above system of equations has naturally the same structure as that in (21).…”

Section: Discrete Formulationmentioning

confidence: 83%

“…were accounted for. PGD has also been successfully used in the context of structural dynamics with the objective of building parametric solutions for industrial problems in a non-intrusive manner [20,21].…”

Section: Introductionmentioning

confidence: 99%

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PGD reduced-order modeling for structural dynamics applications

Vella¹,

Prudhomme²

2022

Computer Methods in Applied Mechanics and Engineering

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Section: Discrete Formulationmentioning

confidence: 75%

“…where we have multiplied the first row by m x . We observe that the above system of equations has naturally the same structure as that in (21).…”

Section: Discrete Formulationmentioning

confidence: 83%

See 1 more Smart Citation

PGD reduced-order modeling for structural dynamics applications

Vella¹,

Prudhomme²

2022

Computer Methods in Applied Mechanics and Engineering

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“…In this work, the PGD approach has been coupled with an eigensolver technique, the inverse power method (IPM) [75], to efficiently identify how a variation of user-defined material and geometric parameters affects the dynamic response of the structure in terms of dominant eigenmodes and related natural frequencies. Similar works have been presented in the field of dynamic problems.…”

Section: Parametric Solutions In Structural Dynamicsmentioning

confidence: 99%

Static and dynamic global stiffness analysis for automotive pre-design

Cavaliere¹

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In order to be worldwide competitive, the automotive industry is constantly challenged to produce higher quality vehicles in the shortest time possible and with the minimum costs of production. Most of the problems with new products derive from poor quality design processes, which often leads to undesired issues in a stage where changes are extremely expensive. During the preliminary design phase, designers have to deal with complex parametric problems where material and geometric characteristics of the car components are unknown. Any change in these parameters might signiﬁcantly aﬀect the global behaviour of the car. A target which is very sensitive to small variations of the parameters is the noise and vibration response of the vehicle (NVH study), which strictly depends on its global static and dynamic stiﬀness. In order to ﬁnd the optimal solution, a lot of conﬁgurations exploring all the possible parametric combinations need to be tested. The current state of the art in the automotive design context is still based on standard numerical simulations, which are computationally very expensive when applied to this kind of multidimensional problems. As a consequence, a limited number of conﬁgurations is usually analysed, leading to suboptimal products. An alternative is represented by reduced order method (ROM) techniques, which are based on the idea that the essential behaviour of complex systems can be accurately described by simpliﬁed low-order models.This thesis proposes a novel extension of the proper generalized decomposi-tion (PGD) method to optimize the design process of a car structure with respect to its global static and dynamic stiﬀness properties. In particular, the PGD method is coupled with the inertia relief (IR) technique and the inverse power method (IPM) to solve, respectively, the parametric static and dynamic stiﬀness analysis of an unconstrained car structure and extract its noise and vibrations properties. A main advantage is that, unlike many other ROM methods, the proposed approach does not require any pre-processing phase to collect prior knowledge of the solution. Moreover, the PGD solution is computed with only one oﬄine computation and presents an explicit dependency on the introduced design variables. This allows to compute the solutions at a negligible computational cost and therefore opens the door to fast optimisation studies and real-time visualisations of the results in a pre-deﬁned range of parameters. A novel algebraic approach is also proposed which allows to involve both material and com-plex geometric parameters, such that shape optimisation studies can be performed. In addition, the method is developed in a nonintrusive format, such that an interaction with commercial software is possible, which makes it particularly interesting for industrial applications. Finally, in order to support the designers in the decision-making process, a graphical interface app is developed which allows to visualise in real-time how changes in the design variables aﬀect pre-deﬁned quantities of interest.

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