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Structural vibration analysis with random fields using the hierarchical finite element method

Structural vibration analysis with random fields using the hierarchical finite element method
Structural vibration analysis with random fields using the hierarchical finite element method
Element-based techniques, like the finite element method, are the standard approach in industry for low-frequency applications in structural dynamics. However, mesh requirements can significantly increase the computational cost for increasing frequencies. In addition, randomness in system properties starts to play a significant role and its inclusion in the model further increases the computational cost. In this paper, a hierarchical finite element formulation is presented which incorporates spatially random properties. Polynomial and trigonometric hierarchical functions are used in the element formulation. Material and geometrical spatially correlated randomness are represented by the Karhunen–Loève expansion, a series representation for random fields. It allows the element integration to be performed only once for each term of the series which has benefits for a sampling scheme and can be used for non-Gaussian distributions. Free vibration and forced response statistics are calculated using the proposed approach. Compared to the standard h-version, the hierarchical finite element approach produces smaller mass and stiffness matrices, without changing the number of nodes of the element, and tends to be computationally more efficient. These are key factors not only when considering solutions for higher frequencies but also in the calculation of response statistics using a sampling method such as Monte Carlo simulation.
1806-3691
Fabro, Adriano
ec8ae99f-417a-4e1e-a912-3c4cff5c11b7
Ferguson, Neil
8cb67e30-48e2-491c-9390-d444fa786ac8
Mace, Brian
b68f95e6-702e-443b-b568-08819e70cb9b
Fabro, Adriano
ec8ae99f-417a-4e1e-a912-3c4cff5c11b7
Ferguson, Neil
8cb67e30-48e2-491c-9390-d444fa786ac8
Mace, Brian
b68f95e6-702e-443b-b568-08819e70cb9b

Fabro, Adriano, Ferguson, Neil and Mace, Brian (2019) Structural vibration analysis with random fields using the hierarchical finite element method. Journal of the Brazilian Society of Mechanical Sciences and Engineering. (doi:10.1007/s40430-019-1579-0).

Record type: Article

Abstract

Element-based techniques, like the finite element method, are the standard approach in industry for low-frequency applications in structural dynamics. However, mesh requirements can significantly increase the computational cost for increasing frequencies. In addition, randomness in system properties starts to play a significant role and its inclusion in the model further increases the computational cost. In this paper, a hierarchical finite element formulation is presented which incorporates spatially random properties. Polynomial and trigonometric hierarchical functions are used in the element formulation. Material and geometrical spatially correlated randomness are represented by the Karhunen–Loève expansion, a series representation for random fields. It allows the element integration to be performed only once for each term of the series which has benefits for a sampling scheme and can be used for non-Gaussian distributions. Free vibration and forced response statistics are calculated using the proposed approach. Compared to the standard h-version, the hierarchical finite element approach produces smaller mass and stiffness matrices, without changing the number of nodes of the element, and tends to be computationally more efficient. These are key factors not only when considering solutions for higher frequencies but also in the calculation of response statistics using a sampling method such as Monte Carlo simulation.

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Fabro_JABCM2017_R1_v2_PURE - Accepted Manuscript
Restricted to Repository staff only until 18 January 2020.
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Accepted/In Press date: 8 January 2019
e-pub ahead of print date: 18 January 2019

Identifiers

Local EPrints ID: 427334
URI: https://eprints.soton.ac.uk/id/eprint/427334
ISSN: 1806-3691
PURE UUID: 110cc4be-f4ee-4192-a12a-b3cb54531ce2
ORCID for Neil Ferguson: ORCID iD orcid.org/0000-0001-5955-7477

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Date deposited: 14 Jan 2019 17:30
Last modified: 20 Jul 2019 01:29

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Contributors

Author: Adriano Fabro
Author: Neil Ferguson ORCID iD
Author: Brian Mace

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