Theory Of Plates

What you'll 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
Requirements
Basic knowledge of elasticity, energy principles, and classification of various plate theories. Familiarity with variational calculus and differential equations.
Description
The course covers the following topics: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.
Overview
Section 1: Bending of Rectangular Plates
Lecture 1 Introduction, Differential equation for cylindrical bending of plates
Lecture 2 Cylindrical bending of a uniformly loaded rectangular plate
Lecture 3 Slope, curvature & moment-curvature relations, Strain energy in pure bending
Section 2: Bending of Circular Plates
Lecture 4 Circular plates - basic relations, differential equation of equillibrium
Lecture 5 Deflections and bending moments of uniformly loaded circular plates
Lecture 6 Annular plates with simply supported outer edges
Section 3: Buckling of Plates
Lecture 7 Governing equation, Deflection of plate under combined loading
Lecture 8 Critical buckling load and stress in a plate under uniaxial and biaxial compress
Section 4: Small deflections of laterally loaded plates
Lecture 9 Differential equation for small deflection of plates, boundary conditions
Lecture 10 Deflection of plates due to sinusoidal loading, Navier's solution for deflection
Lecture 11 Navier's solution for patch and point loads, Green's function, Levy's solution
Lecture 12 Rectangular plate with two opposite edges clamped
Section 5: Approximate methods for Rectangular Plates
Lecture 13 Solution of a rectangular plate using Ritz method
Lecture 14 Finite Difference Method - Introduction, solution for deflection of a plate
Lecture 15 Graphical representation of finite difference equations, deflection of a plate
Intended for ME or MTech Structural Engineering students