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SECTION 3 NONLINEAR NORMAL MODES

SECTION 3 NONLINEAR NORMAL MODES. PRE-STIFFENED NORMAL MODES. Section 2 looked at Normal Modes analysis of unloaded structures. In this section, Normal Modes Analysis of structures which have a static pre-load applied to them will be considered . Typical real-world examples are:

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SECTION 3 NONLINEAR NORMAL MODES

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  1. SECTION 3 NONLINEAR NORMAL MODES

  2. PRE-STIFFENED NORMAL MODES • Section 2 looked at Normal Modes analysis of unloaded structures. In this section, Normal Modes Analysis of structures which have a static pre-load applied to them will be considered. • Typical real-world examples are: • Thin walled pressure vessels, where the pressurization dominates the natural frequencies, such as rocket fuel tanks and satellite oxygen tanks. • Structures subject to significant dead weight loading, such as suspension bridge cables and oil tankers. • Tensioning of strings in musical instruments to achieve required frequencies. • Structures subject to centrifugal loading such as jet engine turbine and fan blades.

  3. NONLINEAR NORMAL MODES • The objective of applying a static load to a structure prior to carry out a Normal Modes Analysis is to allow the Stiffness Matrix to be updated. • There are three terms that can influence the Stiffness Matrix. • Material Nonlinearity. • Geometric Stiffness due to changes in the structural shape (these can be small displacement theory or large displacement theory). • Follower Force stiffness terms as the loading changes its line of action relative to the displacements (again, small displacement theory or large displacement theory). • ContactNon-contact

  4. MULTI-STEP ANALYSIS • Many MSC.Marc analyses require several steps. Usually these will be general (nonlinear) load history steps. • In a series of general analysis steps, the starting condition for each step is the ending condition from the previous step. • In a general step, loads are applied as total values • Example: Cup Forming problem • Step 1: Close Blank-holder • Step 2: Pressurize Blank-holder • Step 3: Move Punch • Step 4: Release Punch • Step 5: Release Holder • Step 6: Release Die

  5. MULTI-STEP ANALYSIS SELECTION • To select a step, you must click on it once in the step Select panel • To unselect a job step, you must click on it once in the Selected Job Steps panel • The steps will be executed in the order they appear in the Selected Job Steps panel • Don’t forget to click Apply when you are done!

  6. MULTI-STEP ANALYSIS blank blankholder die punch True Stress Log Strain • Many MSC.MARC analysis require several steps. Usually there will be several general analysis steps. Occasionally, these may be punctuated by perturbation steps. • In a series of general analysis steps, the starting condition for each step is the ending condition from the previous step. • Note that while much of this section discusses perturbation vs non-perturbation steps, THE MOST COMMON USE OF MULTI-STEPPING IS FOR LOADING HISTORY CONTROL • In a general step, loads are applied as total values • Example: Modified Olson Cup Test • Step 1: close and pressurize blankholder • Step 2: move punch up • Step 3: release punch • Step 4: release blankholder • Step 5: release die The Modified Olson Cup Test is often used to determine the materials properties of a metal for the purpose of stretch forming.

  7. Does the earthquake analysis in Step 6 affect the results of Step 1 and Step 4 procedures? MULTI-STEP ANALYSIS (CONT.) Linear analysis steps are perturbations about a basestate. Example: Preloaded Cantilever Beam Step 1: Preload P1 (Nonlinear Static) Step 2: Natural Frequency Extraction Step 3: Response Spectrum Analysis (Earthquake) Step 4: Preload P2 > P1 (Nonlinear Static) Step 5: Natural Frequency Extraction Step 6: Response Spectrum Analysis (Earthquake) The base state is the ending condition of the last nonlinear step prior to the linear perturbation. In a linear analysis step, the loads are defined as the magnitudes of the load perturbations only. If a general analysis step follows a linear perturbation step, any perturbation response is ignored.

  8. One may combine nonlinear (general) steps with linear (perturbation) steps in the same job. Example: Step 1 (pretension): general analysis step (Nonlinear Static) Step 2 (frequency extraction): linear analysis step performed about the ending condition of step 1 (base state). Step 3 (pull back): general analysis (Nonlinear Static) continuing from the ending condition of step 1 (last nonlinear step). Step 4 (another frequency extraction): linear analysis step performed about the ending condition of step 3 (new base state). Step 5 (dynamic release): general analysis (Nonlinear Transient) continuing from the ending condition of step 3 How does eliminating Steps 2 and 4 change the results of Step 5? MULTI-STEP ANALYSIS (CONT.)

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