Nonlinear Analysis is required when a useful answer cannot be determined by linear methods.
Apply Loads GRADUALLY (incremental solution)
In ANSYS Main Menu > Solution > Analysis Type > Sol'n Controls
General guidelines:
Why ?
More results available for nonlinear, iterative solution
May need MORE for debugging (output of intermediate load steps and substeps)
May
need LESS to conserve disk space
In ANSYS Main Menu > Solution > Analysis Type > Sol'n Controls
Mesh error energy calculations (SERR, SEPC) are
invalid for nonlinear solutions.
Structural mesh error calculations should be linear elastic and may use solid
elements having only structural degrees of freedom and 3D shell elements. [ANSYS
Commands Reference Guide, PRERR command]
How do we
evaluate mesh quality for a nonlinear solution ?
ANSYS Help System
ANSYS Help System > Mechanical APDL > Structural Analysis Guide
Chapter 8, sections 8.1 - 8.6 (Nonlinear Structural Analysis)
Structural Analysis Guide, CH. 8.1 – 8.6 (Nonlinear Structural Analysis)
Causes of nonlinear behavior: changing status, geometric nonlinearities, material nonlinearities
Newton-Raphson approach – loads are applied in small increments (gradually)
At each solution step the “out-of-balance” loads are evaluated
If too high, the stiffness matrix is updated (for the nonlinear features) and solution repeats until
Convergence is reached (when “out-of-balance” loads are below the convergence criteria)
Load Steps, Substeps, and Time
· Load steps are defined by the analyst explicitly over a "time" span
· Within each load step, you can direct the program to perform several solutions (substeps or time steps) to apply the load gradually.
· At each substep, the program will perform a number of equilibrium iterations to obtain a converged solution.
Path-dependent loading (Conservative vs. Non-Conservative)
Non-conservative systems: energy can be lost (not recovered) when loads are removed (may be caused by friction or yielding). Loads must be applied in the proper order.
Automatic time stepping and bisection: balance accuracy, economy, and success vs. solution failure
Load Direction (in Large-Deflection analyses): pressure loads follow the element face as it deflects, point loads remain oriented as they were defined
Small Deflection and Small Strain Analyses: assume the stiffness is not affected by the displacement
Large Deflection Analyses: include large strain, large deflection/rotation, stress stiffening, spin softening
Material nonlinearities: plasticity and work hardening, but also may include materials that behave as visco-elastic, or granular (soil, rock, concrete), porous metals, cast iron, hyperelastic (elastomers/rubber)
Plasticity is a non-conservative, path-dependent phenomenon
Creep/Stress Relaxation: rate dependent (time), high temperature nonlinear behavior
Shape Memory Alloy, Viscoplasticy (time dependent plasticity), Swelling (nuclear)
Section 8.4 includes many examples for material models and combinations
Running a Nonlinear Analysis: 18 individual commands, listed. Automatic solution controls, discussed.
Performing a Nonlinear Static Analysis
Build the model – may include contact and/or nonlinear material properties
Set solution controls and output controls: small or large displacements, automatic time stepping
Can control: equation solver choice, convergence criteria, Newton-Raphson options, etc.
Reading Assignment:
ANSYS Help System > Mechanical APDL > Contact Technology Guide, Chapters 1 – 6, 8 -11