Theory of Plates
Thin plates, plate theory, analysis of circular plates, analysis of rectangular plates, buckling of plates
Description
This course deals with the theory of plate bending; rectangular and circular plates; energy methods and numerical method. The course objectives are:
To apply the differential equation of equilibrium to solve problems of pure and cylindrical bending of rectangular plates with different boundary conditions.
To solve the differential equation of equilibrium for symmetrical bending of circular plates under various loading conditions.
To determine the critical loads and buckling modes for simply supported rectangular plates under uniaxial or biaxial compression with different edge conditions.
To apply the Navier’s approach and Levy type solution to find the deflection and stress distribution for simply supported rectangular plates under various loading conditions.
To use the finite difference method to solve for the deflection and stress distribution for simply supported or fixed rectangular plates under different loading conditions.
Bending of Rectangular Plates: Pure and Cylindrical bending, differential equation, cylindrical bending of uniformly loaded rectangular plates with simply supported and built-in edges. Relations between slope and curvature of slightly bent plates, Moment-curvature relations in pure bending. Strain energy in pure bending.
Bending of circular plates: Symmetrical bending, differential equation of equilibrium, uniformly loaded plates at center, Circular plates with circular holes at the center.
Buckling of Plates: Differential equation for bending of plate under the combined action of in-plane loading and lateral loading, Calculation of critical loads, buckling of simply supported rectangular plates uniformly compressed in one and two directions with different edge conditions.
Small deflections of laterally loaded plates: Differential equation of equilibrium, Boundary conditions, Solution of simply supported rectangular plates under various loading conditions viz. uniformly distributed load (full or partial), concentrated load by Navier’s approach, Levy type solution for rectangular plates under U.D.L with all four edges simply supported or two opposite edges simply supported and other two fixed.
Approximate methods for Rectangular Plates: Finite difference method for simply supported or fixed rectangular plates carrying UDL (full or partial) or central point load, Strain energy approaches Rayleigh-Ritz method.
What You Will Learn!
- Understand the differential equation of equilibrium and the boundary conditions for rectangular and circular plates under pure and cylindrical bending
- Calculate the critical loads and the buckling modes of simply supported rectangular plates under different edge conditions and compression directions
- Solve the differential equation of equilibrium for simply supported rectangular plates under various loading conditions using Navier’s and Levy’s methods
- Apply the finite difference method and the Rayleigh-Ritz method to approximate the deflections and stresses of rectangular plates with different boundaries
Who Should Attend!
- Intended for ME or MTech Structural Engineering students