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CE5514 Plate and Shell Structures

Course Lecturers

A/Prof T Balendra Room: E1A-05-08, Tel: 6874-2159

E-Mail: cvebalen@nus.edu.sg

Prof C M Wang Room: E1A-02-12, Tel: 6874-2157

E-Mail: cvewcm@nus.edu.sg

Department of Civil Engineering National University of Singapore Kent Ridge, Singapore 119260

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CE5514 Module Description This 4-MC module introduces the basic principles of modeling plate and shell structures, fundamental theories of plates and shells and the analytical and numerical tools for analysis of these structures. Students will learn the fundamental behaviour of plate and shell components under static and dynamic loads. The course enables students to acquire the knowledge and analytical skills through workshop-like lectures, homework assignments and a mini-project. At the end of this module, the students should

• be able to state the assumptions and recognize the governing equations of plate and shell theories

• understand the behaviour of plate and shell structures • be able to apply the theories, analytical and numerical tools for the analysis of

plate and shell structures under static loads Syllabus: Plate Structures Introduction Description and examples of plate structures; introduction to Theory of Elasticity; state of stress in elastic bodies; strain and displacement; stress-strain law (2 hrs) Thin Plate Theory for Bending Assumptions of thin plate theory; curvature-displacement relations; stress resultant-displacement relations; equilibrium of stress resultants; the plate equations in Cartesian coordinates; boundary conditions; coordinate transformation; free edges and corners (4 hrs) Analytical Solutions of Plates Analytical solutions of rectangular plates using Navier and Levy solutions; analytical solutions for triangular and elliptical plates; corner supported rectangular and triangular plate structures using polynomial functions (4 hrs) Energy Principles Principle of virtual displacements and principle of minimum potential energy and their applications in deriving the plate equations and boundary conditions; numerical solutions of plates using the Rayleigh-Ritz method and the finite element method (2 hrs) Buckling and Free Vibration of Plates Governing plate equations for buckling and vibration; analytical and numerical solutions for rectangular plates (2 hrs)

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Axisymmetric Plates Formulation in polar coordinates; stress resultants and boundary conditions; axisymmetric bending of circular plates; annular plates; treatment of concentrated loads and edge loads; non-symmetrical bending of circular plates; general solution; distributed and concentrated loads; solutions by superposition (2 hrs) Orthotropic Plates Bending of orthotropic plates; special cases of orthotropic plates (2 hrs) Thick Plates Assumptions of thick plate theory, curvature-displacement relations; stress resultant-displacement relations; equilibrium of stress resultants; the plate equations in Cartesian coordinates; boundary conditions; relationships between solutions of thick plate theory and thin plate theory (3 hrs) Syllabus: Shell Structures Introduction to Shell Structures Definition and examples of shell structures; qualitative description of shell behaviour (1 hr) Membrane Analysis of Cylindrical Shells Geometrical description; membrane equilibrium equations; cylindrical vaults; containment vessels; membrane deformation of cylindrical shells (3 hrs) Membrane Analysis of Shells of Revolution Geometrical description; shell element; stresses and stress resultants; equilibrium equations; shells under axisymmetric load; spherical, conical, orgival domes, and toroidal shells; shells subject to wind load; spherical shells supported on columns. (6 hrs) Membrane Analysis of Shells of Translation Equilibrium equations; hyperbolic paraboloid shells; elliptic paraboloid shells. (3 hrs) Bending Analysis of Circular Cylindrical Shells Equilibrium equations; kinematic relations; constitutive relations; cylindrical shells under axisymmetric load (3 hrs) Axisymmetric Bending Analysis of Shells of Revolution Equilibrium equations; stress resultant-strain displacement relations; governing equations; method of solution; spherical shells of constant thickness (3 hrs) Buckling of Shells Buckling of cylindrical shells; buckling of shells of revolution (2 hrs) References

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Farshad, M., Design and Analysis of Shell Structures, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992.

Gould, P.L., Analysis of Shells and Plates, Springer-Verlag, New York, 1988. Liew, K.M., Wang, C.M., Xiang, Y. and Kitipornchai, S., Vibration of Mindlin Plates:

Programming the p-version Ritz Method, Elsevier, Oxford, 1998. Panc, V., Theories of Elastic Plates. Noordhoff International Publishing, Leyden, The

Netherlands, 1975. Reddy, J.N., Theory and Analysis of Elastic Plates, Taylor and Francis, USA, 1999. Reismann, H., Elastic Plates: Theory and Application, John Wiley and Sons, New York,

1988. Seide, P., Small Elastic Deformations of Thin Shells, Noordhoff International

Publishing, Leyden, The Netherlands, 1975. Szilard, R., Theory and Analysis of Plates, Prentice-Hall, Englewood Cliffs, New

Jersey, 1974. Timoshenko, S.P. and Woinowsky-Krieger, S., Theory of Plates and Shells, McGraw-

Hill, New York, 1959. Ugural, A.C., Stresses in Plates and Shells, 2nd Edition, McGraw-Hill, New York, 1999. Wang, C.M., Reddy, J.N. and Lee, K.H., Shear Deformable Beams and Plates:

Relationships with Classical Solutions, Elsevier, Oxford, 2000. Mathematical Handbook Spiegel, M.R. and Liu, J., Mathematical Handbook of Formulas and Tables, 2nd Edition,

Schaum’s Outline Series, McGraw-Hill, Singapore, 1999. Assessment Continual assessment consists of

• 2 quizzes (20%) • Mini-project (20%)

2-hr final examination paper (60%)