v6.04.124 SSNV124 - Regularized limit analysis. Norton—Hoff’s law

Summary

This test makes it possible to validate the operators used in regularized limit analysis. The limit load is calculated by a kinematic approach regulated by the Norton-Hoff-Friaâ method.

We consider a rectangular plate (modeling A) or a cube (modeling B) or an axisymmetric cylinder (modeling C). The constituent material meets the vonMises resistance criterion and the structure is subjected to loading at the edges. The calculation makes it possible to obtain the parameter of the limit load in the direction of loading.

The structure is modelled by incompressible elements and the load for which the limit load parameter is sought is normalized (unit power).

The resolution by the regularized Norton-Hoff-Friaâ method is carried out by piloting in the command STAT_NON_LINE. A post-processing in command POST_ELEM makes it possible to obtain the value of an upper bound of the limit load, as well as an estimate by lower value, when there is no constant load applied.

The reference solution is analytical and the results are in perfect agreement with the reference values.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
• 2. Benchmark solution
  • 2.1. Calculation method used for the reference solution
  • 2.2. Case plan
  • 2.3. Axisymmetric case
  • 2.4. Three-dimensional case
  • 2.5. Benchmark results
  • 2.6. Bibliographical references
• 3. Modeling A
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
  • 3.3. Tested values
• 4. B modeling
  • 4.1. Characteristics of modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Tested values
• 5. C modeling
  • 5.1. Characteristics of modeling
  • 5.2. Characteristics of the mesh
  • 5.3. Tested values
• 6. Summary of results