BENDING ANALYSIS OF BILATERALLY CLAMPED THICK CROSS-PLY COMPOSITE PLATES

Öz

Bending deformation of composite plates is consistent investigation by means of varying boundary conditions and laminations. In this study bending analysis of laminated composites which has clamped boundaries at bilateral edges while the other opposites are free are investigated by a new analytical solution methodology based on third order shear deformation theory. The aim of this study is to present the analytical methodology for an unsolved boundary condition result in a gap in the literature. Double Fourier series are used to solve highly coupled linear partial differential equations for the clamped boundary conditions prescribed on the edges. The complementary boundary constraints are introduced through discontinuities at the boundaries which are generated by the selected boundary conditions, resulting in the derivation of the complementary solution. The numerical results of the new model is compared by the counterparts obtained by finite element analyses

Anahtar Kelimeler

• Analytical solution, Cross-ply plates, Fourier analysis, Higher order shear deformation theory

KARŞILIKLI KENARLARI ANKASTRE ÇAPRAZ DİZİLİMLİ KALIN KOMPOZİT PLAKLARIN EĞİLME ANALİZİ

Öz

Kompozit plakların farklı sınır şartları ve dizilimler etkisi altında eğilme deformasyonu süregelen bir araştırma konusudur. Bu çalışmada, karşılıklı iki kenarı ankastre diğer kenarları serbest sınır şartlarına sahip lamine kompozitlerin eğilme deformasyonu üçüncü mertebeden kayma deformasyon teorisine dayanan bir analitik çözüm yöntemi ile incelenmiştir. Bu çalışmanın amacı halen literatürde bir boşluk oluşturan çözülmemiş sınır şartları için analitik bir çözüm metodu sunmaktır. Karşılıklı kenarlar için tariflenen ankastre sınır şartı için yüksek mertebeli kısmi diferansiyel denklem çözümlerinde çift Fourier serileri kullanılmıştır. Tanımlanmış sınır şartları etkisiyle çözümde oluşan süreksizlikler sınırlarda tanımlanmış katsayılar ile çözüme dahil edilmiştir. Yeni modelin sonuçları sonlu elemanlar yöntemi analizleri ile elde edilen muadilleri ile karşılaştırılmıştır

Anahtar Kelimeler

• Analitik çözüm, Çapraz dizilimli plaklar, Fourier analizi, Yüksek mertebeli kayma deformasyon teorisi

Kaynakça

1. Y.G. Youssif, 2009. Non-linear Design and Control Optimization of Composite Laminated Doubly Curved Shell, Composite Structures, Vol.88, pp. 468-480, DOI:10.1016/j.compstruct.2008.0 020.
2. Zhen, W., Wanji, C. And Xiaohui, R., 2009. Refined Global-Local Higher Order Theory for Angle- ply Laminated Plates Under Thermo-Mechanical Loads and Finite Element Model, Composite Structures, Vol.88, pp.643-658, DOI:10.1016/j.compstruct.2008.0 011.
3. Swaminathan, K. And Patil, S.S., Analytical Solutions Using a Higher Computational Model with 12 Degrees of Freedom for the Free Vibration Analysis of Antisymmetric Angle-ply Plates, Composite Structures, Vol.82, pp.209-216, DOI:10.1016 / j.compstruct.2007.01.001.
4. Sheng, H.Y. and Ye, J., 2005. State Space Solution for Axisymmetric Bending of Angle-ply Laminated Cylinder with Clamped Edges, Composite Structures, Vol.68, pp.119-128, DOI:10.1016 /j.compstruct.2004.03.006.
5. S.M.R. Khalili, A. Davar, and K.M. Fard, 2012. Free Vibration Analysis of Homogeneous Isotropic Circular Cylindrical Shells Based on a New Three- Dimensional Refined Higher Order Theory, Int.J. Mech.Sci., Vol.56, pp. 1-25, DOI: 10.1016 /j.ijmecsci.2011.11.002.
6. Alipour, M.M., 2016. An Analytical Approach for Bending and Stress Analysis of Cross/Angle-ply Laminated Composites Under Arbitrary Non-uniform Loads and Elastic Foundations, Archives of Civil and Mechanical Engineering, Vol.16, pp. 193-210, DOI:10.1016 /j.acme.2015.11.001.
7. Sarangan, S., Singh, B.N., 2016. Higher Order Closed-Form Solution for the Analysis of Laminated Composite and Sandwich Plates Based on New Shear Deformation Theories, Composite Structures, Vol.138, pp. 391-403, DOI:10.1016 /j.compstruct.2015.11.049.
8. Sarangan, S., Singh, B.N., 2016. Improved Zigzag Theories for Laminated Composite and Sandwich Interlaminar Shear Stress Continuity, Aerospace Science and Technology, Vol:52, pp. 243-255, DOI:10.1016 /j.ast.2016.02.034. with

9. Raghu, P., Preethi, K., Rajagopal, A. and Reddy, J.N., 2016. Nonlocal Third Order Shear Deformation Theory for Analysis of Laminated Plates Considering Surface Stress Effects, Composite Structures, Vol.139, pp.13-29, DOI:10.1016 /j.compstruct.2015.11.068.
10. Kurtaran H., 2015. Geometrically Nonlinear Transient Analysis of Moderately Thick Laminated Composite Shallow Shells with Differential Quadrature Method, Composite Structures, Vol. 125, pp. 605-614, DOI:10.1016 /j.compstruct.2015.02.045.
11. Cheung Y.K., 1976. Finite Strip Method in Structural Analysis, Publication of Pergamon Press Incorporated, 233s. Assaee H.,Hajikazemi M., Ovesy H., 2012. The Effect of Anisotropy on Post-Buckling Behavior of
12. Laminated Plates Using Semi- Energy Finite Strip Method, Composite Structures, Vol:94, pp:1880-1885, DOI:10.1016 /j.compstruct.2012.01.011.
13. Ghannadpour S.A.M., Ovesy H.R., Zia-Dehkordi E., 2015. Buckling and Post-Buckling Behavior of Moderately Thick Plates Using an Exact Finite Strip, Composite Structures, Vol:147, pp:172-180, DOI:10.1016 /j.compstruc.2014. 013.
14. Kant, T. and Swaminathan, K., Estimation of Transverse / Interlaminar Stresses in Laminated Composites – a Selective Review and Survey of Current Developments, Composite Structures, Vol.449, pp.65-75, DOI:10.1016/S0263- (99)00126-9.
15. Nosier, A. and Bahrami, A., 2007. Interlaminar Stresses in Antisymmetric Angle-ply Laminates, Composite Structures, Vol.78, pp.18-33, DOI:10.1016 /j.compstruct.2005.08.007.
16. R.A. Chaudhuri, 1989. On Boundary-Discontinuous Double Fourier Series Solution to a System of Completely Coupled P.D.E.’S. Int. J. Eng. Sci. Vol.27(9), pp. 1005-1022, DOI: /0020-7225(89)90080-3. 1016
17. R.A. Chaudhuri, 2002. On the Roles of Complementary and Admissible Boundary Constraints in Fourier Solutions to Boundary Value Problems of Completely Coupled Rth Order P.D.E.'s., J. Sound Vib., Vol.251, pp. 261–313, DOI:10.1006/jsvi.2001.3913.
18. Reddy, J. N. and Liu, C. F., 1985. A Higher-Order Shear Deformation Theory of Laminated Elastic Shells, Int. J. Eng. Sci., Vol.23, pp.319-330, DOI: 10.1016/0020- (85)90051-5. Appendices