FEMtools™ Sensitivity Analysis

FEMtools™ Sensitivity Analysis includes techniques that allow analysts to get a feeling on how structural responses are influenced by modifications of design variables like spring stiffness, material stiffness, geometry etc. This is done by computing sensitivity coefficients which are defined as the change of a response value (e.g. resonance frequency or mass) for the small perturbation of a parameter value. The coefficients obtained for all combinations of responses and parameters are stored in a sensitivity matrix. The results derived from this matrix can be used for the following purposes:

• What-If analysis - Study the effect of modeling assumptions on the modal parameters or on other response types.
• Design optimization - Find the optimal locations to modify the structure in order to shift structural response values.
• Variational Analysis - Find the relation between design variables and responses in the entire design space.
• Identify sensitive and insensitive areas of the structure for given response and parameter combinations - This will help the analyst to decide which parameters and responses to include in the selection for model updating.
• Model updating - The sensitivity matrix is inverted to find a gain matrix. This gain matrix is multiplied with the difference between predicted and reference response values to find the required parameter changes that compensate for this error.
• Pretest analysis - Sensitivity analysis can be used in pretest planning applications like studying the effect of transducer mass loading on the modal parameters.
• Acoustic sensitivities - Structural sensitivities computed with FEMtools can be exported to acoustic analysis packages where they are used for the calculation of acoustic sensitivities.

Sensitivity coefficients are computed internally by FEMtools using differential or finite difference perturbation methods. Alternatively, FEMtools can be used to pre- and post-process external sensitivity analysis (for example MSC. Nastran SOL 200)

Key Features

• Easy to use definition of design variables and responses
• Powerful and fast sensitivity analysis solver computes first-order gradients for all response and parameter combinations
• Dedicated tables and graphics to examine results (e.g. sensitivity matrix, relation curves)
• Element matrix derivatives and sensitivities can be reused in user-written programs
• Includes FEMTools Application Framework and FEMtools Correlation Analysis sharing the same database and user interface
• Provides an upgrade path to FEMtools Model Updating

Structural Responses

The following reference response types can be selected for sensitivity analysis:

• The mass of the structure or of subcomponents
• Static displacements
• Resonance frequencies
• Individual modal displacements
• MAC–values
• Frequency Response Functions (FRF) values (amplitudes at given frequency)
• FRF Correlation Functions values (signature and amplitude correlation)
• Operational displacement, velocities or accelerations

Design Variables

The following parameter types can be selected for sensitivity analysis:

• Material properties - Young's modulus (isotropic or orthotropic), Poisson's ratio, shear modulus and mass density.
• Geometrical element properties - Spring stiffness, plate thickness and beam cross-sectional properties.
• Lumped properties - Lumped stiffness (boundary conditions) and lumped masses.
• Damping properties – Modal damping, Rayleigh damping coefficients, viscous and structural damper values.

Parameter can be selected at either the local or the global level:

• Local parameters refer to an individual element
• Global parameters refer to sets of elements instead of an individual element

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Last modified: December 20, 2006