#### FEMtools Optimization

**An Integrated Solution for Structural Design Optimization**

FEMtools Optimization is a toolbox for solving general and structural design optimization problems. When combined 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, the optimal design parameters for the considered component or assembly are found considerably faster than conventional development methods using state-of-the-art optimization techniques.

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 functions for:

**Sensitivity Analysis**– Analyses how changes of parameters influences the structural responses.**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.**Design of Experiments and Response Surface Modeling**– Efficient sampling of the design space and create an approximate model.

#### 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. For more information, see FEMtools Model Updating.

#### 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.

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**– Solving minimax optimization problems.**Constraint Screening**– Automatically scans all constraints with every optimization loop and keeps only the effective constraints.

#### Size Optimization

Size optimization allows optimizing the properties of designable elements like bars, plates, etc. The FEMtools size optimization tool offers the following features:

- 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.
- Possibility to solve the optimization problem using the internal or an external FE solver.

#### Shape Optimization

The shape optimization module optimizes the shape of an existing component. The FEMtools shape optimization tool 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.
- Possibility to solve the optimization problem using the internal or an external FE solver

Three methods are available 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. The FEMtools topometry optimization tool 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

The following filters are available:

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

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

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

#### Topology Optimization

The FEMtools topology optimization tool provides a solution for the following 2D and 3D 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.

The following filters are available:

- First order checkerboard filter.
- Second order checkerboard filter.

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.

#### Design of Experiments and Response Surface Modeling

Design of experiment (DOE) techniques aim at sampling the design space in an efficient way with a minimum number of sampling points, as the evaluation of each sampling point requires an additional run of the FE-model. FEMtools provides the following designs: factorial designs, central composite designs, Latin hypercube designs, D-optimal designs, and user-defined designs.

Response Surface Modeling (RSM) is used to build an approximate model from the DOE runs to predict the response of the system in function of the design parameters. This approximate model can then be used to optimize the response of the considered system instead of the finite element model of which it was derived.

##### 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.