v2.02.146 SDLL146 -Validation of « bar » elements in dynamics

Summary:

The objective of this test is to validate the calculation of the mass matrix of elements BARRE. It is verified that this matrix is indeed tri-directional unlike the stiffness matrix (uni-directional parallel to the orientation of the element). To do this, the following calculations are made:

• Calculation of the internal forces and support reactions of an embedded element subjected to a field of gravity in 3 directions (parallel to \(X\), \(Y\) and \(Z\)).

• Projection of the mass matrix on a base composed of three modes (parallel to \(X\), \(Y\) and \(Z\)).

• Calculation of kinetic energy for three speed modes (parallel to \(X\), \(Y\), and \(Z\)).

Note: all calculations are done with the full mass matrix and with the diagonal mass matrix except for the calculation of the kinetic energy which is done with the full mass matrix.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
• 2. Benchmark solution
  • 2.1. Calculation method
• 3. Modeling A
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
  • 3.3. Tested sizes and results
• 4. Summary of results