Journal of Applied and Computational Mechanics

Multiobjective Geometric Analysis of Stiffened Plates under ‎Bending through Constructal Design Method

Document Type : Research Paper

Authors

1 Federal University of Rio Grande - FURG, Graduate Program in Ocean Engineering, Rio Grande, 96203-900, Brazil‎

2 University of Vale do Rio dos Sinos - UNISINOS, Graduate Program in Mechanical Engineering, São Leopoldo, 93022-750, Brazil‎

3 University of Bologna - Department of Mechanical Engineering, Bologna, 40136, Italy

Abstract

Constructal design, finite element method and exhaustive search are applied to analyze different arrangements of steel plates with rectangular or trapezoidal stiffeners. As performance parameters, the maximum deflection and maximum von Mises stress are considered. A non-stiffened plate adopted as reference is studied together with 25 plates with rectangular stiffeners and 25 plates with trapezoidal stiffeners. The results show that trapezoidal stiffeners are more effective in minimizing the maximum deflection in comparison with rectangular stiffeners. However, regarding the minimization of stress, the rectangular stiffeners normally present better performance. When both performance parameters are concomitantly considered, a slight advantage of 4.70% for rectangular geometry is identified.

Keywords

Main Subjects

[1] Rama, G., Marinkovic, D., Zehn, M., High Performance 3-node Shell Element for Linear and Geometrically Nonlinear Analysis of Composite Laminates, Composites Part B: Engineering, 151, 2018, 118-126.
[2] Zhang, H., Shi, D., Wang, Q., Qin, B., Free Vibration of Functionally Graded Parabolic and Circular panels with General Boundary Conditions, Curved and Layered Structures, 4(1), 2017, 52-84.
[3] Rama, G., Marinković, D., Zehn, M., Efficient Three-node Finite Shell Element for Linear and Geometrically Nonlinear Analyses of Piezoelectric Laminated Structures, Journal of Intelligent Material Systems and Structures, 29(3), 2018, 345-357.
[4] Marinković, D., Rama, G., Zehn, M., Abaqus Imlementation of a Corotational Piezoelectric 3-node Shell Element with Drilling Degree of Freedom, Facta Universitatis-Series Mechanical Engineering, 17(2), 2019, 269-283.
[5] Ugural, A.C., Plates and Shells - Theory and Analysis, CRC Press, Boca Raton, 2018.
[6] Ventsel, E., Krauthammer, T., Thin Plates and Shells: Theory, Analysis and Applications, CRC Press, Boca Raton, 2001. DOI: 10.1201/9780203908723
[7] Pama, R.P., Cusens, A.R., Edge Beam Stiffening of Multibeam Bridges, Journal of the Structural Division, 93, 1969, 141-161.
[8] Powell, G.H., Ogden, D.W., Analysis of Orthotropic Steel Plate Bridge Decks, Journal of the Structural Division, 95, 1969, 909-922.
[9] Kurkreti, A.R., Rajapaksa, Y., Analysis Procedure for Ribbed and Grid Plate Systems Used for Bridge Decks, Journal of Structural Engineering, 116(2), 1990, 372-391.
[10] Kurkreti, A.R., Cheraghi, E., Analysis Procedure for Stiffened Plate Systems Using an Energy Approach, Computers & Structures, 14(4), 1993, 649-657.
[11] O’Leary, J.R., Harari, I., Finite Element Analysis of Stiffened Plates, Computers & Structures, 11(5), 1985, 973-985.
[12] Deb, A., Botoon, M., Finite Element Under Models for Stiffened Plates Transverse Loading, Computers & Structures, 3, 1988, 361-372.
[13] Biswal, K.C., Ghosh, A.K., Finite Element Analysis for Stiffened Laminated Plates Using Higher Order Shear Deformation Theory, Computers & Structures, 53(1), 1993, 161-171.
[14] Paiva, J.B., Boundary Element Formulation of Building Slabs, Engineering Analysis with Boundary Elements, 17(2), 1996, 105-110.
[15] Peng, L.X., Kitipornchai, S., Liew, K.M., Analysis of Rectangular Stiffened Plates Under Uniform Lateral Load Based on FSDT and Element-free Galerkin Method, International Journal of Mechanical Sciences, 47(2), 2005, 251-276.
[16] Waidemam, L., Venturini, W.S., BEM Formulation for Reinforced Plates, Engineering Analysis with Boundary Elements, 33(6), 2009, 830-836.
[17] Fernandes, G.R., A BEM Formulation for Linear Bending Analysis of Plates Reinforced by Beams Considering Different Materials, Engineering Analysis with Boundary Elements, 33(8), 2009, 1132-1140.
[18] Helbig, D., Da Silva, C.C.C., Real, M.V., Dos Santos, E.D.; Isoldi, L.A., Rocha, L.A.O., Study About Buckling Phenomenon in Perforated Thin Steel Plates Employing Computational Modeling and Constructal Design Method, Latin American Journal of Solids and Structures, 13(10), 2016, 1912-1936.
[19] Helbig, D., Cunha, M.L., Da Silva, C.C.C., Dos Santos, E.D., Iturrioz, I., Real, M.V., Isoldi, L.A., Rocha, L.A.O., Numerical Study of the Elasto-plastic Buckling in Perforated Thin Steel Plates Using the Constructal Design Method, Research on Engineering Structures and Materials, 4(3), 2018, 169-187.
[20] Rocha, L.A.O., Real, M.V., Correia, A.L.G., Vaz, J., Dos Santos, E.D., Isoldi, L.A., Geometric Optimization Based on the Constructal Design of Perforated Thin Plates Subject to Buckling, Computational Thermal Sciences, 4, 2012, 119-129.
[21] Lorenzini, G., Helbig, D., Real, M.V., dos Santos, E.D., Rocha, L.A.O., Isoldi, L.A., Computational Modeling and Constructal Design Method Applied to the Mechanical Behavior Improvement of Thin Perforated Steel Plates Subject to Buckling, Journal of Engineering Thermophysics, 25, 2016, 197-215.
[22] Da Silva, C.C.C., Helbig, D., Cunha, M.L., Dos Santos, E.D., Rocha, L.A.O., Real, M.V., Isoldi, L.A., Numerical Buckling Analysis of Thin Steel Plates with Centered Hexagonal Perforation Through Constructal Design Method, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41(8), 2019, 309-1-309-18.
[23] Lima, J.P.S., Rocha, L.A.O., Dos Santos, E.D., Real, M.V., Isoldi, L.A., Constructal Design and Numerical Modeling Applied to Stiffened Steel Plates Submitted to Elasto-plastic Buckling, Proceedings of the Romanian Academy Series A-Mathematics Physics Technical Sciences Information Science, 19, 2018, 195-200.
[24] Lima, J.P.S., Cunha, M.L., Dos Santos, E.D., Rocha, L.A.O., Real, M.V., Isoldi, L.A., Constructal Design for the Ultimate Buckling Stress Improvement of Stiffened Plates Submitted to Uniaxial Compressive Load, Engineering Structures, 203, 2020, 109883.
[25] De Queiroz, J., Cunha, M.L., Pavlovic, A., Rocha, L.A.O., Dos Santos, E.D., Troina, G.S., Isoldi, L.A., Geometric Evaluation of Stiffened Steel Plates Subjected to Transverse Loading for Naval and Offshore Applications, Journal of Marine Science and Engineering, 7(1), 2019. 7-18.
[26] Pinto, V.T., Cunha, M.L., Troina, G.S., Martins, K.L., Dos Santos, E.D., Isoldi, L.A., Rocha, L.A.O., Constructal Design Applied to Geometrical Evaluation of Rectangular Plates with Inclined Stiffeners Subjected to Uniform Transverse Load, Research on Engineering Structures and Materials, 4(5), 2019, 379-392.
[27] Troina, G.S., Cunha, M.L., Pinto, V.T., Rocha, L.A.O., Dos Santos, E.D., Fragassa, C., Isoldi, L.A., Computational Modeling and Design Constructal Theory Applied to the Geometric Optimization of Thin Steel Plates with Stiffeners Subjected to Uniform Transverse Load, Metals, 10(2), 2020, 1-29.
[28] Amaral, R.R., Troina, G.S., Fragassa, C., Pavlovic, A., Cunha, M.L., Rocha, L.A.O., dos Santos, E.D., Isoldi, L.A., Constructal Design Method Dealing with Stiffened Plates and Symmetry Boundaries, Theoretical and Applied Mechanics Letters, 10, 2020, 266-372.
[29] Mardanpour, P., Izadpanahi, E., Rastkar, S., Lorente, S., Bejan, A., Constructal Design of Aircraft: Flow of Stresses and Aeroelastic Stability, AIAA Journal, 2019. DOI: 10.2514/1.J057183
[30] Izadpanahi, E., Moshtaghzadeh, M., Radnezhad, H.R., Mardanpour, P., Constructal Approach to Design of Wing Cross-section for Better Flow of Stresses, AIAA Journal, 2020. DOI: 10.2514/6.2020-0275
[31] ANSYS Academic Research Mechanical, Release 19, Help System, Element Reference, ANSYS, Inc.
[32] Heinonen, O., Pajunen, S., Optimal Design of Stiffened Plate Using Metamodeling Techniques, Journal of Structural Mechanics, 44(3), 2011, 218-230.
[33] Troina, G.S., de Queiroz, J.P.T.P., Cunha, M.L., Rocha, L.A.O., dos Santos E.D., Isoldi, L.A., Verificação de Modelos Computacionais para Placas com Enrijecedores Submetidas a Carregamento Transversal Uniforme, CEREUS, 5(2), 2018, 285-298.
[34] Carrijo, E.C., Paiva, J.B, Giogo, J.S., A Numerical and Experimental Study of Stiffened Plates in Bending, Transactions on Modelling and Simulation, 21, 1999, 12-18.
[35] Bejan, A., Lorente, S., Design with Constructal Theory, Wiley, Hoboken, 2008. DOI: 10.1002/9780470432709 
[36] Bejan, A., Zane, J.P., Design in Nature: How the Constructal Law Governs Evolution in Biology, Physics, Technology, and Social Organizations, Doubleday, New York, 2012.
[37] Reis, A.H. Constructal theory: from engineering to physics, and how flow systems develop shape and structure. Applied Mechanics Reviews, 59(5), 2006, 269-281.
[38] Dos Santos, E.D., Isoldi, L.A., Gomes, M.N., Rocha, L.A.O., The Constructal Design Applied to Renewable Energy Systems, In: Rincón-Mejía, E., De las Heras., A. (Ed.), Sustainable Energy Technologies 1ed., 2017, 63-87, CRC Press - Taylor & Francis Group, Boca Raton. DOI: 10.1201/9781315269979
[39] Lorente, S., Lee, J., Bejan, A., The “Flow of Stresses” Concept: the Analogy Between Mechanical Strength and Heat Convection, International Journal of Heat and Mass Transfer, 53(15-16), 2010, 2963-2968.
[40] Rocha L.A.O., Lorente S., Bejan A., Constructal Theory in Heat Transfer,In:Kulacki F. (Ed.), Handbook of Thermal Science and Engineering, Springer, Cham, 2018. DOI: 10.1007/978-3-319-32003-8_66-1
[41] Ganjehkaviri, A., Mohd Jaafar, M.N., Multi-objective Particle Swarm Optimization of Flat Plate Solar Collector Using Constructal Theory, Energy, 194, 2020, 116846.
[42] Hazarika, S.A., Bhanja, D., Nath, S., Fork-shaped Constructal Fin Array Design a Better Alternative for Heat and Mass Transfer Augmentation Under Dry, Partially Wet and Fully Wet Conditions, International Journal of Thermal Sciences, 152, 2020, 106329.
[43] Magalhães, G.M.C., Fragassa, C., de Lemos, R., Isoldi, L.A., Amico, S.C., Rocha, L.A.O., Souza, J.A., dos Santos, E.D., Numerical Analysis of the Influence of  Empty Channels Design on Performance of Resin Flow in a Porous Plate, Applied Sciences, 10(11), 2020, 4054.
[44] Wu, Z., Feng, H., Chen, L., Xie, Z., Cai, C., Xia, S., Optimal Design of Dual-pressure Turbine in OTEC System Based on Constructal Theory, Energy Conversion and Management, 201, 2019, 112179.
[45] Hermany, L., Lorenzini, G., Klein, R.J., Zinani, F.F., Dos Santos, E.D., Isoldi, L.A., Rocha, L.A.O., Constructal Design Applied to Elliptic Tubes in Convective Heat Transfer Cross-flow of Viscoplastic Fluids, International Journal of Heat and Mass Transfer, 116, 2018, 1054-1063.
[46] Cetkin, E., Constructal Microdevice Manifold Design with Uniform Flow Rate Distribution by Consideration of the Tree-branching Rule of Leonardo da Vinci and Hess–Murray Rule, Journal of Heat Transfer, 139, 2017, 082401.
[47] Isoldi, L.A., Real, M.V., Correia, A.L.G., Vaz, J., Dos Santos, E.D., Rocha, L.A.O., Flow of Stresses: Constructal Design of Perforated Plates Subjected to Tension or Buckling, In: Rocha, L.A.O., Lorente, S., Bejan, A. (Ed.), Constructal Law and the Unifying Principle of Design - Understanding Complex Systems, Springer, New York, 2013.
[48] Mandal, N.R., Ship Construction and Welding, Springer, Singapore, 2017.
[49] Pinto, V. T., Cunha, M.L., Martins, K.L., Rocha, L.A.O., dos Santos, E.D., Isoldi, L.A., Bending of Stiffened Plates Considering Different Stiffeners Orientations, Magazine of Civil Engineering, 03(103), 2021. (in press)
[50] Cunha, M.L., Estrada, E.S.D., Lima, J.P.S., Troina, G.S., Dos Santos, E.D., Isoldi, L.A., Constructal Design Associated with Genetic Algorithm to Minimize the Maximum Deflection of Thin Stiffened Steel Plates, Heat Transfer, 49(7), 2020, 4040-4055.
Journal of Applied and Computational Mechanics
Volume 6, Special Issue
December 2020
Pages 1438-1449