v2.01.031 SDLD31 - Elementary validation of time diagrams in dynamics

Summary:

This test case makes it possible to validate the programming of integration diagrams in time in DYNA_NON_LINE and DYNA_VIBRA.

More specifically, for DYNA_NON_LINE we test the following implicit schemes:

1. average acceleration (keyword NEWMARK) with resolution when moving and accelerating;

2. modified average acceleration (keyword HHT with MODI_EQUI =” NON “);

3. HHT complete (HHT keyword with MODI_EQUI =” OUI “);

With the complete HHT diagram, we also test the pursuits because this schema requires a particular initialization. Likewise, we also validate the pursuits for average acceleration with acceleration resolution because it is not tested in other test cases.

As for DYNA_VIBRA, the schemes with constant time steps are tested, i.e.:

1. explicit order 1 diagram says EULER;

2. implicit schema NEWMARK of order 2;

3. Explicit order 4 diagram says DEVOGELAERE

The aim being to study the behavior of the patterns over time, the problem chosen is deliberately very simple: it is a linear system with 1 degree of freedom mass-spring which is subjected to a sinusoidal force.

The reference solution is obtained by re-programming the integration diagrams in Matlab and by calculating the analytical solution.

• 1. Reference issues
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Geometric characteristics
  • 1.4. Boundary conditions and loads
  • 1.5. Initial conditions
• 2. Benchmark solution
  • 2.1. Calculation method
  • 2.2. Reference quantities and results
• 3. Modeling A - DYNA_NON_LINE
  • 3.1. Tested sizes and results
• 4. B and C modeling - DYNA_VIBRA
  • 4.1. Analytical solution
  • 4.2. Tested sizes and results
• 5. Summary of results