FEMtools

FEMtools Optimization

FEMtools Optimization is a toolbox for solving general optimization problems and more specifically for structural design optimization. In combination with FEMtools Model Updating, it provides the unique possibility to perform design optimization on validated and updated finite element models.

Based on the acting loads, the design constraints, and the required structural behavior, FEMtools Optimization computes the optimal design parameters for the considered component or structure. The state-of-the-art optimization techniques of FEMtools Optimization enable to increase the performance of the considered component considerably faster than conventional development methods. FEMtools Optimization has an open architecture providing virtually unlimited flexibility in the problem definition and offering the possibility to solve the optimization problem using your preferred FE-solver.

FEMtools Optimization contains modules for:

General Non-Linear Optimization - For solving arbitrary non-linear optimization problems.
Size Optimization - For optimizing component parameters such as cross-section and thickness.
Shape Optimization - For optimizing the shape of existing components.
Topometry Optimization - Optimizing component parameters on an element-by-element basis
Topology Optimization - Creating new designs with a layout optimized for a given load.

Sensitivity Analysis

Sensitivity analysis is a technique that allows an analyst to get a feeling on how structural responses of a model are influenced by modifications of parameters like spring stiffness, material stiffness, geometry etc. Sensitivity analysis 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.
Variational Analysis
Pretest analysis - Sensitivity analysis can be used in pretest planning applications like studying the effect of transducer mass loading on the modal parameters.
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 change to compensate for this error.
Design optimization - Find the optimal locations to modify the structure in order to shift modal parameter values or other response types.
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 quantify the variation of a response value (e.g. resonance frequency or mass) as a result of modifying a parameter value. The coefficients obtained for all combinations of responses and parameters are stored in a sensitivity matrix. Analyzing this matrix yields information on the sensitive and insensitive zones of the structure. Color graphics are available to visualize these different zones and enable a fast optimization of the parameter selection.

Sensitivity analysis and model updating require that the user select reference responses and parameters.

Sensitivity coefficients are computed internally by FEMtools using a differential or finite difference method. The possibilities depend on the parameter type and on the element formulation. Alternatively, externally computed sensitivity coefficients can be imported. For example, sensitivities computed using SOL 200 in Nastran can be imported in FEMtools for model updating.

Key Features

Selection of all element material properties, geometrical properties, boundary conditions, lumped masses, and damping factors as parameters.
Selection of mass, static and dynamic displacements, resonance frequencies, modal displacements, MAC, FRFs, and FRF correlation functions as responses
Sensitivity for local and global parameters.
Internal sensitivity analysis :absolute or normalized sensitivities, finite difference and differential sensitivities
Pre- and postprocessing of external sensitivity analysis (Nastran SOL 200)
Sensitivity and gain matrix analysis.

Structural Responses

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

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.

General Non-Linear Optimization

Any arbitrary objective or constraint function can be used for optimization by programming it using the FEMtools Script language. There are no fixed limits on the number of optimization parameters, objective functions or constraints.

Optimization Problems:

FEMtools Optimization is build around a powerful general non-linear optimization solver the can handle the following types of optimization problems:

Constrained Optimization - Optimization problems that include an arbitrary number of non-linear constraints.
Multi-Objective Optimization - Optimization problems that include an arbitrary number of objective functions.
Least-squares distance - Optimization problems that focus an minimizing the least-squares distance with a set of reference data.
Pareto Optimization

Size Optimization

Size optimization allows optimizing the properties of designable elements like bars, plates, etc.

Easy selection of a wide range of sizing parameters..
Fast gradient computation with the FEMtools sensitivity module.
Full flexibility in the problem definition by using the FEMtools Script language.

Shape Optimization

The shape optimization module optimizes the shape of an existing component.

Features:

The FEMtools shape optimization module offers the following features:

Modifying FE-models without requiring the underlying CAD data.
Possibility to handle large mesh deformations by using mesh morphing technology.
Full flexibility in the problem definition by using the FEMtools Script language.

Mesh Morphing:

The shape optimization module offers three methods to deform the mesh of the FE-model:

Lattice-Based Free Mesh Deformation - Deformation of the mesh based on a set of brick shaped lattice cells. The mesh is deformed by moving the vertex points of the lattice cells.
Skeleton-Based Free Mesh Deformation - Deformation of the mesh based on a set of control points that are connected by a number of curves (line, spline or circle). The mesh is deformed by moving the control points.
Using a Shape Basis - The deformed mesh is a linear combination of the shapes that define the shape basis. Any arbitrary shape can be used as basis shape

Topometry Optimization

Topometry optimization enables element-by-element size optimization of FE-models.

Design Problems:

The topometry optimization module provides a solution for the following design problems:

Minimum static compliance design - Provides the topometry that minimizes the static compliance considering all the defined load cases.
Maximum fundamental eigenvalue design - Provides the topometry that maximizes the resonant frequency of the first vibration mode.
Minimum maximal FRF-level - Provides the topometry that minimizes the compliance under a harmonic load

Filters:

The topometry module offers the following filters:

First order checkerboard filters.
Second order checkerboard filters.
Mesh independent filters.

Manufacturing Constraints:

Symmetry constraints.
Extrusion constraints.
User-defined manufacturing constraints.

Topology Optimization

Topology optimization module can handle both 2D and 3D design spaces.

Design Problems:

The topology optimization module provides a solution for the following design problems:

Minimum static compliance design - Provides the topology that minimizes the static compliance considering all the defined load cases.
Maximum fundamental eigenvalue design - Provides the topology that maximizes the resonant frequency of the first vibration mode.
Minimum dynamic compliance design - Provides the topology that minimizes the compliance under a harmonic load

Filters:

The topology module offers the following filters:

First order checkerboard filter.
Second order checkerboard filter.

Topologic Optimization

Manufacturing Constraints:

The following constraints are available to improve the manufacturability of the optimal design:

Minimum member size constraints.
Symmetry constraints.
Extrusion constraints.
Die-casting constraints.
User-defined manufacturing constraints.

User Interface

All definition, editing and analysis accessible via intuitive menus and dialog boxes or using free format commands for batch processing and process automation.
Complete electronic documentation.
Dedicated graphics viewers for model inspection and results evaluation.
Point-and-click interactive selection.
Direct access to FEA and test data.
Unlimited customization and extension using FEMtools Script language.