Formation

# Identify and understand the challenges of numerical modeling and finite element simulation

This training addresses the different aspects necessary for an understanding of the challenges of numerical modelling and finite element simulation.

None.

### Training objectives

• Understand the principles of finite elements
• Know the types of elements to choose according to the studied structure
• Start a simple finite element simulation (linear static calculation)
• Learn to post-process results

### Training description

#### Part 1: Introduction and modelling steps

• Basic principle of finite elements - strong and weak formulations
• Finite element modelling / simulation approach (multi-physics complexity, industrial design chain)
• Mathematical reminders (algebra and differential operators)
• Calculation of heat loss in a wall
• Finite difference approach
• Finite element approach
• Practical application by programming in Mathcad
• Summary: finite element modelling loop

#### Part 2: From application in mechanics to the principles of post-processing

• A simple exercise: a tension rod
• Deviatoric stress tensor
• Deformation tensor
• Behavioural law
• Writing in isotropic linear elasticity
• Principle of discretisation by finite elements (weak formulation, isoparametric elements)
• Different types of finite elements (1D, 2D, 3D)
• Boundary conditions and symmetries
• Import of CAD and mesh
• Post-processing principles