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

M. Cinefra; S. Valvano; E. Carrera

Curved and Layered Structures (2015)

  • Volume: 2, Issue: 1
  • ISSN: 2353-7396

Abstract

top
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.

How to cite

top

M. Cinefra, S. Valvano, and E. Carrera. "Heat conduction and Thermal Stress Analysis of laminated composites by a variable kinematic MITC9 shell element." Curved and Layered Structures 2.1 (2015): null. <http://eudml.org/doc/276887>.

@article{M2015,
abstract = {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.},
author = {M. Cinefra, S. Valvano, E. Carrera},
journal = {Curved and Layered Structures},
keywords = {Fourier heat conduction equation; Calculated Thermal Profile; Thermal stress analysis; Finite Element Method; Mixed Interpolated Tensorial Components; Carrera’s Unified Formulation; Shell},
language = {eng},
number = {1},
pages = {null},
title = {Heat conduction and Thermal Stress Analysis of laminated composites by a variable kinematic MITC9 shell element},
url = {http://eudml.org/doc/276887},
volume = {2},
year = {2015},
}

TY - JOUR
AU - M. Cinefra
AU - S. Valvano
AU - E. Carrera
TI - Heat conduction and Thermal Stress Analysis of laminated composites by a variable kinematic MITC9 shell element
JO - Curved and Layered Structures
PY - 2015
VL - 2
IS - 1
SP - null
AB - 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.
LA - eng
KW - Fourier heat conduction equation; Calculated Thermal Profile; Thermal stress analysis; Finite Element Method; Mixed Interpolated Tensorial Components; Carrera’s Unified Formulation; Shell
UR - http://eudml.org/doc/276887
ER -

References

top
  1.  
  2. [1] T. Kant, R. K. Khare, Finite element thermal stress analysis of composite laminates using a higher-order theory, Journal of Thermal Stresses, 17(2) ()1994, 229–255. [Crossref] 
  3. [2] A. A. Khdeir, J. N. Reddy, Thermal stresses and deflections of cross-ply laminated plates using refined plate theories, Journal of Thermal Stresses, 14(4) (1991), 419–438. [Crossref] 
  4. [3] W. Zhen, C.Wanji, A global-local higher order theory for multilayered shells and the analysis of laminated cylindrical shell panels, Composite Structures, 84(4) (2008), 350–361. [Crossref] 
  5. [4] R. K. Khare, T. Kant, A. .K Garg, Closed-form thermo-mechanical solutions of higher-order theories of cross-ply laminated shallow shells, Composite Structures, 59(3) (2003), 313–340. [Crossref] 
  6. [5] A. A. Khdeir, Thermoelastic analysis of cross-ply laminated circular cylindrical shells, International Journal of Solids and Structures, 33(27) (1996), 4007–4017. Zbl0920.73253
  7. [6] A. A. Khdeir, M. D. Rajab, J. N. Reddy, Thermal effects on the response of cross-ply laminated shallow shells, International Journal of Solids and Structures, 29(5) (1992), 653–667. 
  8. [7] A. Barut, E. Madenci, A. Tessler, Nonlinear thermoelastic analysis of composite panels under non-uniform temperature distribution, International Journal of Solids and Structures, 37(27) (2000), 3681–3713. Zbl1090.74551
  9. [8] C. J. Miller, W. A. Millavec, T. P. Richer, Thermal stress analysis of layered cylindrical shells, AIAA Journal, 19(4) (1981), 523–530. [Crossref] Zbl0472.73005
  10. [9] P. C. Dumir, J. K. Nath, P. Kumari, S. Kapuria, Improved eflcient zigzag and third order theories for circular cylindrical shells under thermal loading, Journal of Thermal Stresses, 31(4) (2008), 343–367. [WoS][Crossref] 
  11. [10] Y. S. Hsu, J. N. Reddy, C. W. Bert, Thermoelasticity of circular cylindrical shells laminated of bimodulus composite materials, Journal of Thermal Stresses, 4(2) (1981), 155–177. [Crossref] 
  12. [11] K. Ding, Thermal stresses of weak formulation study for thick open laminated shell, Journal of Thermal Stresses, 31(4) (2008), 389–400. [Crossref] 
  13. [12] E. Carrera, Temperature profile influence on layered plates response considering classical and advanced theories, AIAA Journal, 40(9) (2002), 1885–1896. [Crossref] 
  14. [13] E. Carrera, An assessment of mixed and classical theories for the thermal stress analysis of orthotropic multilayered plates, Journal of Thermal Stresses, 23(9) (2000), 797–831. [Crossref] 
  15. [14] A. Robaldo, E. Carrera, Mixed finite elements for thermoelastic analysis of multilayered anisotropic plates, Journal of Thermal Stresses, 30 (2007), 165–194. [Crossref][WoS] 
  16. [15] P. Nali, E. Carrera, A. Calvi, Advanced fully coupled thermomechanical plate elements for multilayered structures subjected to mechanical and thermal loading, International Journal for Numerical Methods in Engineering, 85 (2011), 869–919. [WoS] Zbl1217.74131
  17. [16] E. Carrera, A. Ciuffreda, Closed-form solutions to assess multilayered-plate theories for various thermal stress problems, Journal of Thermal Stresses, 27 (2004), 1001–1031. [Crossref] 
  18. [17] E. Carrera, M. Cinefra, F. A. Fazzolari, Some results on thermal stress of layered plates and shells by using Unified Formulation, Journal of Thermal Stresses, 36 (2013), 589–625. [WoS][Crossref] 
  19. [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] 
  20. [19] F. A. Fazzolari, E. Carrera, Thermal stability of FGM sandwich plates under various through-the-thickness temperature distributions, Journal of Thermal Stresses, 37 (2014), 1449–1481. [Crossref][WoS] 
  21. [20] S. Brischetto, E. Carrera, Thermal stress analysis by refinedmultilayered composite shell theories, Journal of Thermal Stresses, 32(1-2) (2009), 165–186. [Crossref][WoS] 
  22. [21] S. Brischetto, E. Carrera, Heat conduction and thermal analysis in multilayered plates and shells, Mechanics Research Communications, 38 (2011), 449–455. [Crossref][WoS] Zbl1272.74129
  23. [22] M. Cinefra, E. Carrera, S. Brischetto, S. Belouettar, Thermomechanical analysis of functionally graded shells, Journal of Thermal Stresses, 33 (2010), 942–963. [Crossref] 
  24. [23] A. Robaldo, E. Carrera, A. Benjeddou, Unified formulation for finite element thermoelastic analysis of multilayered anisotropic composite plates, Journal of Thermal Stresses, 28 (2005), 1031– 1065. [Crossref][WoS] 
  25. [24] E. Carrera, Theories and finite elements for multilayered, anisotropic, composite plates and shells, Archives of Computational Methods in Engineering, 9(2) (2002), 87–140. [Crossref] Zbl1062.74048
  26. [25] E. Carrera, Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking, Archives of Computational Methods in Engineering, 10(3) (2003), 215–296. [Crossref] Zbl1140.74549
  27. [26] K. J. Bathe, P. S. Lee, J. F. Hiller, Towards improving the MITC9 shell element, Computers and Structures, 81 (2003), 477–489. 
  28. [27] C. Chinosi, L. Della Croce, Mixed-interpolated elements for thin shell, Communications in Numerical Methods in Engineering, 14 (1998), 1155–1170. Zbl0928.74097
  29. [28] N. C. Huang, Membrane locking and assumed strain shell elements, Computers and Structures, 27(5) (1987), 671–677. Zbl0623.73091
  30. [29] P. Panasz, K. Wisniewski, Nine-node shell elements with 6 dofs/node based on two-level approximations. Part I theory and linear tests, Finite Elements in Analysis and Design, 44 (2008), 784–796. 
  31. [30] A. W. Leissa, Vibration of shells, NASA National Aeronautics and Space Administration, Washington, DC, SP-288, 1973. 
  32. [31] E. Carrera, Multilayered shell theories accounting for layerwise mixed description, Part 1: governing equations, AIAA Journal, 37(9) (1999), 1107–1116. [Crossref] 
  33. [32] E. Carrera, Multilayered shell theories accounting for layerwise mixed description, Part 2: numerical evaluations, AIAA Journal, 37(9) (1999), 1117–1124. [Crossref] 
  34. [33] W. T. Koiter, On the foundations of the linear theory of thin elastic shell, Proc. Kon. Nederl. Akad. Wetensch., 73 (1970), 169–195. Zbl0213.27002
  35. [34] P. G. Ciarlet, L. Gratie, Another approach to linear shell theory and a new proof of Korn’s inequality on a surface, C. R. Acad. Sci. Paris, I,340 (2005), 471–478. Zbl1329.74176
  36. [35] P. M. Naghdi, The theory of shells and plates, Handbuch der Physic, 4 (1972), 425–640. 
  37. [36] M. Cinefra, E. Carrera, S. Valvano, Variable Kinematic Shell Elements for the Analysis of Electro-Mechanical Problems, Mechanics of AdvancedMaterials and Structures, 22(1-2) (2015), 77–106. 
  38. [37] H. Murakami, Laminated composite plate theory with improved in-plane responses, Journal of Applied Mechanics, 53 (1986), 661–666. [Crossref] Zbl0597.73069
  39. [38] J.N. Reddy, Mechanics of Laminated Composite Plates, Theory and Analysis, Journal of Applied Mechanics, CRC Press, 1997. Zbl0899.73002
  40. [39] K. J. Bathe, E. Dvorkin, A formulation of general shell elements - the use of mixed interpolation of tensorial components, International Journal for Numerical Methods in Engineering, 22 (1986), 697–722. Zbl0585.73123
  41. [40] M. L. Bucalem, E. Dvorkin, Higher-order MITC general shell elements. International Journal for Numerical Methods in Engineering, 36 (1993), 3729–3754. Zbl0800.73466
  42. [41] M. Cinefra, S. Valvano, A variable kinematic doubly-curved MITC9 shell element for the analysis of laminated composites, Mechanics of Advanced Materials and Structures, (in press). 
  43. [42] V. Tungikar, B. K. M. Rao, Three dimensional exact solution of thermal stresses in rectangular composite laminates, Composite Structures, 27(4) (1994), 419–430. [Crossref] 
  44. [43] K. Bhaskar, T. K. Varadan, J. S. M. Ali, Thermoelastic solutions for orthotropic and anisotropic composite laminates, Composites: Part B, 27(B) (1996), 415–420. 
  45. [44] T. J. R. Hughes, M. Cohen, M. Horaun, Reduced and selective integration techniques in the finite element methods, Nuclear Engineering and Design, 46 (1978), 203–222. [Crossref] 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.