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Chapter 13 Nonlinear Simulations
1
Chapter 13
Nonlinear Simulations
13.1 Basics of Nonlinear Simulations
13.2 Step-by-Step: Translational Joint
13.3 Step-by-Step: Microgripper
13.4 More Exercise: Snap Lock
13.5 Review
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Chapter 13 Nonlinear Simulations
Section 13.1 Basics of Nonlinear Simulations 2
Section 13.1
Basics of Nonlinear Simulations
Key Concepts
•
Contact Types
•
Contact versus Target
•
Nonlinearities
•
Contact Formulations
•
Causes of Structural Nonlinearities
•
Additional Contact Settings
•
•
Steps, Substeps, and Iterations
Pinball Region
•
Newton-Raphson Method
•
Interface Treatment
•
Force/Displacement Convergence
•
Time Step Controls
•
Solution Information
•
Update Stiffness
•
Line Search
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Chapter 13 Nonlinear Simulations
Section 13.1 Basics of Nonlinear Simulations 3
Nonlinearities
•
[1] In a linear
simulation, [ K ]
(slope of the line)
is constant.
In a nonlinear simulation, the
relation between nodal force { F } and
nodal displacement { D } is nonlinear.
•
we may write
Displacement {D}
K ( D )
⎤ ⎦ D
F
⎡ ⎣
=
{}
{}
•
Challenges of nonlinear simulations
come from the difficulties of solving
the above equation.
[2] In a nonlinear
simulation, [ K ] (slope
of the curve) is
changing with { D }.
Displacement {D}
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Chapter 13 Nonlinear Simulations
Section 13.1 Basics of Nonlinear Simulations 4
Causes of Structural Nonlinearities
•
Geometry Nonlinearity
•
Due to Large Deflection
•
Topology Nonlinearity
•
Contact Nonlinearity
•
Etc.
•
Material Nonlinearity
•
Due to Nonlinear Stress-Strain
Relations
To include geometry
nonlinearity, simply
turn on <Large
Deflection>.
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Chapter 13 Nonlinear Simulations
Section 13.1 Basics of Nonlinear Simulations 5
Steps, Substeps, and Iterations
[1] Number of
steps can be
specified here.
•
Steps (Load Steps)
•
Each step can have its own analysis settings.
•
Substeps (Time Steps)
•
In dynamic simulations, time step is used
for integration over time domain.
•
In static simulation, dividing into substeps is
to achieve or enhance convergence.
•
Iterations (Equilibrium Iterations)
•
Each iteration involves solving a linearized
equilibrium equation.
[2] To switch
between steps,
type a step number
here.
[3] Each step
has its own
analysis
settings.
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