Division of Mechanical Engineering Optimisation

> The Mission
The simulation of engineering processes is today a quite well established procedure, which opens doors to solve new and more complex problems using optimization approaches.
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 difficulties 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 state is attained at the minimum energy. In several applications, constraints must be satisfied.
The Division of Mechanical Engineering Optimization (DiMEO) centre the activity in the scientific area of Simulation and Numerical Optimization applied to industrial and mechanical engineering.

> Saving Costs Becoming Efficient
The development and design of forming tools can be still seen as a “trial-and-error” practice, based on previously obtained experience by engineers, mainly due to complexities inherent to plastic forming processes (large deformations, friction, springback and wrinkles in formed parts, to name a few). 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 and, consequently, lost of competitiveness.

One principal objective of DIMEO is to develop numerical procedures able to determine the desired shape of the forming tools and/or the initial geometry of the metallic blank to be plastically formed (as well as the most suitable process parameters involved) 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.
The mentioned objective corresponds to the resolution of an inverse problem. The aim of inverse problems is to determine one or more of the input data relating to the forming processes simulations, thereby leading to a desired result.

In order to simulate correctly the forming processes, it is also imperative to use complex material models and secure input data. For that reason, other objective of DiMEO is to develop and implement optimization methodologies able to identify the exact parameters for the material constitutive model without the need for time consuming experiments, at the same time granting that the results obtained from numerical simulations are in accordance to physical experiments. Both problems, shape/process and parameter identification problems are defined as inverse problems. As a part of the methodology for the material characterization, multi-axial experimental tests, with local multi-trajectories measurements, are also performed by DiMEO.

Research Topics and aims
A multidisciplinary research team composed by experts from mechanical technology, metallurgic engineering and computational mechanics guarantee that there is useful work produced in industrial and scientific terms.

> Engineering Design Optimization
Modern design techniques seek for the best design to perform the desired tasks. Engineering Optimization deals with the optimal design of elements and systems in all engineering fields. Nowadays, the use of Design Optimization techniques is rapidly growing in most of engineering disciplines, like mechanical engineering. This is due to the increase of technological competition and the development of strong and efficient techniques for several practical applications. Optimization problems, such as shape optimization, topological optimization, industrial processes optimization, metal forming blank and tool optimization, etc can be included.

> MDO – Multidisciplinary Design Optimization
Engineering Systems are increasingly complex and represented by large and sophisticated numerical models. They involve several interacting disciplines or are made up of distinct interacting subsystems that must be considered simultaneously to obtain efficient designs. Multidisciplinary Design Optimization is devoted to the design of complex systems involving interacting subsystems or disciplines. The main scientific challenges of MDO are concerned with the development of strong and efficient numerical techniques and with the computational organization required for the necessary coupling of codes employed in interacting disciplines.

> Inverse problems
Numerical methods for inverse problems in most of cases are based on optimization techniques similar to those employed in optimal design. In this topic, the identification of parameters for material constitutive models and system identification problems can be included.

> Basic Numerical Techniques
Engineering Optimization requires a large set of basic computer tools. This is the case of several CAD tools for geometric modelling, engineering analysis methods, sensitivity analysis as well as mathematical programming and genetic or evolutionary optimization algorithms. DiMEO works with the following optimization techniques: Artificial Intelligence and Neural Networks, Evolutionary Techniques, Fuzzy Optimization, Genetic Algorithms, Mathematical Programming Algorithms, Mixed-Integer Optimization, Optimality Criteria Methods, Optimization with Approximate Models, Response Surface Methods, Metamodels and Surrogates in Optimization, Real-Time Optimization and Reliability-Based Design Optimization. The sensibility analysis can be performed using Analytic and Semi-analytic Formulations, Variational Formulation, Automatic Differentiation or Topological Derivatives.

> Development of Numerical Methods and Techniques to Enhance Finite Element Analysis
Numerical methods in order to improve simulation methods, such as the finite element method are also analysed in DiMEO. Special attention is made to iterative strategies, numerical strategies for coupled problems and large deformation algorithms.

> Numerical Modelling and optimization of Heat Treatments in Steels and High Performance Alloys
The heat treatment processes, and particularly the quenching process, induce severe temperature gradients during the rapid cooling of the material from the complete solution temperature to room temperature.
Residual stresses and strains will also influence the final characteristics and mechanical properties of the part and may compromise its industrial application.
Strain control during the heat treatments processes resorts, almost exclusively, to empiric experience.
At present, except for simple geometries, the only economic and prompt way to assess residual stresses is to measure them with destructive testing techniques. These techniques bring to an end the subsequent utilization of the part.
Numerical simulations of heat treatments allow to find the best control variables in order to avoid the permanent deformations caused by fast non-uniform contraction of the material part.
The main objectives of our mission in this topic are
(i) Increase the knowledge with the use of efficient numerical tools capable of simulation with accuracy the evolution of the thermomechanical and metallurgic state of metal (steel and aluminium alloy) parts with complex geometry submitted to heat treatments;
(ii) Use of non-linear constitutive models and algorithms of thermomechanical coupling for metals;
(iii) Use parallelization techniques to speed up the CPU time;
(iv) Development and construction of the pivot equipment that executes and monitors experimentally the specific quenching test.

> Developed (and in development) Software
SdlOptLab (Optimization Framework)
The SDL optimization lab is designed for specific engineering inverse problems such as the parameter identification and the shape optimization problems. It inherits the large experience gain in such problems by the SiDoLo code and adds the latest developments in direct search optimization algorithms. The SDL Lab
can be used by researchers that wishes to control every step of the engineering optimization procedures or by users non-familiarized with programming languages that want to use an intuitive graphical interface with the optimization problem formulation already implemented and explained. The user subroutines in SDL allow the program to be customized for particular applications.

TopOptF (Topology optimization)
The TopOptF program objective is to find the optimum topology of two and three-dimensional structures. It uses a Finite Element analysis as objective function (stiffness maximization constrained to a volume fraction) and various optimization methods. This program also performs analysis to biomechanical structures, as bones, and its osteointegration conditions.

Adapco (Adaptation and determination of constitutive model parameters)
The Adapco program allows identifying the parameters of thermoelastic-viscoplastic behaviour models that uses internal variables to characterize the state of the material. In order to determine the parameters, it uses an optimization method based in evolutionary algorithms whose search space is real and continuum. The evolutionary algorithm used contains multiple selection, crossover, mutation, elitism, local refinement operators. The software uses a numerical integration method based in an explicit Runge-Kutta method with adaptive step and error control to integrate the constitutive equations written in differential formulation.

Nostradamus (Simulation of three-dimension thermomechanical processes of aluminium alloys)
The Nostradamus is a software developed for the prediction of thermomechanical stresses and strains induced during heat treatments.

> Other Software
Besides the software developed, FEM software, such as ABAQUS and DD3Imp, is also used in DiMEO.

> Competences, experimental and numerical capabilities
. Engineering optimisation;
. Design optimisation in metal forming;
. Design, shape and topology optimisation;
. Material characterisation by inverse analysis;
. Material experimental tests at room and warm temperature: tensile test, shear test, etc.
. Numerical analysis and optimisation of heat treatments.

> Water GRIDS


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