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Snap-Through/Snap-Back of a Thin Hinged Cylindrical Shell, Arc-Length Control, Nonlin

Innovator
Innovator
Hello!,
I try to learn how to setup with success on NX 7.5 Advanced Simulation a nonlinear static analysis problem using arc-length control with the basic nonlinear solver of NX NASTRAN SOL106. The arc-length control is the only method that allows to get analysis convergence when either Load control or Displacement controls fails, for instance, in post buckling analysis when both Force control and Displacement control will breakdown in the neighborhood of turning points (known as snap-through for force control and snap-back for displacement control).

In the past I used quite often the Arc Length Control as well as Load or Displacement Control for nonlinear analysis, not any special complexity, but now with NX 7.5 Advanced Simulation and NX NASTRAN I have to say that is difficult to match the equivalences for max. load parameters, max. displacement value, max. number of arc steps, etc.. then I invite to NX 7.5 Advanced Simulation & NX Nastran EXPERTS to use this simply problem to prepare a tutorial or script to explain step-by-step how to setup & solve this nonlinear static analysis using arc-length control -- thanks!.

TITLE:
Snap-Through/Snap-Back of a Thin Hinged Cylindrical Shell Under a Central Point Load using Arc-Length Control

TYPE:
Geometric Nonlinear static analysis, Shell CQUAD4 elements, Arc-length control, automatic stepping.

REFERENCE:
Crisfield, M. A., “A Fast Incremental/Iterative Solution Procedure That Handles Snap-Through,” Computers & Structures, Vol. 13, pp. 55-62, 1981.

PROBLEM:
Determine the snap-through/snap-back response of a shallow cylindrical shell under a concentrated load (P) at the center of the shell. The curved edges are free and the straight edges are hinged and immovable.

GIVEN:
• R = 2540 mm
• b = 254 mm
• θ = 0.10 rad
• E = 3102.75 MPa
• ν = 0.30
• h (thickness) = 6.35 mm
• P (reference load) = 10 N

MODELING HINTS:
• Due to symmetry, a 10 x 10 mesh is used to model a quarter of the shell.

Arc-length Control Information:
• Max. Load parameter (approx. value) = 100
• Max. Displacement (approx, value) = 30
• Max. number of arc steps = 50
• Desired average number iterations/step = 5
• Initial load parameter = 10
• Unloading check flag = 0
• Arc-length step adjustment coefficient = 0.5

Automatic Stepping Information:
• Min. (arc) step increment = 1.E-8
• Max. (arc) step increment = 30

RESULTS:
The attached picture show the curve of the load multiplier factor (LFACT) versus central deflection.

Best regards,
Blas.