Buckling Analysis of Variable Stiffness Composite Laminates by Semi-Analytical Finite Strip Method
Authors
Abstract
Plates made of laminated composite materials with variable stiffness can have wide applications in various branches of engineering due to such advantages as high strength /stiffness to weight ratio. In these composites, curved fibers are used to reinforce each lamina instead of the straight fibers. In this paper, the application of finite strip method for the buckling analysis of moderately thick composite plates with variable stiffness is investigated. For buckling analysis, a semi-analytical finite strip method based on the first-order shear deformation theory is employed. In this method, all displacements are presumed by the appropriate harmonic shape functions in the longitudinal direction and polynomial interpolation functions in the transverse direction. The minimum potential energy method has been used to develop the stability formulations. This analysis examines the effect of using curved fibers instead of straight fibers on the laminate composites. The critical loads obtained from this analysis are compared with those of other researchers and the efficiency and accuracy of the developed finite strip method are confirmed. Comparison of the analysis results of these plates shows that changing the slope of the fibers can lead to a significant change in the buckling response. Also, increasing the number of the terms of shape functions in the longitudinal direction has a significant effect on the convergence to the desired results.
Keywords
1. Wang, S., and Dawe, D. J., “Spline Finite Strip Analysis of the Buckling and Vibration of Composite Prismatic Plate Structures”, International Journal of Mechanical Sciences, Vol. 39, No. 10, pp. 1161-1180, 1997.
2. Lam, S. S. E., and Zou, G. P., “Higher-Order Shear Deformable Finite Strip for the Flexure Analysis of Composite Laminates”, Engineering Structures, Vol. 23, No. 2, pp. 198-206, 2001.
3. Hatami, S., Azhari, M., and Saadatpour, M. M., “Stability and Vibration of Elastically Supported, Axially Moving Orthotropic Plates”, Iranian Journal of Science and Technology, Transaction B, Engineering, Vol. 30, No. B4, pp. 427-446, 2006.
4. Hatami, S., Azhari, M., and Saadatpour, M. M., “Free Vibration of Moving Laminated Composite Plates”, Composite Structures, Vol. 80, No. 4, pp. 609-620, 2007.
5. Ovesy, H. R., and Fazilati, J., “Buckling and Free Vibration Finite Strip Analysis of Composite Plates with Cutout Based on Two Different Modeling Approaches”, Composite Structures, Vol. 94, No. 3, pp. 1250-1258, 2012.
6. Daraei, B., and Hatami, S., “Free Vibration Analysis of Variable Stiffness Composite Laminates with Flat and Folded Shapes”, Journal of Solid Mechanics, Vol. 8, No. 3, pp. 662-678, 2016.
7. Fazilati, J., “Stability Analysis of Variable Stiffness Composite Laminated Plates with Delamination Using Spline-FSM”, Latin American Journal of Solids and Structures, Vol. 14, No. 3, pp. 528-543, 2017.
8. Hyer, M. W. and Lee, H. H., “The Use of Curvilinear Fiber Format to Improve Buckling Resistance of Composite Plates with Central Circular Holes”, Composite structures, Vol. 18, No.3, pp. 239-261, 1991.
9. Waldhart, C., “Analysis of Tow-Placed, Variable-Stiffness Laminates”, Master’s Thesis, Virginia Polytechnic Institute and State University, Blacksburg, 1996.
10. Langley, P. T., “Finite Element Modeling of Tow-Placed Variable-Stiffness Composite Laminates”, Master’s Thesis, Virginia Polytechnic Institute and State University, Blacksburg, 1999.
11. Tatting, B. F. and Gürdal, Z., “Design and Manufacture of Elastically Tailored Tow Placed Plates”, NASA/CR-2002–211919, 2002.
12. Tatting, B. F. and Guerdal, Z., “Automated Finite Element Analysis of Elastically-Tailored Plates”, NASA/CR-2003-212679, 2003.
13. Gürdal, Z., Tatting, B. F. and Wu, C. K., “Variable Stiffness Composite Panels: Effects of Stiffness Variation on the in-Plane and Buckling Response”, Composites Part A: Applied Science and Manufacturing, Vol. 39, No. 5, pp. 911-922, 2008.
14. Lopes, C. S., Gürdal, Z. and Camanho, P. P., “Variable-Stiffness Composite Panels: Buckling and First-Ply Failure Improvements over Straight-Fibre Laminates”, Computers and Structures, Vol. 86, No.9, pp. 897-907, 2008.
15. Lopes, C. S., Gürdal, Z. and Camanho, P. P., “Tailoring for Strength of Composite Steered-Fibre Panels with Cutouts”, Composites Part A: Applied Science and Manufacturing, Vol. 41, No. 12, pp. 1760-1767, 2010.
16. Wu, Z., Raju, G. and Weaver, P. M., “Postbuckling Analysis of Variable Angle Tow Composite Plates”, International Journal of Solids and Structures, Vol. 50, No. 10, pp. 1770-1780, 2013.
17. Akbarzadeh, A. H., Nik, M. A. and Pasini, D., “The Role of Shear Deformation in Laminated Plates with Curvilinear Fiber Paths and Embedded Defects”, Composite Structures, Vol. 118, pp. 217-227, 2014.
18. Yazdani, S., Rust, W. J. and Wriggers, P., “Delamination Growth in Composite Laminates of Variable Stiffness”, International Journal for Numerical Methods in Engineering, Vol. 108, No. 11, pp. 1406-1424, 2016.
19. Hao, P., Yuan, X., Liu, H., Wang, B., Liu, C., Yang, D. and Zhan, S., “Isogeometric Buckling Analysis of Composite Variable-Stiffness Panels”, Composite Structures, Vol. 165, pp. 192-208, 2017.
20. Manickam, G., Bharath, A., Das, A. N., Chandra, A., and Barua, P., “Thermal Buckling Behaviour of Variable Stiffness Laminated Composite Plates”, Materials Today Communications, Vol. 16, pp. 142-151, 2018.
21. Rasool, M., and Singha, M. K., “Stability Behavior of Variable Stiffness Composite Panels under Periodic in-Plane Shear and Compression”, Composites Part B: Engineering, Vol. 172, pp. 472-484, 2019.
22. Dawe, D.J., “Finite Strip Buckling and Postbuckling Analysis”, In Buckling and Postbuckling of Composite Plates, Springer, pp. 108-153, 1995.
23. Reddy, J. N., “Mechanics of Laminated Composite Plates and Shells: Theory and Analysis”, CRC press, 2003.
24. Ribeiro, P. and Akhavan, H., “Non-Linear Vibrations of Variable Stiffness Composite Laminated Plates”, Nonlinear Dynamics, Vol. 94, No. 8, pp. 2424-2432, 2012.
25. Roufaeil, O. L. and Dawe, D. J., “Vibration Analysis of Rectangular Mindlin Plates by the Finite Strip Method”, Computers and Structures, Vol. 12, No. 6, pp. 833-842, 1980.
26. Dawe, D. J. and Craig, T. J., “Buckling and Vibration of Shear Deformable Prismatic Plate Structures by a Complex Finite Strip Method”, International Journal of Mechanical Sciences, Vol. 30, No. 2, pp. 77-99, 1988.
27. Ovesy, H. R., Ghannadpour, S. A. M., and Zia-Dehkordi, E., “Buckling Analysis of Moderately Thick Composite Plates and Plate Structures Using an Exact Finite Strip”, Composite Structures, Vol. 95, pp. 697-704, 2013.
28. Ghannadpour, S. A. M., and Ovesy, H. R., “The Application of an Exact Finite Strip to the Buckling of Symmetrically Laminated Composite Rectangular Plates and Prismatic Plate Structures”, Composite Structures, Vol. 89, No.1, pp. 151-158, 2009.
29. Shukla, K. K., and Nath, Y., “Analytical Solution for Buckling and Post-Buckling of Angle-Ply Laminated Plates under Thermomechanical Loading”, International Journal of Non-Linear Mechanics, Vol. 36, No. 7, pp. 1097-1108, 2001.
30. Kam, T. Y., and Chang, R. R., “Buckling of Shear Deformable Laminated Composite Plates”, Composite Structures, Vol. 22, No. 4, pp. 223-234, 1992.
31. Moita, J. S., Soares, C. M. M., and Soares, C. A. M., “Buckling and Dynamic Behaviour of Laminated Composite Structures Using a Discrete Higher-Order Displacement Model”, Computers and Structures, Vol. 73, No. 1-5, pp. 407-423, 1999.
32. Jones, R. M., Morgan, H. S., and Whitney, J. M., “Buckling and Vibration of Antisymmetrically Laminated Angle-Ply Rectangular Plates”, Journal of Applied Mechanics, Vol. 40, No. 4, pp. 1143-1144, 1973.
33. Fazilati, J., “Stability Analysis of Variable Stiffness Composite Laminated Plates with Delamination Using Spline-FSM”, Latin American Journal of Solids and Structures, Vol. 14, No. 3, pp. 528-543, 2017.
34. Loja, M. A. R., Barbosa, J. I., and Soares, C. M., “Dynamic Instability of Variable Stiffness Composite Plates”, Composite Structures, Vol. 182, pp. 402-411, 2017.
2. Lam, S. S. E., and Zou, G. P., “Higher-Order Shear Deformable Finite Strip for the Flexure Analysis of Composite Laminates”, Engineering Structures, Vol. 23, No. 2, pp. 198-206, 2001.
3. Hatami, S., Azhari, M., and Saadatpour, M. M., “Stability and Vibration of Elastically Supported, Axially Moving Orthotropic Plates”, Iranian Journal of Science and Technology, Transaction B, Engineering, Vol. 30, No. B4, pp. 427-446, 2006.
4. Hatami, S., Azhari, M., and Saadatpour, M. M., “Free Vibration of Moving Laminated Composite Plates”, Composite Structures, Vol. 80, No. 4, pp. 609-620, 2007.
5. Ovesy, H. R., and Fazilati, J., “Buckling and Free Vibration Finite Strip Analysis of Composite Plates with Cutout Based on Two Different Modeling Approaches”, Composite Structures, Vol. 94, No. 3, pp. 1250-1258, 2012.
6. Daraei, B., and Hatami, S., “Free Vibration Analysis of Variable Stiffness Composite Laminates with Flat and Folded Shapes”, Journal of Solid Mechanics, Vol. 8, No. 3, pp. 662-678, 2016.
7. Fazilati, J., “Stability Analysis of Variable Stiffness Composite Laminated Plates with Delamination Using Spline-FSM”, Latin American Journal of Solids and Structures, Vol. 14, No. 3, pp. 528-543, 2017.
8. Hyer, M. W. and Lee, H. H., “The Use of Curvilinear Fiber Format to Improve Buckling Resistance of Composite Plates with Central Circular Holes”, Composite structures, Vol. 18, No.3, pp. 239-261, 1991.
9. Waldhart, C., “Analysis of Tow-Placed, Variable-Stiffness Laminates”, Master’s Thesis, Virginia Polytechnic Institute and State University, Blacksburg, 1996.
10. Langley, P. T., “Finite Element Modeling of Tow-Placed Variable-Stiffness Composite Laminates”, Master’s Thesis, Virginia Polytechnic Institute and State University, Blacksburg, 1999.
11. Tatting, B. F. and Gürdal, Z., “Design and Manufacture of Elastically Tailored Tow Placed Plates”, NASA/CR-2002–211919, 2002.
12. Tatting, B. F. and Guerdal, Z., “Automated Finite Element Analysis of Elastically-Tailored Plates”, NASA/CR-2003-212679, 2003.
13. Gürdal, Z., Tatting, B. F. and Wu, C. K., “Variable Stiffness Composite Panels: Effects of Stiffness Variation on the in-Plane and Buckling Response”, Composites Part A: Applied Science and Manufacturing, Vol. 39, No. 5, pp. 911-922, 2008.
14. Lopes, C. S., Gürdal, Z. and Camanho, P. P., “Variable-Stiffness Composite Panels: Buckling and First-Ply Failure Improvements over Straight-Fibre Laminates”, Computers and Structures, Vol. 86, No.9, pp. 897-907, 2008.
15. Lopes, C. S., Gürdal, Z. and Camanho, P. P., “Tailoring for Strength of Composite Steered-Fibre Panels with Cutouts”, Composites Part A: Applied Science and Manufacturing, Vol. 41, No. 12, pp. 1760-1767, 2010.
16. Wu, Z., Raju, G. and Weaver, P. M., “Postbuckling Analysis of Variable Angle Tow Composite Plates”, International Journal of Solids and Structures, Vol. 50, No. 10, pp. 1770-1780, 2013.
17. Akbarzadeh, A. H., Nik, M. A. and Pasini, D., “The Role of Shear Deformation in Laminated Plates with Curvilinear Fiber Paths and Embedded Defects”, Composite Structures, Vol. 118, pp. 217-227, 2014.
18. Yazdani, S., Rust, W. J. and Wriggers, P., “Delamination Growth in Composite Laminates of Variable Stiffness”, International Journal for Numerical Methods in Engineering, Vol. 108, No. 11, pp. 1406-1424, 2016.
19. Hao, P., Yuan, X., Liu, H., Wang, B., Liu, C., Yang, D. and Zhan, S., “Isogeometric Buckling Analysis of Composite Variable-Stiffness Panels”, Composite Structures, Vol. 165, pp. 192-208, 2017.
20. Manickam, G., Bharath, A., Das, A. N., Chandra, A., and Barua, P., “Thermal Buckling Behaviour of Variable Stiffness Laminated Composite Plates”, Materials Today Communications, Vol. 16, pp. 142-151, 2018.
21. Rasool, M., and Singha, M. K., “Stability Behavior of Variable Stiffness Composite Panels under Periodic in-Plane Shear and Compression”, Composites Part B: Engineering, Vol. 172, pp. 472-484, 2019.
22. Dawe, D.J., “Finite Strip Buckling and Postbuckling Analysis”, In Buckling and Postbuckling of Composite Plates, Springer, pp. 108-153, 1995.
23. Reddy, J. N., “Mechanics of Laminated Composite Plates and Shells: Theory and Analysis”, CRC press, 2003.
24. Ribeiro, P. and Akhavan, H., “Non-Linear Vibrations of Variable Stiffness Composite Laminated Plates”, Nonlinear Dynamics, Vol. 94, No. 8, pp. 2424-2432, 2012.
25. Roufaeil, O. L. and Dawe, D. J., “Vibration Analysis of Rectangular Mindlin Plates by the Finite Strip Method”, Computers and Structures, Vol. 12, No. 6, pp. 833-842, 1980.
26. Dawe, D. J. and Craig, T. J., “Buckling and Vibration of Shear Deformable Prismatic Plate Structures by a Complex Finite Strip Method”, International Journal of Mechanical Sciences, Vol. 30, No. 2, pp. 77-99, 1988.
27. Ovesy, H. R., Ghannadpour, S. A. M., and Zia-Dehkordi, E., “Buckling Analysis of Moderately Thick Composite Plates and Plate Structures Using an Exact Finite Strip”, Composite Structures, Vol. 95, pp. 697-704, 2013.
28. Ghannadpour, S. A. M., and Ovesy, H. R., “The Application of an Exact Finite Strip to the Buckling of Symmetrically Laminated Composite Rectangular Plates and Prismatic Plate Structures”, Composite Structures, Vol. 89, No.1, pp. 151-158, 2009.
29. Shukla, K. K., and Nath, Y., “Analytical Solution for Buckling and Post-Buckling of Angle-Ply Laminated Plates under Thermomechanical Loading”, International Journal of Non-Linear Mechanics, Vol. 36, No. 7, pp. 1097-1108, 2001.
30. Kam, T. Y., and Chang, R. R., “Buckling of Shear Deformable Laminated Composite Plates”, Composite Structures, Vol. 22, No. 4, pp. 223-234, 1992.
31. Moita, J. S., Soares, C. M. M., and Soares, C. A. M., “Buckling and Dynamic Behaviour of Laminated Composite Structures Using a Discrete Higher-Order Displacement Model”, Computers and Structures, Vol. 73, No. 1-5, pp. 407-423, 1999.
32. Jones, R. M., Morgan, H. S., and Whitney, J. M., “Buckling and Vibration of Antisymmetrically Laminated Angle-Ply Rectangular Plates”, Journal of Applied Mechanics, Vol. 40, No. 4, pp. 1143-1144, 1973.
33. Fazilati, J., “Stability Analysis of Variable Stiffness Composite Laminated Plates with Delamination Using Spline-FSM”, Latin American Journal of Solids and Structures, Vol. 14, No. 3, pp. 528-543, 2017.
34. Loja, M. A. R., Barbosa, J. I., and Soares, C. M., “Dynamic Instability of Variable Stiffness Composite Plates”, Composite Structures, Vol. 182, pp. 402-411, 2017.
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