Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2015 | 2 | 1 |
Tytuł artykułu

Heat conduction and Thermal Stress Analysis of laminated composites by a variable kinematic MITC9 shell element

Treść / Zawartość
Warianty tytułu
Języki publikacji
The present paper considers the linear static thermal stress analysis of composite structures by means of a shell finite element with variable through-thethickness kinematic. The temperature profile along the thickness direction is calculated by solving the Fourier heat conduction equation. The refined models considered are both Equivalent Single Layer (ESL) and Layer Wise (LW) and are grouped in the Unified Formulation by Carrera (CUF). These permit the distribution of displacements, stresses along the thickness of the multilayered shell to be accurately described. The shell element has nine nodes, and the Mixed Interpolation of Tensorial Components (MITC) method is used to contrast the membrane and shear locking phenomenon. The governing equations are derived from the Principle of Virtual Displacement (PVD). Cross-ply plate, cylindrical and spherical shells with simply-supported edges and subjected to bi-sinusoidal thermal load are analyzed.Various thickness ratios and curvature ratios are considered. The results, obtained with different theories contained in the CUF, are compared with both the elasticity solutions given in the literature and the analytical solutions obtained using the CUF and the Navier’s method. Finally, plates and shells with different lamination and boundary conditions are analyzed using high-order theories in order to provide FEM benchmark solutions.
Opis fizyczny
  • Department of Aeronautics
    and Space Engineering, Politecnico di Torino, Corso Duca degli
    Abruzzi, 24, 10129 Turin, Italy
  • Department of Aeronautics
    and Space Engineering, Politecnico di Torino, Corso Duca degli
    Abruzzi, 24, 10129 Turin, Italy
  • Department of Aeronautics
    and Space Engineering, Politecnico di Torino, Corso Duca degli
    Abruzzi, 24, 10129 Turin, Italy
  • ---
  • [1] T. Kant, R. K. Khare, Finite element thermal stress analysis of compositelaminates using a higher-order theory, Journal of ThermalStresses, 17(2) ()1994, 229–255.[Crossref]
  • [2] A. A. Khdeir, J. N. Reddy, Thermal stresses and deflections ofcross-ply laminated plates using refined plate theories, Journalof Thermal Stresses, 14(4) (1991), 419–438.[Crossref]
  • [3] W. Zhen, C.Wanji, A global-local higher order theory for multilayeredshells and the analysis of laminated cylindrical shell panels,Composite Structures, 84(4) (2008), 350–361.[Crossref]
  • [4] R. K. Khare, T. Kant, A. .K Garg, Closed-form thermo-mechanicalsolutions of higher-order theories of cross-ply laminated shallowshells, Composite Structures, 59(3) (2003), 313–340.[Crossref]
  • [5] A. A. Khdeir, Thermoelastic analysis of cross-ply laminated circularcylindrical shells, International Journal of Solids and Structures,33(27) (1996), 4007–4017.
  • [6] A. A. Khdeir, M. D. Rajab, J. N. Reddy, Thermal effects on the responseof cross-ply laminated shallow shells, International Journalof Solids and Structures, 29(5) (1992), 653–667.
  • [7] A. Barut, E. Madenci, A. Tessler, Nonlinear thermoelastic analysisof composite panels under non-uniform temperature distribution,International Journal of Solids and Structures, 37(27)(2000), 3681–3713.
  • [8] C. J. Miller, W. A. Millavec, T. P. Richer, Thermal stress analysis oflayered cylindrical shells, AIAA Journal, 19(4) (1981), 523–530.[Crossref]
  • [9] P. C. Dumir, J. K. Nath, P. Kumari, S. Kapuria, Improved eflcientzigzag and third order theories for circular cylindrical shells underthermal loading, Journal of Thermal Stresses, 31(4) (2008),343–367.[WoS][Crossref]
  • [10] Y. S. Hsu, J. N. Reddy, C. W. Bert, Thermoelasticity of circularcylindrical shells laminated of bimodulus composite materials,Journal of Thermal Stresses, 4(2) (1981), 155–177.[Crossref]
  • [11] K. Ding, Thermal stresses of weak formulation study for thickopen laminated shell, Journal of Thermal Stresses, 31(4) (2008),389–400.[Crossref]
  • [12] E. Carrera, Temperature profile influence on layered plates responseconsidering classical and advanced theories, AIAA Journal,40(9) (2002), 1885–1896.[Crossref]
  • [13] E. Carrera, An assessment of mixed and classical theories for thethermal stress analysis of orthotropic multilayered plates, Journalof Thermal Stresses, 23(9) (2000), 797–831.[Crossref]
  • [14] A. Robaldo, E. Carrera, Mixed finite elements for thermoelasticanalysis of multilayered anisotropic plates, Journal of ThermalStresses, 30 (2007), 165–194.[Crossref][WoS]
  • [15] P. Nali, E. Carrera, A. Calvi, Advanced fully coupled thermomechanicalplate elements for multilayered structures subjectedto mechanical and thermal loading, International Journal for NumericalMethods in Engineering, 85 (2011), 869–919.[WoS]
  • [16] E. Carrera, A. Ciuffreda, Closed-form solutions to assessmultilayered-plate theories for various thermal stress problems,Journal of Thermal Stresses, 27 (2004), 1001–1031.[Crossref]
  • [17] E. Carrera, M. Cinefra, F. A. Fazzolari, Some results on thermalstress of layered plates and shells by using Unified Formulation,Journal of Thermal Stresses, 36 (2013), 589–625.[WoS][Crossref]
  • [18] S. Brischetto, R. Leetsch, E. Carrera, T. Wallmersperger, B. Kröplin,Thermo-mechanical bending of functionally graded plates,Journal of Thermal Stresses, 31(3) (2008), 286–308.[WoS][Crossref]
  • [19] F. A. Fazzolari, E. Carrera, Thermal stability of FGM sandwichplates under various through-the-thickness temperature distributions,Journal of Thermal Stresses, 37 (2014), 1449–1481.[Crossref][WoS]
  • [20] S. Brischetto, E. Carrera, Thermal stress analysis by refinedmultilayeredcomposite shell theories, Journal of Thermal Stresses,32(1-2) (2009), 165–186.[Crossref][WoS]
  • [21] S. Brischetto, E. Carrera, Heat conduction and thermal analysisin multilayered plates and shells, Mechanics Research Communications,38 (2011), 449–455.[Crossref][WoS]
  • [22] M. Cinefra, E. Carrera, S. Brischetto, S. Belouettar, Thermomechanicalanalysis of functionally graded shells, Journal ofThermal Stresses, 33 (2010), 942–963.[Crossref]
  • [23] A. Robaldo, E. Carrera, A. Benjeddou, Unified formulation forfinite element thermoelastic analysis of multilayered anisotropiccomposite plates, Journal of Thermal Stresses, 28 (2005), 1031–1065.[Crossref][WoS]
  • [24] E. Carrera, Theories and finite elements for multilayered,anisotropic, composite plates and shells, Archives of ComputationalMethods in Engineering, 9(2) (2002), 87–140.[Crossref]
  • [25] E. Carrera, Theories and finite elements for multilayered platesand shells: a unified compact formulation with numerical assessmentand benchmarking, Archives of Computational Methods inEngineering, 10(3) (2003), 215–296.[Crossref]
  • [26] K. J. Bathe, P. S. Lee, J. F. Hiller, Towards improving the MITC9shell element, Computers and Structures, 81 (2003), 477–489.
  • [27] C. Chinosi, L. Della Croce, Mixed-interpolated elements for thinshell, Communications in Numerical Methods in Engineering, 14(1998), 1155–1170.
  • [28] N. C. Huang, Membrane locking and assumed strain shell elements,Computers and Structures, 27(5) (1987), 671–677.
  • [29] P. Panasz, K. Wisniewski, Nine-node shell elements with 6dofs/node based on two-level approximations. Part I theory andlinear tests, Finite Elements in Analysis and Design, 44 (2008),784–796.
  • [30] A. W. Leissa, Vibration of shells, NASA National Aeronauticsand Space Administration, Washington, DC, SP-288, 1973.
  • [31] E. Carrera, Multilayered shell theories accounting for layerwisemixed description, Part 1: governing equations, AIAA Journal,37(9) (1999), 1107–1116.[Crossref]
  • [32] E. Carrera, Multilayered shell theories accounting for layerwisemixed description, Part 2: numerical evaluations, AIAA Journal,37(9) (1999), 1117–1124.[Crossref]
  • [33] W. T. Koiter, On the foundations of the linear theory of thin elasticshell, Proc. Kon. Nederl. Akad. Wetensch., 73 (1970), 169–195.
  • [34] P. G. Ciarlet, L. Gratie, Another approach to linear shell theoryand a new proof of Korn’s inequality on a surface, C. R. Acad. Sci.Paris, I,340 (2005), 471–478.
  • [35] P. M. Naghdi, The theory of shells and plates, Handbuch derPhysic, 4 (1972), 425–640.
  • [36] M. Cinefra, E. Carrera, S. Valvano, Variable Kinematic Shell Elementsfor the Analysis of Electro-Mechanical Problems, Mechanicsof AdvancedMaterials and Structures, 22(1-2) (2015), 77–106.
  • [37] H. Murakami, Laminated composite plate theory with improvedin-plane responses, Journal of Applied Mechanics, 53 (1986),661–666.[Crossref]
  • [38] J.N. Reddy, Mechanics of Laminated Composite Plates, Theoryand Analysis, Journal of Applied Mechanics, CRC Press, 1997.
  • [39] K. J. Bathe, E. Dvorkin, A formulation of general shell elements -the use of mixed interpolation of tensorial components, InternationalJournal for Numerical Methods in Engineering, 22 (1986),697–722.
  • [40] M. L. Bucalem, E. Dvorkin, Higher-order MITC general shell elements.International Journal for Numerical Methods in Engineering,36 (1993), 3729–3754.
  • [41] M. Cinefra, S. Valvano, A variable kinematic doubly-curvedMITC9 shell element for the analysis of laminated composites,Mechanics of Advanced Materials and Structures, (in press).
  • [42] V. Tungikar, B. K. M. Rao, Three dimensional exact solution ofthermal stresses in rectangular composite laminates, CompositeStructures, 27(4) (1994), 419–430.[Crossref]
  • [43] K. Bhaskar, T. K. Varadan, J. S. M. Ali, Thermoelastic solutionsfor orthotropic and anisotropic composite laminates, Composites:Part B, 27(B) (1996), 415–420.
  • [44] T. J. R. Hughes, M. Cohen, M. Horaun, Reduced and selectiveintegration techniques in the finite element methods, NuclearEngineering and Design, 46 (1978), 203–222.[Crossref]
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.