Introduction

 

This section demonstrates the use of different element types available for ParaGeo in some validation examples. The examples comprise 2D and 3D test cases, which are solved using explicit and implicit solvers. The default constitutive model is von-Mises elastoplasticity model.

 

By the end of this tutorial, the user should be more familiar with:

1.Using appropriate element types to solve the respective validation examples

2.Setting up test cases (e.g., boundary conditions, etc) for the validation examples

3.Evaluating numerical solutions using corresponding theoretical/reference solutions

 

Tutorial Examples

 

Example 1: Internally Pressurised Cylinder

 

A long metallic thick-walled cylinder is subjected to internal pressure, which is increased gradually until the collapse pressure is reached. The vertical and horizontal boundaries are constrained with symmetry boundary conditions.

 

Quarter symmetry model of internally pressurised cylinder

 

 

 

Example 2: Strip Footing Collapse

 

A strip footing lying on soil is subjected to vertical pressure until the bearing capacity of the footing is reached. The simulation model is constrained with symmetry boundary conditions on the right, left and bottom boundaries.

 

 

 

Vertical pressure is applied through prescribed displacement u until collapse

 

 

Example 3: Cook's Membrane

 

Cook's membrane is a tapered panel made with rubber-like material. One of its sides is clamped, while the opposite side is subjected to shearing load. The membrane deforms under a mixture of shear and bending strains.

 

 

Cook's membrane subjected to shearing load F

 

 

Example 4: Billet Upsetting

 

A cylindrical billet is compressed between two flat, rigid, perfectly rough dies. The top and bottom boundaries are constrained in horizontal directions.

 

 

Simulation model of billet upsetting