178
Views
36
CrossRef citations to date
0
Altmetric
Original Articles

A variable kinematic shell formulation applied to thermal stress of laminated structures

&
Pages 803-827 | Received 18 Oct 2016, Accepted 23 Oct 2016, Published online: 30 Nov 2016

References

  • J. N. Reddy and D. H. Robbins, Theories and Computational Models for Composite Laminates, Appl. Mech. Rev., vol. 47, pp. 147–165, 1994.
  • T. K. Varadan and K. Bhaskar, Review of Different Theories for the Analysis of Composites, J. Aerosp. Soc. India, vol. 49, pp. 202–208, 1997.
  • E. Carrera, Developments, Ideas and Evaluation Based Upon Reissner’s Mixed Variational Theorem in the Modeling of Multilayered Plates and Shells, Appl. Mech. Rev., vol. 54, pp. 301–329, 2001.
  • T. Kant and R. K. Khare, Finite Element Thermal Stress Analysis of Composite Laminates Using a Higher-Order Theory, J. Thermal Stresses, vol. 17, no. 2, pp. 229–255, 1994.
  • A. A. Khdeir and J. N. Reddy, Thermal Stresses and Deflections of Cross-Ply Laminated Plates Using Refined Plate Theories, J. Thermal Stresses, vol. 14, no. 4, pp. 419–438, 1991.
  • W. Zhen and C. Wanji, A Global-Local Higher Order Theory for Multilayered Shells and the Analysis of Laminated Cylindrical Shell Panels, Compos. Struct., vol. 84, no. 4, pp. 350–361, 2008.
  • K. R. Khare, T. Kant, and A. K. Garg, Closed-Form Thermo-Mechanical Solutions of Higher-Order Theories of Cross-Ply Laminated Shallow Shells, Compos. Struct., vol. 59, pp. 313–340, 2003.
  • A. A. Khdeir, Thermoelastic Analysis of Cross-Ply Laminated Circular Cylindrical Shells, Int. J. Solids Struct., vol. 33, no. 27, pp. 4007–4017, 1996.
  • A. A. Khdeir, M. B. Rajab, and J. N. Reddy, Thermal Effects on the Response of Cross-Ply Laminated Shallow Shells, Int. J. Solids Struct., vol. 29, no. 5, pp. 653–667, 1992.
  • A. Barut, E. Madenci, and A. Tessler, Nonlinear Thermoelastic Analysis of Composite Panels under Non-Uniform Temperature Distribution, Int. J. Solids Struct., vol. 37, no. 27, pp. 3681–3713, 2000.
  • C. J. Miller, W. A. Millavec, and T. P. Richer, Thermal Stress Analysis of Layered Cylindrical Shells, AIAA J., vol. 19, no. 4, pp. 523–530, 1981.
  • P. C. Dumir, J. K. Nath, P. Kumari, and S. Kapuria, Improved Efficient Zigzag and Third Order Theories for Circular Cylindrical Shells under Thermal Loading, J. Thermal Stresses, vol. 31, no. 4, pp. 343–367, 2008.
  • Y. S. Hsu, J. N. Reddy, and C. W. Bert, Thermoelasticity of Circular Cylindrical Shells Laminated of Bimodulus Composite Materials, J. Thermal Stresses, vol. 4, no. 2, pp. 155–177, 1981.
  • K. Ding, Thermal Stresses of Weak Formulation Study for Thick Open Laminated Shell, J. Thermal Stresses, vol. 31, no. 4, pp. 389–400, 2008.
  • A. S. D. Wang and F. W. Crossman, Calculation of Edge Stresses in Multi-Layer by Sub-Structuring, J. Compos. Mater., vol. 12, pp. 76–83, 1978.
  • N. J. Pagano and S. R. Soni, Global-Local Laminate Variational Model, Int. J. Solids Struct., vol. 19, no. 3, pp. 207–228, 1983.
  • R. Jones, R. Callinan, K. K. Teh, and K. C. Brown, Analysis of Multi-Layer Laminates Using Three-Dimensional Super Elements, Int. J. Numer. Meth. Eng., vol. 20, no. 3, pp. 583–587, 1984.
  • A. Pagani, S. Valvano, and E. Carrera, Analysis of Laminated Composites and Sandwich Structures by Variable-Kinematic MITC9 Plate Elements, J. Sandw. Struct. Mater. doi: 10.1177/1099636216650988
  • E. Carrera, A. Pagani, and S. Valvano, Shell Elements with Through-the-Thickness Variable Kinematics for the Analysis of Laminated Composite and Sandwich Structures (submitted).
  • M. Botshekanan, Dehkordi, M. Cinefra, S. M. R. Khalili, and E. Carrera, Mixed LW/ESL Models for the Analysis of Sandwich Plates with Composite Faces, Compos. Struct., vol. 98, pp. 330–339, 2013.
  • M. Botshekanan, Dehkordi, S. M. R. Khalili, and E. Carrera, Non-Linear Transient Dynamic Analysis of Sandwich Plate with Composite Face-Sheets Embedded with Shape Memory Alloy Wires and Flexible Core- Based on the Mixed LW (Layer-wise)/ESL (Equivalent Single Layer) Models, Compos. Part B Eng., vol. 87, pp. 59–74, 2016.
  • E. Carrera, Theories and Finite Elements for Multilayered, Anisotropic, Composite Plates and Shells, Arch. Comput. Method. Eng., vol. 9, no. 2, pp. 87–140, 2002.
  • E. Carrera, Theories and Finite Elements for Multilayered Plates and Shells: a Unified Compact Formulation with Numerical Assessment and Benchmarking, Arch. Comput. Method. Eng., vol. 10, no. 3, pp. 215–296, 2003.
  • E. Carrera, Temperature Profile Influence on Layered Plates Response Considering Classical and Advanced Theories, AIAA J., vol. 40, no. 9, pp. 1885–1896, 2002.
  • P. Nali, E. Carrera, and A. Calvi, Advanced Fully Coupled Thermo-Mechanical Plate Elements for Multilayered Structures Subjected to Mechanical and Thermal Loading, Int. J. Numer. Meth. Eng., vol. 85, pp. 869–919, 2011.
  • E. Carrera and A. Ciuffreda, Closed-Form Solutions to Assess Multilayered-Plate Theories for Various Thermal Stress Problems, J. Thermal Stresses, vol. 27, pp. 1001–1031, 2004.
  • E. Carrera, An Assessment of Mixed and Classical Theories for the Thermal Stress Analysis of Orthotropic Multilayered Plates, J. Thermal Stresses, vol. 23, no. 9, pp. 797–831, 2000.
  • A. Robaldo and E. Carrera, Mixed Finite Elements for Thermoelastic Analysis of Multilayered Anisotropic Plates, J. Thermal Stresses, vol. 30, pp. 165–194, 2007.
  • S. Brischetto, R. Leetsch, E. Carrera, T. Wallmersperger, and B. Kröplin, Thermo-Mechanical Bending of Functionally Graded Plates, J. Thermal Stresses, vol. 31, no. 3, pp. 286–308, 2008.
  • S. Brischetto and E. Carrera, Thermal Stress Analysis by Refined Multilayered Composite Shell Theories, J. Thermal Stresses, vol. 32, pp. 165–186, 2009.
  • S. Brischetto and E. Carrera, Heat Conduction and Thermal Analysis in Multilayered Plates and Shells, Mech. Res. Commun., vol. 38, pp. 449–455, 2011.
  • M. Cinefra, E. Carrera, S. Brischetto, and S. Belouettar, Thermo-Mechanical Analysis of Functionally Graded Shells, J. Thermal Stresses, vol. 33, pp. 942–963, 2010.
  • K. J. Bathe and E. Dvorkin, A Formulation of General Shell Elements - The Use of Mixed Interpolation of Tensorial Components, Int. J. Numer. Meth. Eng., vol. 22, pp. 697–722, 1986.
  • K. J. Bathe and F. Brezzi, A Simplified Analysis of Two Plate Bending Elements-the MITC4 and MITC9 Elements, Proceedings of the International Conference on Numerical Methods in Engineering: Theory and Applications, NUMETA ’87, Swansea, 6–10 July, 1987.
  • K. J. Bathe, P. S. Lee, and J. F. Hiller, Towards Improving the MITC9 Shell Element, Comput. Struct., vol. 81, pp. 477–489, 2003.
  • N. C. Huang, Membrane Locking and Assumed Strain Shell Elements, Comput. Struct., vol. 27, no. 5, pp. 671–677, 1987.
  • M. Cinefra, S. Valvano, and E. Carrera, Heat Conduction and Thermal Stress Analysis of Laminated Composites by a Variable Kinematic MITC9 Shell Element, Curve. Layer. Struct., vol. 1, pp. 301–320, 2015.
  • M. Cinefra, E. Carrera, and S. Valvano, Variable Kinematic Shell Elements for the Analysis of Electro-Mechanical Problems, Mech. Adv. Mater. Struct., vol. 22, no. 1-2, pp. 77–106, 2015.
  • M. Cinefra, S. Valvano, and E. Carrera, A Layer-Wise MITC9 Finite Element for the Free-Vibration Analysis of Plates with Piezo-Patches, Int. J. Smart Nano Mater., vol. 6, no. 2, pp. 85–104, 2015.
  • E. Carrera, Multilayered Shell Theories Accounting for Layerwise Mixed Description, Part 1: Governing Equations, AIAA J., vol. 37, no. 9, pp. 1107–1116, 1999.
  • E. Carrera, Multilayered Shell Theories Accounting for Layerwise Mixed Description, Part 2: Numerical Evaluations, AIAA J., vol. 37, no. 9, pp. 1117–1124, 1999.
  • H. Murakami, Laminated Composite Plate Theory with Improved In-Plane Responses, J. Appl. Mech., vol. 53, pp. 661–666, 1986.
  • J. N. Reddy, Mechanics of Laminated Composite Plates and Shells, Theory and Analysis, CRC Press, Boca Raton, Florida, 1997.
  • J. N. Reddy, An Evaluation of Equivalent-Single-Layer and Layerwise Theories of Composite Laminates, Compos. Struct., vol. 25, pp. 21–35, 1993.
  • T. J. R. Hughes, M. Cohen, and M. Horaun, Reduced and Selective Integration Techniques in the Finite Element Methods, Nucl. Eng. Des., vol. 46, pp. 203–222, 1978.
  • M. Cinefra and S. Valvano, A Variable Kinematic Doubly-Curved MITC9 Shell Element for the Analysis of Laminated Composites, Mech. Adv. Mater. Struct., vol. 23, no. 11, pp. 1312–1325, 2016.
  • M. Cinefra, S. Valvano, and E. Carrera, Thermal Stress Analysis of Laminated Structures by a Variable Kinematic MITC9 Shell Element, J. Thermal Stresses, vol. 39, no. 2, pp. 121–141, 2016.
  • V. Tungikar and B. K. M. Rao, Three Dimensional Exact Solution of Thermal Stresses in Rectangular Composite Laminates, Compos. Struct., vol. 27, no. 4, pp. 419–430, 1994.
  • K. Bhaskar, T. K. Varadan, and J. S. M. Ali, Thermoelastic Solutions for Orthotropic and Anisotropic Composite Laminates, Compos. Part B Eng., vol. 27, no. 5, pp. 415–420, 1996.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.