판이론 강의 개요

1. Tensor Notation and Calculus of Variation

2. Review of Three Dimensional Nonlinear Elasticity

Lagrangian Strain

Stress - Piolar Kirchhoff Stress Tenssor

-- First Kind

-- Second Kind

3. Statics of Plates

Classical Linear Theory

Shear Deformation Theory

Von Karman Plate Theory, Margure Theory - Initial Curvature

Approximate Theory of Plate - Berger

4. Dynamics of Plate

Steady State Solution

Transient Solution

5. Thermal Deformation of Plate

6. Special Topics

< 참고 문헌 >

1. Panc, V., theories of Elastic Plate, Noordhoff International Pub. 1975

2. Chia, C.Y., Nonlinear Analysis of Plates, Mc-Graw Hill, 1980

3. Dym, C.L., Solid Mechanics : A Variational Approach, Mc-Graw Hill, 1973

4. Washizu, K., Variational methods in Elasticity and Plasticity, Pergamon Press, 1968

5. Reddy, J.N., Energy and Variational Methods in Applied Mechanics, John Wiley &        Sons, 1992

6. Vasiliev, V.V. et al., Mechanics of Composite Structures, Taylor & Francis, 1993

7. Timoshenko, S.P. et al., Theory of Plates and Shells, Mc-Graw Hill, 1959

판이론(Theory of Plates) 참고문헌

1. Leissa.A.W. A Comparison of Approximate Methods for the Plate Bending Problems, AIAA J. Vol.7, No.5, pp.920-928, 1969

2. Karamanlulis.D et al., Mixed Finite Element Models for Plate Bending Analysis, Computer & Structures, Vol.19, No.3, pp.431-445, 1984

3. Singer J, et al., On the Equivalence of the Galerkin and Rayleigh-Ritz Methods, J. Royal Aero. Soc., Vol.66, pp.592, 1962

4. Haisler, W.E. et al., Development and Evaluation of Solution Procedures for Geometrically Non-linear Structural Analysis, AIAA J. Vol.10, No.3, pp.  , 1972

5. Banerjee.B. et al., A New Approach to an Analysis of Thin Elastic Plates, Int. J. Nonlinear Mech., Vol.16, No.1, pp.47-52, 1981

6. Laura.P.A. et al., Study of Small Amplitude Vibrations of Clamped Rectangular Plates Using Polynimial Approximations, J. Acoustical Soc. America, Vol.41, No.4, pp.836-839, 1966

7. Vendhan.C.P., A Study of Berger Equation Applied to Nonlinear Vibrations of Elastic Plates, Int. J. Mech. Sci., Vol.17, pp.461-468, 1972

8. Berger, H.M., A New Approach to the Analysis of Large Deflections of Plates, J. App. Mech., pp.465-472, 1955

9. Barton, M.V., Vibration of Rectangular and Skew Cantilever Plates, J. App. Mech. pp.129-134, 1951

10. Reddy, J.N., A Small Strain and Moderate Rotation Theory of Elastic Anisotropic Plates, J. App. Mech., Vol.54, pp.623-626, 1987

11. Bathe, K.J., et al., Short Communication - A Four-Node Plate Bending Element Based on Mindle/Reissner Plate Theory and a Mixed Interpolation, Int. J. Numerical Methods in Eng. Vol.21, pp.367-338, 1985

12. Dawe, D.J., Vibrations of Rectangular Plates of Variable Thickness, J. Mech. Eng. Sci., Vol.8, No.1, pp.42-50, 1966

13. Mei, C. et al., A Finite Element Method for Nonlinear Forced Vibrations of Rectangular Plates, AIAA J., Vol.23, No.7, pp.1104-1110, 1985

14. Alwar, R.S. et al., Nonlinear Analysis of Orthotropic Skew Plates, AIAA J., Vol.11, No.4, pp.495-498, 1973

15. Sathamoorthy. M. et al., Effect of Transverse Shear and Rotatory Inertia on Large Amplitude Vibration of Anisotropic Skew Plate : Part 1 - Theory, Part 2 - Numerical Results, Trans of ASME, Vol.47, pp.128-138, 1980

16. Soedel. W., Vibration of Shell and Plates, Marchel Decker, 1993

- Chap.1 Historical Development of Continuous Structural Elements

17. Plass, H.J. et al., Applications of Reissner's Vibrational Principle to Cantilever Plate Deflection and Vibration Problems, J. App. Mech., March, pp.127-135, 1962

18. Reissner, E., The Effect of Transverse Shear Deformation on the Bending of Elastic Plates, J. Appl. Mech., June A 69-A 77, 1945

19. Prathap, G., On the Berger Approximation : A Critical Re-examination, J. Sound and Vib. 66(2), pp.149-154, 1979

20. Goldberg, M.A., A Modified Large Deflection Theory of Plates, ****

21. Lo, K.H. et al., A Higher Order Theory of Plate Deformation, Part 1 : Homogeneous Plates, J. Appl. Mech., Vol.4, pp.663-668, 1977

22. Reddy, J.N., A Simple Higher-Order Theory for Laminated Composite Plates, J. Appl. Mech., Vol.51, pp.745-752, 1984

23. Reddy, J.N. et al., Stability and Vibration of Isotropic, Orthotropic and Laminated Plates According to a Higher Order Shear Deformation Theory, J. Sound and Vib. 98(2), pp.157-170, 1985

24. Reddy, J.N., A General Nonlinear Third-Order Theory of Plates with Moderate Thickness, Int. J. Nonlinear Mech., Vol.25, No.6, pp.676-686, 1990

25. Kapania, R.K. et al., Recent Advances in Analysis of Laminated Beams and Plates,

Part 1 : Shear Effects and Buckling

Part 2 : Analysis of Vibration & Wave Propagation

AIAA J., Vol.27, No.2, pp.923-946, 1989

26. Leissa, A.W., Dynamic Analysis - The Relative Complexaties of Plate & Shell Vibrations.

27. Reissner, E., Reflections on the Theory of Elastic Plates, Appl. Mech. Review, Vol.38, No.11, pp.1453-1465, 1985

28. Bert, C.W., Recent Research in Composite & Sandwitch Plate Dynamics

29. Simmonds, J.G., Exact Equations for the Inextensional Deformation of Cantilevered Plates, J. Appl. Mech., Vol.46, pp.631-636, 1979

30. Thorntor, E.A., Thermal Structures : Four Decade of Progress, J. Aircraft, Vol.29. No.3, pp.485-498, 1992

각이론(Theory of Shells) 참고문헌

1. Soedel, Vibrations of Shells and Plates, Marshall-Decker, 1994.

2. Reddy,J N.,Energy and Variational Methods in Applied Mechanics,John-Wiely & Sons,1992.

3. Lee,S.W., Theory of Shells, University of Maryland.

4. Timoshenko S.P. et al., Theory of Plates and Shells, McGraw-Hill,1959.

5. Calcot,L.R.,The Analysis of Laminated Composite Structures, van Nostrand Co.,1969.

6. Magrab,E.B.,Vibrations of Elastic Structural Members, Sijthoff & Noordhoff,1979.

7. Noordson,F.I. Shell Theory, Elsebier Science Pub. Co., 1985.

8. Kollar,L et al. Buckling of Shells for Engineers

9. Dowell,E.H.,Aeroelasticity of Plates and Shells, Noordhood Intenational Pub.,1975.

10.Ugral,A.C., Stresses in Plates and Shells, McGraw Hill,1981.

11.Seide,P., Small Elastic Deformations of Thin Shells, Noordhoof International Pub., 1975.

12.Flugge,W., Stresses in Shells, Springer Verlag,1973.

13.Volmir,A.S., A Translation of Flexible Plates and Shells, Technical Report AFFDL-TR-66-216,1967.

14.Mason,J., Variational Incremental and Energy Methods in Solid Mechanics and Shell           Theory , Elsevier Scientific Pub. Co.,1980.

15.Ramm,E.,Buckling of Shells, Springer-Verlag,1982.

16.Mollmann,H.,Introduction to the Theory of Thin Shells, John Wieley & Sons, 1981.

17.Low.P.G. et al. Thin Shell Theory, Wolter-Noordhoff Pub.,1970.

18.Steele,C.R., Shells of Revolution with Axisymmetric Loading, Stanford        University,1980.

19.Ashwell,D.G. et al., Finite Elements for Thin Shells and Curved Members, John-Wiley & Sons, 1976.

20.Jawad,M.H., The Theory and Design of Plate and Shell Structures, Chapman & Hall,1994.

* ONail,B.,Elementary Differential Geometry, Academic Press, 1966.