v2.01.102 SDLD102 - Transitional substructure: System 3 masses-4 springs

Summary:

The field of application of this test concerns the dynamics of structures. It makes it possible to validate the integration schemes with adaptive time steps” ADAPT_ORDRE2 “and” RUNGE_KUTTA_54 “of the transitory calculation operator on a modal basis as well as the linear transient response calculation on a modal basis calculated by substructuration (for the 5 integration schemes:” EULER “,” “for the 5 integration schemes:” “,” DEVOGE “,” “,” NEWMARK “,” RUNGE_KUTTA_32 “and” ADAPT_ORDRE2 “). In particular, the case of applying reduced damping to the dynamic modes of the substructure projection bases is treated.

The aim is to determine the transient response of a system composed of 3 masses and 4 springs, embedded at its ends and subjected to a constant force from the initial moment. The springs are modelled by elements of type “DIS_TR” and the masses by elements of type “DIS_T”.

Six models are proposed. In the third modeling, the structure is depreciated. Transient calculation methods by substructuring with Craig-Bampton (“CRAIGB”) and MacNeal (“MNEAL”) interfaces are tested. The consideration of option RELA_EFFO_DEPL is also tested in the case of a response calculation by dynamic substructuring. The reference results associated with them are the result of an analytical calculation. In the third, a reduced damping of \(\text{1\%}\) is imposed on the dynamic modes of the substructure projection bases. The transient equation verified by the complete structure was obtained analytically. Its resolution, which acts as a reference, was achieved by the Maple software.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
  • 1.4. Initial conditions
• 2. Benchmark solution
  • 2.1. Calculation method used for the reference solution
  • 2.2. Benchmark results
  • 2.3. Uncertainty about the solution
  • 2.4. Bibliographical reference
• 3. Modeling A
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the substructure mesh
  • 3.3. Tested sizes and results
• 4. B modeling
  • 4.1. Characteristics of modeling
  • 4.2. Characteristics of the substructure mesh
  • 4.3. Tested sizes and results
• 5. C modeling
  • 5.1. Characteristics of modeling
  • 5.2. Characteristics of the substructure mesh
  • 5.3. Tested sizes and results
• 6. D modeling
  • 6.1. Characteristics of modeling
  • 6.2. Tested sizes and results
• 7. Modeling E
  • 7.1. Characteristics of modeling
  • 7.2. Tested sizes and results
• 8. F modeling
  • 8.1. Characteristics of modeling
  • 8.2. Tested sizes and results
• 9. Summary of results