Finite Elements and Numerical Optimization in Engineering

The simulation of engineering processes using the Finite element method (FEM) is today a quite well established procedure, which opens doors to solving new and more complex problems using optimization approaches together with the FEM.

Optimization problems, such as, for instance, shape or topology optimization problems, use the finite element method along with optimization algorithms to reach an effective result. However, the difficulty of these kinds of problems is increased by the addition of the optimization algorithms intricacy to the known FEM simulation complexities. This fact makes these problems as one of the most challenging problems in engineering.

The use of optimization methods also allow to solve inverse problems, such as the parameter identification of material constitutive models used in the FEM. Additionally, several physical phenomena are naturally represented and simulated by an optimization problem.

This is the case when the "equilibrium" is attained at the minimum of an energy function and it is typical in, for instance, the case of contact problems in solids mechanics or biomechanical problems.

Engineering Optimization can have strong applications in industry. In metal forming, the development and design of forming tools can be still seen as a “trial-and-error” practice mainly due to complexities inherent to plastic forming processes. In industries, such as the automotive, where complex and innovative parts are constantly required at the shortest time possible, this practice can lead to large economical costs.

In this field, one of the goals of engineering optimization is to use automatic numerical procedures to determine the desired shape of the forming tools and the initial geometry of the metallic blank to be plastically formed in order to provide a final part after forming with the lowest level of imperfections. Doing so, common problems on open metallic parts such as springback, wrinkling, buckling instabilities, flow localization and fracture, are intended to be avoided. Additionally, other parameter such as, for instance, optimum blank holder pressure, optimum friction, minimum number of forming steps, to name but a few, are very useful for these kind of industrial processes.

This Awareness Seminar brought together experts in these areas of knowledge, to discuss the current state-of-the-art of numerical simulation techniques together with numerical optimization processes, and attempted to establish the future guidelines in the field.

Presentations

1_nafems_aveiro,_optimization_of_multiple_similar_parts_in_aeronautical_components.pdf

Optimisation of Multiple Similar Parts in Aeronautical Components. Tool Development and Applications
Enrique Marchante Parodi, Sener Ingeniería y Sistemas S.A.

2_aveiro_nafems_cad-based_shape_optimization_-_esther_andres.pdf

CAD-Based Aerodynamic Shape Design with the DLR TAU Code
Fernando Monge Gómez, Fluid Dynamics Dept, INTA, Madrid

3.1_nafems_nas_opt_2010_jpc.pdf

Topology Optimisation of Composite Structures
Part I: Asymptotic Expansion Homogenisation
J. Pinto-da-Cruz & J.A. Oliveira, University of Aveiro

3.2_nafems_nas_opt_2010_jalex.pdf

Topology Optimisation of Composite Structures
Part II: Multiscale Topology Optimisation
J. Pinto-da-Cruz & J.A. Oliveira, University of Aveiro

4_presentacionnafems-ferminnavarrina.pdf

Higher Order Sensitivity Analysis: A Unified Approach
Fermín Navarrina, Universidade da Coruña

modefrontier2.pdf

Multi-Disciplinary Methodologies for Process Integration and Design Optimization
GinoDuffett, AperioTec - EnginSoft