BOUNDARY DISCONTINUOUS FOURIER ANALYSIS OF A DOUBLY CURVED CROSS-PLY LAMINATED COMPOSITE SHELL

Abstract

A new analytical solution to the problem of deformation for a cross-ply, thick laminated composite shell in a rectangular plan form is presented. The solution methodology is based on boundary discontinuous generalized double Fourier series approach and used to solve a system of five highly coupled linear partial differential equations which are generated from Higher Order Shear Deformation Theory (HSDT). Boundary conditions are defined as follows; two opposite edges are SS3 and the others are SS1. The major result of the present study is to declare analytic solution functions of defined boundary discontinuity which is unavailable in the literature. 

Keywords

• Laminated composite plate
• HSDT
• boundary-discontinuity
• Fourier analysis
• doubly curved shell

SÜREKSİZ SINIRLARA SAHİP, ÇİFT EĞRİLİKLİ, ÇAPRAZ KATLI LAMİNE KOMPOZİT KABUĞUN FOURIER ANALİZİ

Abstract

Bu çalışmada, çapraz katlı, kalın, ortogonal kompozit kabuğun SS3-SS1 sınır şartları altında deformasyonunun belirlenebilmesi için yeni bir analitik çözüm sunulmuştur. Çözüm tekniği süreksiz sınırlar için düzenlenmiş çiftli Fourier serilerine dayanır ve Yüksek Mertebeli Deformasyon Teorileri kullanılarak oluşturulmuş kısmi diferansiyel denklemler kullanılır. Kullanılan sınır şartları; iki karşılıklı kenar için SS3 ve diğer kenarlar için ise SS1 olarak tanımlanmıştır. Çalışmanın başlıca sonucu henüz literatürde bulunmayan bahse konu sınır koşullarının analitik çözümüne ait kısmi diferansiyel denklemlerin belirlenmesidir

Keywords

• Lamine kompozit levha
• sinir süreksizliği
• Fourier analizi
• HSDT
• çift eğrilikli kabuk

References

1. Kabir H.R.H., Al-Khaleefi A.M., Chaudhuri Reaz A., (2001). Free vibration analysis of thin arbitrarily laminated anisotropic plates using boundary-continuous displacement Fourier approach. Composite Structures, 53.
2. Jones R.M., (1999). Mechanics of Composite Materials. Second Ed. Philadelphia, PA: Taylor and Francis,
3. Whitney J.M., (1971). Fourier Analysis of clamped anisotropic plates. ASME Journal of Applied Mechanics, 38.
4. Chaudhuri R.A., Balaraman K., Kunukkasseril XV., (2005). A combined theoretical and experimental investigation on free vibration of thin symmetrical laminated plates. Composite Structures, 67.
5. Chaudhuri R.A., Kabir H.R.H., (1992). Influence of laminations and boundary conditions on the response of moderately thick cross-ply rectangular plates. Journal of Composite Materials, 26.
6. Chaudhuri R.A., Kabir H.R.H., (1992). Fourier analysis of clamped moderately thick arbitrarily laminated plates. AIAA Journal, 30.
7. Chaudhuri R.A., Kabir H.R.H., (1993). Vibration of clamped moderately thick general cross-ply plates using a generalized Navier’s approach. Composite Structures, 24.
8. Chaudhuri R.A., Kabir H.R.H., (1994). Effect of boundary constraint on the frequency response of moderately thick flat laminated panels. Composite Engineering, 4.

9. Kabir H.R.H., Chaudhuri R.A., (1994). Vibration of clamped moderately thick arbitrarily laminated plates using generalized Navier’s approach. Journal of Sound and Vibration, 171. [10] Kabir H.R.H., (1999). On the frequency response of moderately thick simply supported rectangular plates with arbitrary lamination. International Journal of Solids and Structures, 36. [11] Kabir R.H.Humayun, Al-Khaleefi A.M., Al-Marzouk M., (2003). Double orthogonal set of solution functions for cross ply laminated shear flexible cylindrical/doubly curved panels. Composite Structures, 59.
10. Khalili M.R., Malekzadeh K., Mittal R.K., (2005). A new approach to static and dynamic analysis of composite plates with different boundary conditions. Composite Structures, 69. [13] Öktem A.S., Chaudhuri R.A., (2007). Levy type analysis of cross-ply plates based on higher order theory. Composite Structures, 78.
11. Reddy J.N., Wang C.M., Lim G.T., Ng K.H., (2001). Bending solutions of Levinson beams and plates in terms of the classical theories. Int. Journal of Solids and Structures, 38. [15] Reddy, J.N., (2003). Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. 2nd edition, CRC Press, Boca Raton, FL.
12. Chaudhuri, R. A., (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 Vibr. 251, pp. 261–313.
13. Oktem A.S., Chaudhuri R.A., (2008). Effect of inplane bondary constraints on the response of thick general (unsymmetric) cross ply laminates. Composite Structures, 83.
14. Oktem A.S., Chaudhuri R.A., (2008). Boundary discontinous Fourier analysis of thick cross ply clamped plates. Composite Structures, 82.
15. Oktem A.S., Chaudhuri R.A., (2007). Levy type Fourier analysis of thick doubly curved panels. Composite Structures, 80.
16. Oktem A.S., Chaudhuri R.A., (2007). Fourier analysis of thick cross ply Levy type clamped doubly curved panels. Composite Structures, 80.
17. Oktem A.S., Chaudhuri R.A., (2007). Fourier solution to a thick cross ply Levy type clamped plate problem. Composite Structures, 79.
18. Oktem A.S., Chaudhuri R.A., (2009). Sensitivity of the response of thick cross ply doubly curved panels to edge clamping. Composite Structures, 87.
19. Reddy, J.N., (1985). A Higher Order Shear Deformation Theory of Laminated Elastic Shells. Int. Journal of Engineering, Vol.23, No:3, pp.319-330.