Bending analysis of laminated composite and sandwich beams according to refined trigonometric beam theory

A. S. Sayyad; Y. M. Ghugal; N. S. Naik

Curved and Layered Structures (2015)

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

Abstract

top
A trigonometric beam theory (TBT) is developed for the bending analysis of laminated composite and sandwich beams considering the effect of transverse shear deformation. The axial displacement field uses trigonometric function in terms of thickness coordinate to include the effect of transverse shear deformation. The transverse displacement is considered as a sum of two partial displacements, the displacement due to bending and the displacement due to transverse shearing. Governing equations and boundary conditions are obtained by using the principle of virtual work. To demonstrate the validity of present theory it is applied to the bending analysis of laminated composite and sandwich beams. The numerical results of displacements and stresses obtained by using present theory are presented and compared with those of other trigonometric theories available in literature along with elasticity solution wherever possible.

How to cite

top

A. S. Sayyad, Y. M. Ghugal, and N. S. Naik. "Bending analysis of laminated composite and sandwich beams according to refined trigonometric beam theory." Curved and Layered Structures 2.1 (2015): null. <http://eudml.org/doc/276823>.

@article{A2015,
abstract = {A trigonometric beam theory (TBT) is developed for the bending analysis of laminated composite and sandwich beams considering the effect of transverse shear deformation. The axial displacement field uses trigonometric function in terms of thickness coordinate to include the effect of transverse shear deformation. The transverse displacement is considered as a sum of two partial displacements, the displacement due to bending and the displacement due to transverse shearing. Governing equations and boundary conditions are obtained by using the principle of virtual work. To demonstrate the validity of present theory it is applied to the bending analysis of laminated composite and sandwich beams. The numerical results of displacements and stresses obtained by using present theory are presented and compared with those of other trigonometric theories available in literature along with elasticity solution wherever possible.},
author = {A. S. Sayyad, Y. M. Ghugal, N. S. Naik},
journal = {Curved and Layered Structures},
keywords = {bending; shear deformation; shear correction factor; shear stress; trigonometric; laminated; sandwich},
language = {eng},
number = {1},
pages = {null},
title = {Bending analysis of laminated composite and sandwich beams according to refined trigonometric beam theory},
url = {http://eudml.org/doc/276823},
volume = {2},
year = {2015},
}

TY - JOUR
AU - A. S. Sayyad
AU - Y. M. Ghugal
AU - N. S. Naik
TI - Bending analysis of laminated composite and sandwich beams according to refined trigonometric beam theory
JO - Curved and Layered Structures
PY - 2015
VL - 2
IS - 1
SP - null
AB - A trigonometric beam theory (TBT) is developed for the bending analysis of laminated composite and sandwich beams considering the effect of transverse shear deformation. The axial displacement field uses trigonometric function in terms of thickness coordinate to include the effect of transverse shear deformation. The transverse displacement is considered as a sum of two partial displacements, the displacement due to bending and the displacement due to transverse shearing. Governing equations and boundary conditions are obtained by using the principle of virtual work. To demonstrate the validity of present theory it is applied to the bending analysis of laminated composite and sandwich beams. The numerical results of displacements and stresses obtained by using present theory are presented and compared with those of other trigonometric theories available in literature along with elasticity solution wherever possible.
LA - eng
KW - bending; shear deformation; shear correction factor; shear stress; trigonometric; laminated; sandwich
UR - http://eudml.org/doc/276823
ER -

References

top
  1. [1] Timoshenko S.P., On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars, Philos. Mag., 1921, 41, 742–746. 
  2. [2] Levinson M., A New Rectangular Beam Theory, J. Sound Vib., 1981, 74, 81–87. [Crossref] Zbl0453.73058
  3. [3] Levinson M., On Bickford’s Consistent Higher Order Beam Theory, Mech. Res. Commun., 1985, 12, 1–9. Zbl0568.73064
  4. [4] Reddy J.N., Mechanics of laminated composite plates and shells: Theory and Analysis, 2nd ed., Boca Raton, FL: CRC Press, 2004. Zbl1075.74001
  5. [5] Krishna Murty A.V., Toward A Consistent Beam Theory, AIAA J., 1984, 22, 811–816. [Crossref] 
  6. [6] Ghugal Y.M., Shimpi R.P., A trigonometric shear deformation theory for flexure and free vibration of isotropic thick beams, Proceedings of Structural Engineering Convention (SEC−2000, IIT Bombay, India) 2000. 
  7. [7] Soldatos K.P., A Transverse Shear Deformation Theory for Homogeneous Monoclinic Plates, Acta Mech., 1992, 94, 195–200. [Crossref] Zbl0850.73130
  8. [8] Karama M., Afaq K.S., Mistou S., Mechanical Behaviour of Laminated Composite Beam by the New Multi-Layered Laminated Composite Structures Model with Transverse Shear Stress Continuity, Int. J. Solids Struct., 2003, 40, 1525–1546. [Crossref] Zbl1087.74579
  9. [9] Sayyad A.S., Comparison of Various Refined Beam Theories for the Bending and Free Vibration Analysis of Thick Beams, Appl. Comput. Mech., 2011, 5, 217–230. 
  10. [10] Sayyad A.S., Ghugal Y.M., Borkar R.R., Flexural Analysis of Fibrous Composite Beams under Various Mechanical Loadings using Refined Shear Deformation Theories, Compos.: Mech. Comput. App. An Int. J., 2014, 5(1), 1–19. 
  11. [11] Vo T.P., Thai H.T., Static Behaviour of Composite Beams using Various Refined Shear Deformation Theories, Compos. Struct., 2012, 94(8), 2513–2522. 
  12. [12] Chakrabarti A., Chalak H.D., Iqbal M.A., Sheikh A.H., A New FE Model Based on Higher Order Zigzag Theory for the Analysis of Laminated Sandwich Beam with Soft Core, Compos. Struct., 2011, 93, 271–279. 
  13. [13] Aguiar R.M., Moleiro F., Soares C.M.M., Assessment of Mixed and Displacement-Based Models for Static Analysis of Composite Beams of Different Cross-Sections, Compos. Struct., 2012, 94, 601–616. 
  14. [14] Onate E., Eijo A., Oller S., Simple and Accurate Two-Noded Beam Element for Composite Laminated Beams using a Refined Zigzag Theory, Comput. Methods Appl. M., 2012, 213-216, 362– 382. [WoS] 
  15. [15] Tessler A., Di Sciuva M., Gherlone M., A Refined Zigzag Beam Theory for Composite and Sandwich Beams, J. Compos. Mater., 2009, 43, 1051–1081. [Crossref] 
  16. [16] Carrera E., Giunta G., Refined Beam Theories Based on a Unified Formulation, Int. J. Appl. Mech., 2010, 2, 117-43. [Crossref] 
  17. [17] Carrera E., Giunta G., Nali P., Petrolo M., Refined Beam Elements with Arbitrary Cross-Section Geometries, Comput. Struct., 2010, 88, 283-93. [WoS][Crossref] 
  18. [18] Wanji C., Zhen W., A New Higher-Order Shear Deformation Theory and Refined Beam Element of Composite Laminates, Acta Mech. Sinica, 2005, 21, 65–69. [Crossref] Zbl1200.74088
  19. [19] Kapuria S., Dumir P.C., Jain N.K., Assessment of Zigzag Theory for Static Loading, Buckling, Free and Forced Response of Composite and Sandwich Beams, Compos. Struct., 2004, 64, 317– 327. 
  20. [20] Catapano A., Giunta G., Belouettar S., Carrera E., Static Analysis of Laminated Beams via a Unified Formulation, Compos. Struct., 2011, 94, 75–83. 
  21. [21] Icardi U., A Three Dimensional Zig-Zag Theory for Analysis of Thick Laminated Beams, Compos. Struct., 2001, 52, 123–135. 
  22. [22] Subramanian P., Flexural Analysis of Symmetric Laminated Composite Beams Using C1 Finite Element, Compos. Struct., 2001, 54, 121-126. 
  23. [23] Reddy J.N., Nonlocal Theories for Bending, Buckling and Vibration of Beams, Int. J. Eng. Sci., 2007, 45, 288–307. [Crossref][WoS] Zbl1213.74194
  24. [24] Goyal V.K., Kapania R.K., A Shear-Deformable Beam Element for the Analysis of Laminated Composites, Finite Elem. Anal. Des., 2007, 43, 463 – 477. [WoS] 
  25. [25] Wanji C., Li L., Xu M., A Modified Couple Stress Model for Bending Analysis of Composite Laminated Beams with First Order Shear Deformation, Compos. Struct., 2011, 93, 2723–2732. 
  26. [26] Shi G., Voyiadjis G.Z., A Sixth-Order Theory of Shear Deformable Beams with Variational Consistent Boundary Conditions, J. Appl. Mech., 2011, 78, 1 -11. [Crossref][WoS] 
  27. [27] Tornabene F., Fantuzzi N., Viola E., Carrera E., Static Analysis of Doubly-Curved Anisotropic Shells and Panels using CUF Approach, Differential Geometry and Differential Quadrature Method, Compos. Struct., 2014, 107, 675 – 697. 
  28. [28] Pagani A., Carrera E., Banerjee J.R., Cabral P.H., Caprio G., Prado A., Free Vibration Analysis of Composite Plates by Higher- Order 1D Dynamic Stiffness Elements and Experiments, Compos. Struct., 2014, 118, 654–663. 
  29. [29] Pagani A., Carrera E., Boscolo M., Banerjee J.R., Refined Dynamic Stiffness Elements Applied to Free Vibration Analysis of Generally Laminated Composite Beamswith Arbitrary Boundary Conditions, Compos. Struct., 2014, 110, 305–316. 
  30. [30] Viola E., Tornabene F., Fantuzzi N., Static Analysis of Completely Doubly-Curved Laminated Shells and Panels using General Higher-Order Shear Deformation Theories, Compos. Struct., 2013, 101, 59–93. 
  31. [31] Viola E., Rossetti L., Fantuzzi N., Tornabene F., Static Analysis of Functionally Graded Conical Shells and Panels using the Generalized Unconstrained Third Order Theory Coupled with the Stress Recovery, Compos. Struct., 2014, 112, 44–65. 
  32. [32] Natarajan S., Ferreira A.J.M., Xuan H.N., Analysis of Cross-Ply Laminated Plates using Isogeometric Analysis and Unified Formulation, Curved and Layer. Struct., 2014, 1, 1–10. 
  33. [33] Mohazzab A.H., Dozio L., Prediction of natural frequencies of laminated curved panels using refined 2-D theories in the spectral collocation method, Curved and Layer. Struct., 2015, 2, 1–14. 
  34. [34] Arya H., Shimpi R.P., Naik N.K., A Zigzag Model for Laminated Composite Beams, Compos. Struct., 2002, 56, 21–24. 
  35. [35] Sayyad A.S., Ghugal Y.M., Effect of Transverse Shear and Transverse Normal Strain on Bending Analysis of Cross-Ply Laminated Beams, Int. J. Appl. Math. Mech., 2011, 7(12), 85-118. Zbl05999049
  36. [36] Shimpi R.P., Ghugal Y.M., A Layerwise Trigonometric Shear Deformation Theory for Two Layered Cross-Ply Laminated Beams, J. Reinf. Plast. Compos., 1999, 18, 1516–1543. 
  37. [37] Ghugal Y.M., Shinde S.B., Flexural Analysis of Cross-Ply Laminated Beams using Layerwise Trigonometric Shear Deformation Theory, Lat. Am. J. Solids Struct., 2013, 10, 675 – 705. [WoS][Crossref] 
  38. [38] Kant T., Manjunatha B.S., On Accurate Estimation of Transverse Stresses in Multilayer Laminates, Comput. Struct. 1994, 50(3), 351-365. [Crossref] 
  39. [39] Pagano N., Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates, J. Compos.Mater. 1970, 4, 20–34. 

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.