A Multiobjective Optimization Framework for Strength and Stress Concentration in Variable Axial Composite Shells: A metaheuristic approach

Santana, Pedro Bührer; Gomes, Herbert Martins; Ferreira, António Mendes; Tita, Volnei

doi:10.1590/1679-78257577

Pedro Bührer Santana ^**Corresponding author

writing original draft

visualization

validation

software

methodology

investigation

formal analysis

data curation

conceptualization

Universidade Federal do Rio Grande do Sul, Departamento de Engenharia Mecânica, R. Sarmento Leite, Porto Alegre, 90050-170, RS, Brasil. E-mail: pedro.santana@ufrgs.br, herbert@mecanica.ufrgs.br

https://orcid.org/0000-0001-7717-8518

Herbert Martins Gomes

writing review and editing

methodology

conceptualization

Universidade Federal do Rio Grande do Sul, Departamento de Engenharia Mecânica, R. Sarmento Leite, Porto Alegre, 90050-170, RS, Brasil. E-mail: pedro.santana@ufrgs.br, herbert@mecanica.ufrgs.br

https://orcid.org/0000-0001-5635-1852

António Mendes Ferreira

writing review and editing

writing original draft

methodology

conceptualization

Faculdade de Engenharia da Universidade do Porto, Departamento de Engenharia Mecânica, Rua Dr. Roberto Frias s/n, 4200-465, Porto, Portugal. E-mail: ferreira@gcloud.fe.up.pt

https://orcid.org/0000-0003-4043-9838

Volnei Tita

writing review and editing

writing original draft

supervision

conceptualization

Universidade de São Paulo, Escola de Engenharia de São Carlos, Departamento de Engenharia Aeronáutica, Av. João Dagnone, 1100 – Jardim Santa Angelina, 13563-120, São Carlos (SP), Brasil. E-mail: voltita@sc.usp.br

Faculdade de Engenharia da Universidade do Porto, Departamento de Engenharia Mecânica, Rua Dr. Roberto Frias s/n, 4200-465, Porto, Portugal. E-mail: ferreira@gcloud.fe.up.pt

https://orcid.org/0000-0002-8199-1162

*Corresponding author

Author’s Contributions: PB Santana, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization; HM Gomes, Writing – re-view & editing, Methodology, Conceptualization; V Tita, Writing – review & editing, Writing – original draft, Supervision, Conceptualization; AJM Ferreira: Writing – review & editing, Writing – original draft, Methodology, Conceptualization.

Editor: Marco L. Bittencourt and Josué Labaki

Material	$E_{1}$ (GPa)	$E_{2} (G P a)$	$ν_{12}$	$G_{12} (G P a)$	$X^{T}$ (MPa)	$X^{C}$ (MPa)	$Y^{T}$ (MPa)	$Y^{C}$ (MPa)	$S^{L}$ (MPa)
Scotchply 1002	36.8	8.27	0.26	4.14	1062	610	31	1186	72
T300/N5208	181	10.3	0.28	7.17	1500	1500	40	246	68

Material		$θ_{{C P}_{1}}$	$θ_{{C P}_{2}}$	$θ_{{C P}_{3}}$	$θ_{{C P}_{4}}$	$θ_{{C P}_{5}}$	$θ_{{C P}_{6}}$	$θ_{{C P}_{7}}$	$θ_{{C P}_{8}}$	$θ_{{C P}_{9}}$	LARC03	$K_{t}$
Scotchply 1002	Design I	1.4382	1.6115	1.6704	1.6010	1.3754	1.6045	1.6618	1.6886	1.4324	0.0643	2.7565
	Design II	1.4184	1.0942	1.7884	1.6021	1.4990	1.6068	1.7915	1.0687	1.3760	0.1484	2.2248
	Design III	1.2809	0.4619	1.2369	1.6012	1.4265	1.6021	1.2332	0.4353	1.2576	0.2325	1.5270
T300/N5208	Design I	1.7679	1.9347	1.7101	1.5208	1.5816	1.5637	1.7296	1.4324	1.4514	0.1508	2.4964
	Design II	1.7934	2.1320	1.7261	1.5114	1.5716	1.5775	1.7375	1.8529	1.4069	0.1687	2.0247
	Design III	1.7112	2.1777	1.7798	1.5679	1.4926	1.5637	1.3632	0.7869	1.3317	0.2820	1.5781

Material		$θ_{{C P}_{1}}$	$θ_{{C P}_{2}}$	$θ_{{C P}_{3}}$	$θ_{{C P}_{4}}$	$θ_{{C P}_{5}}$	$θ_{{C P}_{6}}$	$θ_{{C P}_{7}}$	$θ_{{C P}_{8}}$	$θ_{{C P}_{9}}$	$Φ / F I$	$K_{t}$
Tsai-Wu	Design I	1.7549	1.6770	1.6340	1.0885	1.5611	1.1609	1.8940	1.7311	1.7988	0.1300	4.3778
	Design II	0.9723	0.5071	1.0474	2.4991	2.2191	2.4082	1.2975	0.4308	1.2364	0.2879	2.8529
	Design III	2.6176	-0.7076	2.7075	0.1166	2.8777	0.1704	2.4367	0.4310	2.4826	0.6243	1.7059
LARC03	Design I	1.1153	1.3791	1.2226	2.0893	1.6219	2.0752	1.1925	1.1325	1.2616	0.2820	1.5781
	Design II	0.8918	-0.1020	1.0630	2.2149	2.2799	2.1766	0.8690	-0.2296	0.9583	0.1687	2.0247
	Design III	2.3196	-0.4485	2.3335	0.1656	2.9013	0.3149	2.4506	0.3973	2.3199	0.1508	2.4964

g = {1.12}^{2} \frac{Λ_{22}^{0}}{Λ_{44}^{0}} {(\frac{Y^{T}}{S^{L}})}^{2} ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ where ​ Λ_{22}^{0} = 2 (\frac{1}{E_{2}} - \frac{ν_{12}^{2}}{E_{1}}) and Λ_{44}^{0} = \frac{1}{G_{12}}

Φ = \frac{X^{C} - X^{T}}{X^{C} X^{T}} σ_{1} + \frac{Y^{C} - Y^{T}}{Y^{C} Y^{T}} σ_{2} + \frac{1}{X^{C} X^{T}} σ_{1}^{2} + \frac{1}{Y^{C} Y^{T}} σ_{2} + {\frac{1}{X^{C} X^{T} Y^{C} Y^{T}}}^{1 / 2} σ_{1} σ_{2} + \frac{1}{{(S^{L})}^{2}} τ_{12}

[1] *Corresponding author

Brasil

Brasil

A Multiobjective Optimization Framework for Strength and Stress Concentration in Variable Axial Composite Shells: A metaheuristic approach

Abstract

Graphical Abstract