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Deep multiobjective design optimization of CFRP isogrid tubes using lichtenberg algorithm

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Abstract

The lattice structures use has increased in several sectors due to the potential for mass reduction without significant rigidity loss. In this paper, an isogrid tube multi-objective optimization considering six objectives is presented. The finite element method was applied to develop a numerical model for this complex structure, and a new optimization algorithm called the Multi-objective Lichtenberg Algorithm was used to find all the best possible designs. The optimizations were made considering two methodologies: (i) using a surrogate model derived from the design of experiments considering the response surface model and (ii) finite element updating, a direct link between the meta-heuristic and the numerical model. The latter is unprecedented in the literature for isogrid tubes and proved to be the best methodology, besides not even needing explicit equations. It discovered isogrid tube designs using TOPSIS that reduced at least 45.69% of the mass, 18.4% of the instability coefficient, 61.76% of the TW, and increased the natural frequency by at least 52.57%. The results show that optimizations via finite element updating associated with meta-heuristics not only allow the true interpretation of complex problems nature through real Pareto fronts, but can also deliver innovative results.

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Data Availability

Data Availability MOLA can be accessed at https://www.mathworks.com/matlabcentral/fileexchange/99689-multi-objective-lichtenberg-algorithm-mola. Specific enquiries should be direct to the authors.

Abbreviations

PSO:

Particle swarm optimization

LA:

Lichtenberg algorithm

RSM:

Response surface method

FEM:

Finite element method

PF:

Pareto front

IGD:

Inverted generational distance

SP:

Spacing

MS:

Maximum spread

φ :

Angle between helical ribs

δ c :

Width of circular ribs

δ H :

Width of helicoidal ribs

R 2 :

Indicator of model fit

LF:

Lichtenberg figure

R c :

Creation radius

N p :

Number of particles

S :

Stickiness coefficient

Ref:

Refinement

N iter :

Number of iterations

M :

Figure switching factor

CCD:

Central composite design

CFRP:

Carbon fiber-reinforced polymer

DOE:

Design of experiments

FEM:

Finite element method

E 1 :

Elasticity modulus direction longitudinal

E 2 :

Elasticity modulus direction transverse

S :

Standard deviation

G 12 :

Shear modulus in plane

k :

Number of design parameter

TWT :

Tsai-Wu under torsion efforts

TWC :

Tsai-Wu under compression efforts

λT :

Buckling coefficient under torsion efforts

λC :

Buckling coefficient under compression efforts

y:

RSM response

α :

Distance from center point

α c :

Distance between circular crossbars

α h :

Distance between helical crossbars

β :

Constant coefficients

ε :

Random error term or noise

ω n :

Natural frequency

m :

Mass

h :

Thickness

TOPSIS:

Technique for order of preference by similarity to ideal solution

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Funding

The authors would like to acknowledge the financial support from the Brazilian agency CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnológico—431219/2018–4), CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) and FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais—APQ-00385–18).

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Authors and Affiliations

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

    João Luiz Junho Pereira, Matheus Brendon Francisco, Ronny Francis Ribeiro, Sebastião Simões Cunha & Guilherme Ferreira Gomes

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  1. João Luiz Junho Pereira
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  2. Matheus Brendon Francisco
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  3. Ronny Francis Ribeiro
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  4. Sebastião Simões Cunha
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  5. Guilherme Ferreira Gomes
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The authors contributed to each part of this paper equally. The authors read and approved the final manuscript.

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Correspondence to João Luiz Junho Pereira.

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Pereira, J.L.J., Francisco, M.B., Ribeiro, R.F. et al. Deep multiobjective design optimization of CFRP isogrid tubes using lichtenberg algorithm. Soft Comput 26, 7195–7209 (2022). https://doi.org/10.1007/s00500-022-07105-9

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