Theory of Plates

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Abdul Azeem

6:18:25

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1 - Bending of Rectangular Plates

1 - Introduction Differential equation for cylindrical bending of plates.mp4

14:54

1 - ToP-U1.pdf

2 - Cylindrical bending of a uniformly loaded rectangular plate.mp4

22:34

3 - Slope curvature momentcurvature relations Strain energy in pure bending.mp4

29:45

2 - Bending of Circular Plates

4 - Circular plates basic relations differential equation of equillibrium.mp4

30:16

4 - ToP-U2.pdf

5 - Deflections and bending moments of uniformly loaded circular plates.mp4

21:41

6 - Annular plates with simply supported outer edges.mp4

14:46

3 - Buckling of Plates

7 - Governing equation Deflection of plate under combined loading.mp4

31:13

7 - ToP-U3.pdf

8 - Critical buckling load and stress in a plate under uniaxial and biaxial compress.mp4

22:30

4 - Small deflections of laterally loaded plates

9 - Differential equation for small deflection of plates boundary conditions.mp4

17:59

9 - ToP-U4.pdf

10 - Deflection of plates due to sinusoidal loading Naviers solution for deflection.mp4

25:33

11 - Naviers solution for patch and point loads Greens function Levys solution.mp4

34:10

12 - Rectangular plate with two opposite edges clamped.mp4

17:55

5 - Approximate methods for Rectangular Plates

13 - Solution of a rectangular plate using Ritz method.mp4

23:24

13 - ToP-U5.pdf

14 - Finite Difference Method Introduction solution for deflection of a plate.mp4

38:21

15 - Graphical representation of finite difference equations deflection of a plate.mp4

33:24

Description

Thin plates, plate theory, analysis of circular plates, analysis of rectangular plates, buckling 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

Who is this for?

Intended for ME or MTech Structural Engineering students

What You Need to Know?

Basic knowledge of elasticity, energy principles, and classification of various plate theories. Familiarity with variational calculus and differential equations.

More details

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 Navierâ€™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 Navierâ€™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.
Who this course is for:
Intended for ME or MTech Structural Engineering students

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Structural Engineering

Abdul Azeem

Instructor's Courses

I am a Civil Structural Engineer with over seven years of experience teaching graduate courses in structural engineering. I have taught advance solid mechanics, theory of plates, finite element methods, advanced structural analysis and design of prestressed concrete structures. I am also well versed with structural analysis and design software packages.

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