Samer Adeeb

Finite Element Analysis: Videos and Tutorials

Videos and Tutorials:

Problem 1: Deep Beam
Problem 2: Bernoulli vs. Timoshenko Cantilever Beams
Problem 3: Inflating a Balloon of Shell Elements
Problem 4: Elasto-Plastic Buckling of a Plate
Problem 5: Cylinder in Contact with a Rigid Plate

Problem 1: Deep Beam

In this problem we look at the analysis of a deep beam with a concentrated load in the middle. This problem serves as an introduction to for input and output of a PLANE solid linear elastic model into ABAQUS.problem 1
Problem description:

Mesh, Material and Section:

Assembly:

Viewing Results:

Importing into Excel:


Problem 2: Bernoulli vs. Timoshenko Cantilever Beams

The dimensions of the beam are L=5m, b=0.25m, h=0.5m. The Material properties are: E=200,000MPa, G=77,000MPa. The concentrated load at the cantilever end is P=10MN. The effective shear area for the Timoshenko beam is A_y=k_1A=0.85A. Note that in some texts, the inverse of this relationship is given A_y=\frac{A}{k_2}=\frac{A}{1.18}. The exact solution for the vertical displacement at the cantilever end for the Bernoulli beam is given by:

    \[ v=\frac{PL^3}{3EI}=0.8m \]

While that for the Timoshenko beam is given by:

    \[ v=\frac{PL^3}{3EI}+\frac{PL}{GA_y}=0.806m \]

problem 2
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Problem 3: Inflating a Balloon of Shell Elements

In this example we look at using hyperelastic material and shell elements for a highly nonlinear problem.
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Problem 4: Elasto-Plastic Buckling of a Plate

A plate that is 2mm thick and 50mm wide is loaded until it buckles around the minor axis. The problem will be considered as a plane problem. The Euler buckling load can be calculated as follows:

    \[ P_{cr}=\frac{pi^2EI}{L^2}=65.8N \]

    \[ \sigma_{cr}=\frac{P_{cr}}{A}=0.658MPa \]

The critical load per 1mm width of the plate is given by:

    \[ \frac{P_{cr}}{b}=\frac{65.8}{50}=1.316 \frac{N}{mm} \]

The relationship between the true stress and the plastic strain is given by:

True Stress(MPa) Plastic Strain
800 0
900 0.1%
1000 0.3%
1100 0.7%
1200 2%

 

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Problem 5: Cylinder in Contact with a Rigid Plate

In this example, an arbitrary cylinder is resting on a rigid base. The friction coefficient is taken as 0.2.

Problem 5
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Page Comments

  1. CHANDRASHEKHAR LAKAVATH says:

    Thank you verymuch sir.
    if your time permits then please add more examples of FEM-abaqus related to civil engineering applications (examples on earthquake loading and prestressing concept ect.)

    really thank you very-much sir

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