Erol ŞENOCAK, Hakan TANRIÖVER

Kompozit plakların dinamik nonlineer davranışı

Bu çalışma kapsamında Galerkin yöntemi kullanılarak kompozit plakların dinamik nonlineer davranışları üzerine analizler gerçekleştirildi. Birinci dereceden kayma şekil değiştirmesi teorisi ve von Karman tipi nonlineerlik kullanıldı ve olayı yöneten diferansiyel denklemler, plak yer değiştirme fonksiyonlarına yaklaşım için uygun polinomların seçilmesi ile çözüldü. Galerkin ve Newton-Raphson yöntemleri Newmark doğrudan zaman integrasyonu yöntemiyle beraber kullanılarak kompozit plakların dinamik büyük çökme analizleri araştırıldı. Elde edilen çözümler Chebyshev serileri ve sonlu elemanlar yöntemlerinin çözümleri ile karşılaştırıldı. Bu yaklaşım yöntemlerinin sonuçları ile uyum içinde kalındığı gözlendi. Çözüm aşamasında işlemler mümkün olduğunca analitik olarak yapıldı ve bütün problemlerde analitik-sayısal tip yaklaşım uygulandı.

Dynamic nonlinear behavior of composite plates

Employing Galerkin technique, analyses on the dynamic nonlinear behavior of composite plates are performed in the course of this study. First order shear deformation theory and von Karman type nonlinearity are utilized and the governing differential equations are solved by choosing suitable polynomials as trial functions to approximate the plate displacement functions. The trial functions satisfy the geometric boundary conditions, whereas natural boundary conditions are not satisfied. In this case, simultaneous approximation is made to the solutions of differential equations and to the boundary conditions. The choice of trial functions is crucial to approximate the two dimensional displacement field. Dynamic large deflection analysis of composite plates is investigated using the Galerkin and the Newton- Raphson methods with Newmark direct time integration scheme. In order to demonstrate the applicability of the present method, linear transient analysis of an isotropic plate is considered at first. Geometrically nonlinear transient analysis of a cross-ply laminate is accomplished as a case study. The solutions are compared to that of Chebyshev series and finite elements. A very close agreement has been observed with these approximating methods. The method is found to determine closely the displacements with a few number of terms. In the solution process, analytical computation has been done wherever it is possible, and analytical-numerical type approach has been made for all problems.

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ABAQUS User’s Examples and Theory Manual, (2003). Version 6.4, ABAQUS Inc., Providence, RI, USA.
Ali, S.A. ve Al-Noury, S., (1986). Nonlinear dynamic response of rectangular plates, Computers and Structures, 22, 4, 621-9.
Bauer, H.F., (1968). Nonlinear response of elastic plates to pulse excitations, Jorunal of Applied Mechanics, 35, 1, 47-52.
Chen, J., Dawe, D. J. ve Wang, S., (2000). Nonlinear transient analysis of rectangular composite laminated plates, Composite Structures, 49, 129-39.
Chia, C. Y., (1988). Geometrically nonlinear behavior of composite plates, ASME Applied Mechanics Review, 41, 12, 439-51.
Finlayson, B. A., (1972). The Method of Weighted Residuals and Variational Principles, 7-14, Academic Press, New York.
Kirby, R.M. ve Yosibash, Z., (2004). Solution of von Karman dynamic non-linear plate equations using a pseudo-spectral method, Computer Methods in Applied Mechanics and Engineering, 193, 575-99.
Nath, Y. ve Shukla, K. K., (2001). Nonlinear transient analysis of moderately thick laminated rectangular plates, Journal of Sound and Vibration, 247, 3, 509-26.
Newmark, N. M., (1959). A Method of computation for structural dynamics, ASCE Journal of the Engineering Mechanics Division, 8, 67-94.
Reddy, J. N., (1983a). Dynamic transient analysis of layered anisotropic composite material plates, International Journal for Numerical Methods in Engineering, 19, 237-55.
Reddy, J. N., (1983b). Geometrically nonlinear transient analysis of laminated composite plates, American Institute of Aeronautics and Astronautics Journal, 21, 4, 621-9.
Reddy, J. N., (1997). Mechanics of Laminated Composite Plates, CRC Press, New York.
Sathyamoorthy, M., (1998). Nonlinear Analysis of Structures, CRC Press, New York.
Şenocak, E. ve Tanrıöver, H., (2001). Large deflection analysis of laminated composite plates. Proceedings of 6th Pasific International Conference on Aerospace Science and Technology, Kaohsiung, Taiwan.
Tanrıöver, H. ve Şenocak, E., (2004a). Large deflection analysis of unsymmetrically laminated composite plates: Analytical-numerical type approach, International Journal of Non-Linear Mechanics, 39, 8, 1385-92.
Tanrıöver, H. ve Şenocak, E., (2004b). Dynamic nonlinear behavior of composite plates, Proceedings of ASCE Aerospace Division International Conference on Engineering, Construction, and Operations in Challenging Environments (Earth & Space 2004), TX, USA.
Tanrıöver, H. ve Şenocak, E., (2004c). Nonlinear transient analysis of orthotropic plates, Journal of Aerospace Engineering, hakem aşamasında.
Tanrıöver, H., (2004). Dynamic nonlinear behavior of composite plates, Doktora tezi, İTÜ Fen Bilimleri Enstitüsü, İstanbul.
Wang, Y.Y., Lam, K.Y. ve Liu, G.R., (2000). The effect of rotatory inertia on the dynamic response of laminated composite plate, Composite Structures, 48, 265-73.
Whitney, J. M., (1987). Structural analysis of laminated anisotropic plates, 263-311, Technomic Publ; Lancaster, Pennysylvania.
Wolfram, S., (1988). MathematicaTM : A system for doing mathematics by computer, Addison-Wesley, Redwood City, CA.
Zienkiewicz, O. C. ve Morgan, K., (1983). Finite Elements and Approximation, 39-95, John Wiley & Sons, Singapore.