Dynamic Analysis in FEMAP presented by Philippe Tremblay Marc Lafontaine marc.lafontaine@mayasim.com 514-951-3429 date May 24 th, 2016
Agenda NX Nastran Transient, frequency response, random, response spectrum, DDAM Methods SAToolkit for Nastran Sine Random 2
Agenda NX Nastran Transient, frequency response, random, response spectrum, DDAM Methods SAToolkit for Nastran Sine Random 3
Transient analysis Typical Applications Automotive Rough road vibration Driveline dynamics Power-train dynamics Gear induced vibration Aerospace & Defense Launch load vibration Transportation loading Electronics Drop loads determine stress on internal components Transportation loading Industrial Machine vibration Rail impact 4
Frequency Reponse Analysis Typical Applications Automotive Wheel unbalance Driveline dynamics Power-train dynamics Gear induced vibration Electric motor dynamics Aerospace & Defense Launch load vibration Industrial Machine vibration 5
Random Analysis Typical Applications Automotive Rough road vibration Aerospace & Defense Launch load vibration Transportation loading Aerodynamic loads Electronics Transportation loading 6
Shock Response Spectrum Analysis SRS analysis is used to simulate response due to: Earthquakes Blasts Pyrotechnic shock It is a simple and conservative method to simulate a transient event User can select methods used to combine modal responses 7
Shock Response Spectrum Analysis Loads are acceleration versus frequency Actually responses of SDOF systems to a transient input Typically amplification factor Q=10 is assumed 8
DDAM The Dynamic Design Analysis Method (DDAM) is a procedure that is used to determine the shock response of equipment mounted on-board a ship to underwater explosions. 9
DDAM The DDAM procedure consists of 3 steps: 1. NX Nastran performs a modal analysis and calculates the corresponding modal participation factors and modal effective masses 2. The Naval Shock Analysis FORTRAN program uses the modal effective masses and natural frequencies calculated in step1 and user-supplied inputs from either a DDAM control file or command line entry to compute shock design accelerations. 3. NX Nastran uses the shock design accelerations computed by NAVSHOCK in Phase 2, and the modal participation factors and natural frequencies calculated by NX Nastran in Phase 1 to compute the shock response of the structure. 10
Methods Linear/Nonlinear Transient Analysis Linear methods used if possible Transient analysis can optionally include effects of: Geometric nonlinearities Contact Large displacement Follower forces Material nonlinearities Plasticity 11
Methods Modal vs Direct Transient, Frequency Response Modal solutions More computationally efficient Provides an undertstanding of of the structural behavior Direct solutions Can account for nonlinearities Avoids modal sufficiency issues Comprehensive support of damping Discrete dampers Frequency-dependent damping Frequency-dependent stiffness 12
Agenda NX Nastran Transient, frequency response, random, response spectrum, DDAM Methods SAToolkit for Nastran Sine Random 13
SAToolkit for Nastran Vertical applications for base-driven excitations: Sine (Frequency Response) Random 14
SAToolkit for Nastran Efficient modal, linear approach Best-in-class accuracy and performance Use Nastran eigenvectors Advanced integration algorithms Exact Von Mises stress & margins of safety Exact composite ply stresses & failure metrics Parallelization 15
Sine Processor Modal superposition using all computed normal modes or a selected subset Computes absolute (with rigid body modes) or relative (with respect to the base) displacements, velocities and accelerations Optionally accounts for modal truncation using either: Residual vectors (default) Residual flexibility via DMAP
Sine Processor Results Maxima over all frequencies By frequency Phase-consistent Von Mises stresses and margins of safety Using efficient, analytical expression Phase-consistent composite failure metrics (V7) Using efficient, analytical expression Automatic generation of XY plots
Sine Processor In frequency response analysis, all stress components are complex numbers. A particular stress component may be expressed as follows: ij ij cos ij ij ij Component Magnitude Reference Phase Angle Component Phase Angle When the phase angle difference of the various components is almost 0 or 180 degrees, the calculation of the failure metrics is simple. However, stress components will typically have different phase angles. Therefore, computation of failure metrics requires more effort. 18
Optimal Phase Angles Numerical Method Vary the reference phase angle θ from 0 to 2π. For each phase angle, calculate the value for each stress component. Calculate the FI/SR/MS using the stress components values. Identify the maximum FI value or the minimum SR/MS value. Limitations This approach is relatively slow. Accuracy depends on the phase angle step. 19
Optimal Phase Angles Analytical Method The stress tensor is given by: 11 22 33 12 13 23 11 22 33 12 13 23 cos cos cos cos cos cos xx yy zz xy xz yz MPa The optimal phase angles will be a function of and. We will consider the case of quadratic failure theories. ij ij 20
Optimal Phase Angles Analytical Method General equation for quadratic Failure Index is given by: FI 2 2 2 2 2 2 1 11 2 22 3 33 4 12 5 13 6 23 7 11 22 8 11 33 9 22 33 10 11 11 22 12 33 Since cos, the Failure Index is only a function of θ. ij ij ij The optimal angles are obtained when FI is maximal: FI 0 21
Optimal Phase Angles Analytical Method After some trigonometric manipulations, we have: FI where Asin 2 B cos 2 C sin D cos 0 A, B, C, D f,, ij ij k This equation can be transformed to a quartic polynomial using a variable change: 4 3 2 ax bx cx dx e 0 where a, b, c, d f A, B, C, D The solution to this quartic polynomial explicitly provides the optimal angles θ. 22
Optimal Phase Angles Example 1 Let s compute Von Mises stress for the following stress tensor: 2 4 11 10.0cos / 22 5.0cos /3 33 8.0cos / MPa 12 3.5cos /5 0.0 13 2.0cos / 2 23 The Von Mises stress is given by: 2 VM 2 xx 2 yy 2 zz 3 2 2 2 xy xz yz xx yy xx zz yy zz 23
Optimal Phase Angles Example 1 There are 4 optimal angles Solution: VM 15.77MPa 1.94rad 1000 discretization points were needed to converge Numerical approach took 0.4 seconds Analytical approach took 0.002 seconds 24
SAToolkit Random Processor Statistics are required to assess the probability of the response s magnitude Random theory assumes that the input follows a Gaussian distribution. The same assumption applies to the response Source: Wikipedia p x 1 2 ( x ) e 2 2 2 25
SAToolkit Random Processor Examples of response quantities that do not follow Gaussian distributions Von Mises stress Source: Wikipedia 26
SAToolkit Random Processor Examples of response quantities that do not follow Gaussian distributions Tsai-Wu composite failure index 27
Non-Gaussian responses: limitations For response quantities that do not follow Gaussian distributions: The relationship between the probability density function and the standard deviation sigma no longer holds: p x 1 2 ( x ) e 2 2 2 Hence it is not meaningful to express the peak results as a function of the standard deviation, for example 3-sigma 28
Evaluation of non-gaussian responses To evaluate response quantities that do not follow Gaussian distributions, numerical approximations are required: Segalman or Fast approximation method for Von Mises stress 29
Evaluation of non-gaussian responses Need to validate the approximation using Monte Carlo simulation Can also compute the error in assuming a Gaussian peak to rms ratio 30
Peak Results True peak stresses and failure metrics based on a probability level that is either: Directly specified, OR Equivalent to a Gaussian pdf with specified standard deviation eg 99.73% = 3 sigma 31
Efficient and accurate integration Uses NX Nastran eigenvectors from a SOL 103 run High-performance integration algorithm Does not require frequency card (FREQ) definition Avoids the risk of error by under-specification of number of computation frequencies Only need to supply the minimum and maximum frequency bounds for the simulation 32
Results Elemental Ply stresses, strains and failure metrics Homogeneous stresses and strains, Von Mises stresses Shell resultants, 1D and 3D element forces Nodal Acceleration, displacement, velocity, grid point force, mpc force, spc force Relative or absolute displacements, velocities and accelerations Results expressed in op2 format Displayed in FEMAP V11.1 as contour plots Number of positive crossings All entities or selected groups N0 U U 2 2 S( ) S( ) d 1 1 L U 2 2 S( ) d L L d RMS 33
Space Antenna Random Simulation Demo Time! 34
Muffler Random Simulation Demo Time! 35
A larger model still Test Model Statistics: Nodes : 503,880 Elements: 375,216 Modes: 736 OP2 File Size: 63.3 GB Run times for exact Von Mises of 166,020 elements (3 axis): Regular License Method: Segalman (single thread) Advanced License Method: Fast Approx (single thread) Advanced License Method: Fast Approx (parallel 16 threads) More than 24 hours 3h 1h 15 min
Random Processor 37
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