Stiffeners Mechanical Effect Analysis by Numerical Coupling

Journal of Solid Mechanics

مقاله 15، دوره 12، شماره 2، شهریور 2020، صفحه 476-492   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.22034/jsm.2019.1876608.1482

نویسندگان

R Naceur Bouharkat¹؛ A Sahli^{* 1}؛ S Sahli²

¹Laboratoire de Recherche des Technologies Industrielles, Université Ibn Khaldoun de Tiaret , Département de Génie Mécanique, Route de zaroura , Algérie

²Université d'Oran 2 Mohamed Ben Ahmed, Algérie

چکیده

Given any structure, we seek to find the solution of mechanical problem as precisely and efficiently as possible. Within this condition, the BEM is robust and promising development, standing out in the analysis of cases with occurrence of large stress gradients, as in problems of fracture mechanics. Moreover, in BEM the modeling of infinite means is performed naturally, without the use of approximations. For methods involving domain integration, such as FEM, this is not possible, as models with high number of elements are usually adopted and their ends are considered flexible supports. This paper deals with the development of numerical models based on the BEM for mechanical analysis of stiffened domains. In the modeling of hardeners, immersed in a medium defined by the BEM, we tried to use both the FEM, already present in the literature, and the BEM 1D, being a new formulation. The objective was to perform the coupling of BEM with FEM and BEM 1D for elements of any degree of approximation, evaluating both isotropic and anisotropic medium. In addition, a complementary objective was to verify the effects of the adoption of different discretization and approximation degrees on the stiffeners. However, the coupling with the BEM 1D leaded to more stable results and better approximations. It was observed that the FEM results were instable for many results, mainly in the quadratic approximations. When the approximation degree rises, the methods tend to converge to equivalent results, becoming very close in fourth degree approximation. Lastly, it was observed stress concentration in the stiffeners ends. In these regions, the discretization and the approximation degree have large influence to the numerical response.                                

کلیدواژه‌ها

BEM؛ BEM/FEM coupling؛ BEM/BEM 1D coupling؛ Reinforced media؛ Stiffeners modelling

مراجع

[1] Barzegar F., Maddipudi S., 1994, Generating reinforcement in FE modelling of concrete structures, Journal of Structures Engineering 20(5): 1656-1662.
[2] Gomes H.M., Awruch A.M.S., 2001, Some aspects on three-dimensional numerical modelling of reinforced concrete structures using the finite element method, Advances in Engineering Software 32(4): 257-277.
[3] LE V., Anh et Royer J., 1996, Boundary formulation for three-dimensional anisotropic crack problems, Applied Mathematical Modelling 20(9): 662-674.
[4] Leonel E.D., 2006, Boundary Element Method Applied to Analysis of Multi-Fractured Solids, Sao Carlos, University of Sao Paulo.
[5] Leonel E.D., 2009, Nonlinear Boundary Element Method Models for Fracture Problem Analysis and Application of Reliability and Optimization Models in Fatigue Structures, São Carlos, Department of Structural Engineering.
[6] Oliveira Hugo Luiz et L., Edson D., 2013, Cohesive crack growth modelling based on an alternative nonlinear BEM formulation, Engineering Fracture Mechanics 111: 86-97.
[7] Oliveira Hugo Luiz et L., Edson D., 2013, Dual BEM formulation applied to analysis of multiple crack propagation, Key Engineering Materials 2013: 99-106.
[8] Nourine L., 2010, Boundary element method analysis of cracked anisotropic bodies, The Journal of Strain Analysis for Engineering Design 45: 45-56.
[9] Sahli A., 2014, Failure analysis of anisotropic plates by the boundary element method, Journal of Mechanics 30: 561-570.
[10] Sahli A., 2015, Effects of variation of material properties on the stress intensity factors of cracked anisotropic bodies, Matériaux & Techniques 103: 109.
[11] Debbagui S., Sahli A., Sahli S., 2017, Optimisation and failure criteria for composite materials by the bound-ary element method, Mechanics 23: 506-513.
[12] Kebdani S., Sahli A., Sahli S., 2018, Thermoelastic fracture parameters for anisotropic plates, Journal of Solid Mechanics 10: 435-449.
[13] Sahli A., Fatiha Arab M., Sahli S., 2019, Composite parameters analysis with boundary element method, Journal of Materials and Engineering Structures 5: 387-398.
[14] Kadri M., Sahli A., Sahli S., 2019, Fracture parameters for cracked cylindrical shells, Journal of Solid Mechanics 11: 91-104.
[15] Sahli A., Sahli S., Mechanical and structural reliability-based algorithm optimization, Journal of Materials and Engineering Structures 6: 215-232.
[16] Zienkiewicz O.C., Kelly D.W., Bettess P., 1977, The coupling of the finite element method and boundary solution procedures, International Journal for Numerical Methods in Engineering 11(2): 355-375.
[17] Shaw R.P., Falby W., 1978, FEBIE—a combined finite element-boundary integral equation method, Computers & Fluids 6(3): 153-160.
[18] Brebbia C.A., Georgiou P., 1979, Combination of boundary and finite elements in elastostatics, Applied Mathematical Modelling 3(3): 212-220.
[19] Wearing J. L., Burstow M. C., 1994, Elasto-plasticanalysis using a coupled boundary element finite element technique, Engineering Analysis with Boundary Elements 14(1): 39-49.
[20] Coda H.B., Venturini W.S., Aliabadi M. H., 1999, A general 3D BEM/FEM coupling applied to elastodynamic continua/frame structures interaction analysis, International Journal for Numerical Methods in Engineering 46(5): 695-712.
[21] Coda H.B., Venturini W.S., 1999, On the coupling of 3D BEM and FEM frame model applied to elastodynamic analysis, International Journal of Solids and Structures 36(31-32): 4789-4804.
[22] Elleithy W.M., Tanaka M., Guzik A., 2004, Interface relaxation FEM–BEM coupling method for elasto-plastic analysis, Engineering Analysis with Boundary Elements 28(7): 849-857.
[23] Ganguly S., Layton J.B., Balakrishna C., 2000, Symmetric coupling of multi‐zone curved Galerkin boundary elements with finite elements inelasticity, International Journal for Numerical Methods in Engineering 48(5): 633-654.
[24] Bia R.A., Ostrowski Z., Kassab A.J., Yin Q., Sciubba E., 2002, Coupling BEM, FEM and analytic solutions in steady-state potential problems, Engineering Analysis with Boundary Elements 26(7): 597-611.
[25] Coda H.B., 2001, Dynamic and static non-linear analysis of reinforced media: a BEM/FEM coupling approach, Computers & Structures 79(31): 2751-2765.
[26] Leite L.G., Coda H.B., Venturini W.S., 2003, Two-dimensional solids reinforced by thin bars using the boundary element method, Engineering Analysis with Boundary Elements 27(3): 193-201.
[27] Fernandes G.R., Venturini W. S., 2002, Non-linear boundary element analysis of plates applied to concreteslabs, Engineering Analysis with Boundary Elements 26(2): 169-181.
[28] Brebbia C.A., Domınguez J., 1992, Boundary Elements: An Introductory Course, Computational Mechanics Publications, McGraw Hill Company, London.
[29] Cruz J. M. F., 2012, Contribution to the Static and Dynamic Analysis of Frames by the Boundary Element Method, Federal University of Paraíba.