r5.05.05 Dynamic nonlinear algorithm

Summary:

The operator DYNA_NON_LINE [DYNA_NON_LINE] is used for the nonlinear dynamic analysis of structures by direct integration in time. Nonlinearities can come from the behavior of the material, from the connections (touch-friction), or from large geometric transformations (large displacements and large rotations).

The organization of DYNA_NON_LINE is very similar to that of the quasistatic nonlinear operator STAT_NON_LINE [R5.03.01]. Prioritily, all behavioral relationships developed in the context of STAT_NON_LINE work in that of DYNA_NON_LINE.

The general formulation of the nonlinear dynamic problem is presented here in order to specify the joints between purely dynamic aspects and those already treated in other operators or formulations available in Code_Aster: management of boundary conditions, fluid-structure couplings, damping, damping, damping, calculation in relative coordinate systems, then the properties of the temporal numerical integration scheme, which is developed independently of any behavioral relationship. We explain how this one is articulated with Newton’s algorithm to deal with material and geometric nonlinearities.

We have three complementary and effective implicit time schemes:

• the Newmark family,

• the modified average acceleration (« HHT » in DYNA_NON_LINE, with the option MODI_EQUI =” NON “),

• the complete HHT diagram (« HHT » in DYNA_NON_LINE, with the option MODI_EQUI =” OUI “), as well as its « without overshooting » version proposed in [bib35] (” NOHHT “in DYNA_NON_LINE).

The operator also proposes two explicit diagrams:

• the central differences,

• the Tchamwa-Wielgosz dissipative diagram.

We give some tips for good use that the documentation [Conseils généraux d’utilisation de l’opérateur DYNA_NON_LINE] complements.

• 1. Ratings
• 2. Nonlinear dynamics: spatial discretization of the continuous problem
  • 2.1. Discretization of the linear dynamics problem
  • 2.2. Discretization of the nonlinear dynamics problem
  • 2.3. Taking into account an initial prestressed state
  • 2.4. Problems coupled fluid-vibro-acoustic structure
  • 2.5. Taking into account laws of viscous behavior and damping
  • 2.6. equations in « relative » motion [R4.05.01]
• 3. Temporal integration diagram: diagram of NEWMARK and method of NEWTON
  • 3.1. NEWMARK diagram
  • 3.2. Prediction phase
  • 3.3. Correction phase using the NEWTON method
  • 3.4. Update
  • 3.5. Stop criterion
• 4. Qualities and faults of the NEWMARK schema
  • 4.1. Properties of the diagram of NEWMARK
  • 4.2. Energy point of view
  • 4.3. NEWMARK schema properties for nonlinear problems
  • 4.4. Choice of time steps
• 5. A variant of the Newmark schema: the HHT and modified mean acceleration diagrams
  • 5.1. Motivation
  • 5.2. Figure HHT and modified mean acceleration method
  • 5.3. Properties of the modified mean acceleration scheme
  • 5.4. Properties of schema HHT
  • 5.5. Scheme HHT and overshooting
• 6. Explicit diagrams
  • 6.1. The schema of centered differences
  • 6.2. The Chamwa-Wielgosz diagram [bib34]
  • 6.3. Explicit schema performance in Code_Aster
  • 6.4. Explicit Ritz-based calculations with subdomains in Code_Aster
• 7. Mass shift
• 8. example
• 9. Conclusion
• 10. Bibliography