It is possible to create semi-automated and automated design tools by combining numerical optimization techniques with finite element analysis methods.My colleagues and students have created both sequential and parallel numerical optimization software libraries for design optimization. These libraries have both gradient-based techniques (e.g. Method of Feasible Directions) and population-based techniques (e.g. Genetic Algorithm, Differential Evolution)
Finite-element (FE) based design optimization (DO) is now a relatively well-established methodology for engineering design. The use of this methodology involves several areas and techniques such as geometric modeling, mesh generation, finite element analysis, numerical optimization etc. Advances in each of these areas have made the overall design process more versatile especially when and where there is a tight integration between these areas. This integration enables an end-to-end solution with reduced designer intervention. Yet there remain more challenges to meet and hurdles to overcome. As finite element models have become more detailed and address multi-physics scenarios, the execution time has also increased in spite of advances in hardware technology. Compressing the design cycle time so as to reduce the time required for design and redesign process, requires more advances in hardware, software and especially, algorithms. Structural optimization can be broadly classified into topology, shape and sizing optimization. Topology optimization is used to generate conceptual designs for specified loads and boundary conditions inside a specific design space. Sizing optimization involves the modification of the cross section or thickness of structural elements to obtain an optimum objective function (minimum weight, maximum stiffness, etc.) while satisfying constraints (stress, displacement, etc.).
Similarly, shape optimization involves the modification of the parameters that control the shape of the model. Shape optimization, in particular, can be classified into parametric and non-parametric approaches. Parametric shape optimization necessitates tight integration and full associativity between a Computer-Aided Design (CAD) solid model and the FEA model. Any changes to the solid model e.g. a perturbation in a linear dimension should result in a corresponding update in the FE model. Such an association makes it possible to use any parameter in the solid model as a potential shape optimization design variable.
The biggest advantage of this approach is that at the end of the design process, the designer obtains the final dimensions of the solid model directly making it possible to use the model information in downstream applications such as manufacturability analyses or process planning.
Additionally, this approach ensures that the geometry stays consistent, i.e. a straight line remains a straight line, slope continuity is retained and enforced etc. while shape design changes take place. However, this approach requires careful model building. Boundary conditions and loads must be prescribed on the geometry and not directly on the FE model. The solid model geometry must be parameterized carefully to ensure behavior consistent with the designer’s intent.
Finally, in all parametric based shape optimization, changes in design variables result in a regeneration of the FE mesh and this significantly increases software complexity and computation time for large meshes and large numbers of design variables. Non-parametric shape optimization, on the other hand, works directly on the finite element model. Users specify the shape variables by selecting FE nodes and specifying how the changes in the nodal coordinates are to take place.
There are advantages to this approach.
First, the mesh stays the same (number of nodes and elements does not change) leading to smoother convergence. Second, no special action needs to take place with the specification of loads and boundary conditions. Third, the geometric or more solid modeler and the mesh generator are not invoked during the shape changes.
The biggest challenge is to ensure that mesh distortion is postponed as much as possible since recreation of the model (after mesh distortion) necessitates user interaction. In addition, unless special action is taken, it may be quite difficult for the designer to specify shape changes that stay consistent with the original design intent.
Finally, there is the problem of taking the final results and recreating the solid model for effective use by a downstream application. The main aim of design optimization is to reduce the design cycle time to increase the efficiency of the overall process.