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An efficient two-step damage identification method using sunflower optimization algorithm and mode shape curvature (MSDBI–SFO)

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Abstract

Laminated composite structures performance and behavior can be affected by damage that is not always visible on the surface. The need to monitor the health of these structures has continuously increased, which can be achieved in a fast and cost-effective way by numerical simulations. This paper presents an efficient two-step approach for damage identification in laminated composite plates. The first step uses mode shape and its derivatives (mode shape curvature) to locate the damages based on modal data. The proposed indicator utilizes modal analysis information extracted from finite element analysis. Then, a new metaheuristic Sunflower Optimization method (SFO) is employed to assess the correct severity of induced damages. This technique considers the damage detection problem as an inverse problem with minimization of an objective function. Numerical examples considering laminated composite plate with one and two induced damaged sites (delamination) are considered. The results indicate that the proposed method not only successfully identifies the location and severity of multi-damage cases in the composite structures, but also provides a better efficiency in terms of time saving and computational costs.

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Abbreviations

\({{U}_{{z}_{i}}}^{{\rm optimization}}\) :

Modal calculated displacement in z-direction for mode i

\({{U}_{z}}_{i}^{real}\) :

Modal damaged displacement in z-direction for mode i

\({\overrightarrow{s}}_{i}\) :

Sunflowers displacements towards the sun

E j :

Eigenvalue

Ex :

Elasticity modulus direction x

Ey :

Elasticity modulus direction y

Ez :

Elasticity modulus direction z

Gxy :

Shear modulus plane xy

Gxz :

Shear modulus plane xz

Gyz :

Shear modulus plane yz

J :

Fitness function

K :

Stiffness matrix

l x :

Element length in direction x

l y :

Element length in direction x

N e :

Damaged element number

N pop :

Number of plants in total population

P :

Power supply

Q :

Amount of heat received by each sunflower

r i :

Distance between current best plant and plant i

X :

Design vector

x,y :

Coordinate axes plane x–y

x :

Coordinate axis y

α :

Damage severity

θ d,(i, j) :

Damaged slope

θ h,(i, j) :

Undamaged slope

κ d,(i, j) :

Damaged curvature

κ h,(i, j) :

Undamaged curvature

νxy :

Poisson ratio plane xy

νxz :

Poisson ratio plane xz

νyz :

Poisson ratio plane yz

ρ :

Density

Φ d,(i, j) :

Damaged mode shape i at node location j

Φ h,(i, j) :

Undamaged mode shape i at node location j

λ :

Constant value that defines an “inertial” displacement of plants

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Acknowledgements

The authors are grateful to the Brazilian Funding Institutions CAPES, CNPq and FAPEMIG (Grant number APQ-00385-18) for the financial supports.

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Authors and Affiliations

  1. Mechanical Engineering Institute, Federal University of Itajubá—UNIFEI, Itajubá, Brazil

    Guilherme Ferreira Gomes & Rafael Simões Giovani

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  1. Guilherme Ferreira Gomes
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  2. Rafael Simões Giovani
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Correspondence to Guilherme Ferreira Gomes.

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Gomes, G.F., Giovani, R.S. An efficient two-step damage identification method using sunflower optimization algorithm and mode shape curvature (MSDBI–SFO). Engineering with Computers 38, 1711–1730 (2022). https://doi.org/10.1007/s00366-020-01128-2

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