Unit 10
F
Geometric nonlinear analysis In this unit, you'll investigate the capabilities of geometric nonlinear analysis. Specifically, you'll learn: - types of geometric nonlinear problems that can be solved - how to define incremental loads - how to perform a nonlinear analysis
characteristics - solver characteristics
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103
Simulating different types of nonlinear problems
120 100 80 s s e r t
60
s
40 20 10
0.0010
0.005 0.010
0.05 0.10
0.5 1.0
strain
Instructor notes: There are three types of nonlinear analysis in I-DEAS – geometry, plasticity and creep. Geometry nonlinear solutions also allow nonlinear loads. A geometry nonlinear solution can be performed simultaneously with either creep or plasticity analysis. There are three basic types of nonlinear analysis: 1. Boundary conditions (contact/gaps) 2. Material 3. Geometric nonlinear (large displacements)
With IDEAS, you can simulate problems that are nonlinear because of: - material plasticity - material creep - geometry - loads - boundary conditions
You can perform material and geometric nonlinear solutions simultaneously.
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Simulating a geometric nonlinear problem
Instructor notes: In a geometry nonlinear solution, deflections of the structure are large compared with the original dimensions of the structure. Changes in stiffness and loads occur as the structure deforms.
In a geometric nonlinear problem, you can simulate: - large deflections - deflectiondependent loads - deflectiondependent stiffness
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Geometric nonlinear analysis
105
Simulating a geometric nonlinear problem
F
Instructor notes: When the beam is initially loaded, only bending forces are present, but as deflections occur, bending loads transition to membrane loads. The deflections in a linear solution are unrealistically high. Also, the distance between endpoints is reduced during deflections. A linear analysis does not make this calculation.
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Consider this geometric nonlinear problem: - Membrane behavior becomes more significant as deflections increase. - Overall width changes as deflections occur.
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Performing a geometric nonlinear analysis
Instructor notes: The steps to perform a geometry nonlinear analysis are similar to those required for a linear solution. Curved beams can be included in the model, but they are formulated with small deflection theory. Loads can be applied in increments (time varying) if desired. But this is not always required for a geometry nonlinear analysis. If deflections are very large, increments may be required to reach equilibrium. You can investigate results at several load amplitudes in a single solution by using time varying loads. Incrementing loads requires definition of time varying loads and definition of time increments in a solution set (time increments are also called time points or solution points).
To perform a geometric nonlinear analysis: 1.
Create a finite element model avoid curved beam elements.
2.
Define timevarying loads or restraints, and a boundary condition set for nonlinear statics. Constant loads can also be included.
3.
Create a solution set and define time increments for the solution.
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1999 SDRC
Geometric nonlinear analysis
107
Incremental load intervals
Force
Linear
Nonlinear
Applied force
Displacement
Instructor notes: Time intervals are really load intervals. Time is a variable. For the load control method, these are the exact locations of solution.
Solution time intervals define load increments based on a variable called time. Time intervals allow you to: - control incremental load steps
Discuss graph and point out that time intervals can be defined to control how quickly the load should be applied. This is done to aid convergence.
- define output for specific load steps
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- control convergence for each load increment
Creating load variations
Instructor notes: Creation of time varying loads is used in all types of nonlinear analysis. Stress the importance of selecting the nonlinear static analysis type before creating loads. Notice most loads and restraints can be time varying; accelerations can’t at this time.
You can gradually increment loads during a nonlinear solution using a variable called time. To create time variations: 1.
Pick Nonlinear Statics.
2.
Pick Force, Pressure, Temperature , or Displacement Restraint to create a load or restraint.
3.
Pick the nodes, vertices, edges, or surfaces.
4.
Pick Time Variation or Time...
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1999 SDRC
Geometric nonlinear analysis
109
Defining time variations
Points Function
Instructor notes: When adding time variation, you can enter a function or a table of points (time vs. amplitude). The time variation amplitude scales the amplitude in the load definition. After creating the time variation, don’t forget to apply (select) it for the load definition. For geometry and plasticity, time doesn’t mean time. It’s just a scale that allows a relationship between changing load amplitudes and solution points. For creep analysis time is realistic.
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To define a time variation: 1. Pick the Points or Function definition method. 2.
Enter the amplitude data points or the function expression.
3.
Pick Graph... to verify the time variation.
4.
Pick Dismiss, then OK from the Time Variation forms.
5.
On the load or restraint form, pick the ?" icon and select the time variation to be used for the force or restraint.
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1999 SDRC
What happens to load behavior during an analysis?
load direction is fixed
Instructor notes: Loads can either follow geometry as it deflects, or can remain in a constant direction during a geometry nonlinear analysis. The type of load (node or element based) determines the behavior.
load follows geometry
In a geometric nonlinear analysis, you can define loads that maintain their original direction or ones that update their direction based on displacements. - Loads applied to nodes, vertices, and surface tractions maintain their original direction. - Surface pressures and loads applied to element edges or faces update when deformations occur. - Mid beam loads update with deformations if they are applied in the element coordinate system.
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Geometric nonlinear analysis
111
Defining solution steps
Instructor notes:
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To create a solution set for a plasticity analysis: 1.
Pick Solution Set..., Create...
2.
Pick Loading and Solution Control...
3.
Toggle on Material Nonlinearity and/or Geometric Nonlinearity.
4.
Pick Add..., Modify, or Subincrement...
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1999 SDRC
Defining time interval increments
Instructor notes: After the initial time interval (solution point) is defined, it can be subdivided into a number of equally spaced points. Each new point has the same definition as the original, except for end time. After subdividing, each new point can be modified or additional points can be added.
When defining time interval subincrements, you can: - subincrement a time interval into equally spaced time intervals. - add individual time intervals for nonuniform spacing.
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Geometric nonlinear analysis
113
Solver capabilities
Instructor notes: If you put a pencil on a table, the strain is zero. If you rotate the pencil 90 degrees, the strain is still zero. However, engineering strain would be calculated as one, so you would use a different FE measure to include second order terms. Strain measure not appropriate for finite strain.
A geometric nonlinear solver will calculate the displacement from the deformed configuration. The solver uses the Almansi Strain and Cauchy (true) stress definitions. The following can be included: - large displacements - large rotations - small strains (less than 5% - 10%)
The following cannot be included: - adaptive meshing not available - changes in shell thickness and beam cross sections not accounted for 114
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