Gabriel Bugeda

A simple method for automatic update of finite element meshes

A simple method to automatically update the finite element mesh of the analysis domain is proposed. The method considers the mesh as a fictitious elastic body subjected to prescribed displacements at selected boundary points. The mechanical properties of each mesh element are appropriately selected in order to minimize the deformation and the distortion of the mesh elements. Different selection strategies have been used and compared in their application to simple examples. The method avoids the use of remeshing in the solution of shape optimization problems and reduces the number of remeshing steps in the solution of coupled fluid–structure interaction problems. Copyright

Numerical analysis of stereolithography processes using the finite element method

Stereolithography (SLA) is one of the most important techniques used in rapid prototyping processes. It has a great industrial interest because it allows for dramatic time savings with respect to traditional manufacturing processes. One of the main sources of error in the final dimensions of the prototype is the curl distortion effect owing to the shrinkage of the resin during the SLA process. Presents a study of the influence of different constructive and numerical parameters in the curl distortion, an analysis which was made using the computer code stereolithography analysis program, developed to model SLA processes using the finite element method. Also briefly presents this code.

Structural shape sensitivity analysis for nonlinear material models with strain softening

This paper describes some considerations around the analytical structural shape sensitivity analysis when the structural behaviour is computed using the finite element method with a nonlinear constitutive material model. Traditionally, the structural sensitivity analysis is computed using an incremental approach based on the incremental procedures for the solution of the structural equilibrium problem. In this work, a direct (nonincremental) formulation for computing these structural sensitivities, that is valid for some specific nonlinear material models, is proposed. The material models for which the presented approach is valid are characterized by the fact that the stresses at any timet can be expressed in terms of the strains at the timet and, in some cases, the strains at a specific past timetu (tu<t). This is the case of elasticity (linear as well as nonlinear), perfect plasticity and damage models. A special strategy is also proposed for material models with strain softening.For the cases where it is applicable, the sensitivity analysis proposed here allows us to compute the structural sensitivities around any structural equilibrium point after finishing the solution process and it is completely independent of the numerical scheme used to solve the structural equilibrium problem. This possibility is particularized for the case of a damage model considering a strain-softening behaviour. Finally, the quality and reliability of the proposed approach is assessed through its application to some examples.

A methodology for adaptive mesh refinement in optimum shape design problems

Abstract This work presents a methodology based on the use of adaptive mesh refinement (AMR) techniques in the context of shape optimization problems analyzed by the Finite Element Method (FEM). A suitable and very general technique for the parametrization of the optimization problem using B-splines to define the boundary is first presented. Then, mesh generation using the advancing front method, the error estimation and the mesh refinement criteria are dealt with in the context of a shape optimization problems. In particular, the sensitivities of the different ingredients ruling the problem (B-splines, finite element mesh, design behaviour, and error estimator) are studied in detail. The sensitivities of the finite element mesh coordinates and the error estimator allow their projection from one design to the next, giving an “a priori knowledge” of the error distribution on the new design. This allows to build up a finite element mesh for the new design with a specified and controlled level of error. The robustness and reliability of the proposed methodology is checked out with some 2D examples.

Lift maximization with uncertainties for the optimization of high lift devices using Multi-Criterion Evolutionary Algorithms

In this paper, the aerodynamic shape optimization problems with uncertain operating conditions has been addressed. After a review of robust control theory and the possible approaches to take into account uncertainties, the use of Taguchi robust design methods in order to overcome single point design problems in Aerodynamics is proposed. Under the Taguchi concept, a design with uncertainties is converted into an optimization problem with two objectives which are the mean performance and its variance, so that the solutions are as less sensitive to the uncertainty of the input parameters as possible. Furthermore, the Multi-Criterion Evolutionary Algorithms (MCEAs) are used to capture a set of compromised solutions (Pareto front) between these two objectives. The flow field is analyzed by Navier-Stokes computation using an unstructured mesh. The proposed approach drives to the solution of a multi-objective optimization problem that is solved using a modification of a Non-dominated Sorting Genetic Algorithm (NSGA). In order to reduce the number of expensive evaluations of the fitness function a Response Surface Modeling (RSM) is employed to estimate the fitness value using the polynomial approximation model. During the solution of the optimization problem a Semi-torsional Spring Analogy is used for the adaption of the computational mesh to all the obtained geometrical configurations. The proposed approach is applied to the robust optimization of the 2D high lift devices of a business aircraft by maximizing the mean and minimizing the variance of the lift coefficients with uncertain free-stream angle of attack at landing and takeoff flight conditions, respectively.

Some algorithms to correct a geometry in order to create a finite element mesh

Abstract One of the major difficulties in meshing 3D complex geometries is to deal with non-proper geometrical definitions coming from CAD systems. Typically, CAD systems do not take care of the proper definition of the geometries for the analysis purposes. In addition, the use of standard CAD files (IGES, VDA, …) for the transfer of geometries between different systems introduce some additional difficulties. In this work, a collection of algorithms to repair and/or to improve the geometry definitions are provided. The aim of these algorithms is to make as easy as possible the generation of a mesh over complex geometries given some minimum requirements of quality and correctness. The geometrical model will be considered as composed of a set of NURBS lines and trimmed surfaces. Some examples of application of the algorithms and of the meshes generated from the corrected geometry are also presented in this work.

Multi-objective design optimization of morphing UAV aerofoil/wing using hybridised MOGA

The paper investigates two advanced Computational Intelligence Systems (CIS) for a morphing Unmanned Aerial Vehicle (UAV) aerofoil/wing shape design optimisation. The first CIS uses Genetic Algorithm (GA) and the second CIS uses Hybridized GA (HGA) with the concept of Nash-Equilibrium to speed up the optimisation process. During the optimisation, Nash-Game will act as a pre-conditioner. Both CISs; GA and HGA, are based on Pareto optimality and they are coupled to Euler based Computational Fluid Dynamic (CFD) analyser and one type of Computer Aided Design (CAD) system during the optimisation. For the practical test case, one type of morphing techniques; Leading and Trailing Edge Deformation (LTED) is considered to control flow over the aerofoil/wing. LTED to a Natural Laminar Flow (NLF) aerofoil is applied to maximise the lift coefficients (Cl) at both the take-off and landing conditions. Two applications on LTED with low/middle and high design complexities are optimised using GA and HGA. The optimisation efficiency for GA and HGA are compared in terms of computational cost and design quality. Numerical results clearly show that Nash-Game helps a GA based CIS to accelerate the optimisation process and also to produce higher performance solutions in solving both the low/middle and high complex design optimisation problems. In addition numerical CFD study demonstrates that the implementation of morphing technique on the aerofoil/wing significantly improves the lift coefficients at both the take-off and landing conditions when compared to the baseline design.

Optimum aerodynamic shape design for fluid flow problems including mesh adaptivity

We present a methodology for solving shape optimization problems in the context of fluid flow problems including adaptive remeshing. The method is based on the computation of the sensitivities of the geometrical design parameters, the mesh, the flow variables and the error estimator to project the refinement parameters from one design to the next. The efficiency of the proposed method is checked out in two 2D optimization problems using a full potential model coupled with a boundary layer model. The first one corresponds to an internal flow problem and the second one corresponds to an external flow problem. The work presented here can be considered as a continuation of previous work. The sensitivity analysis corresponding to both an incompressible potential flow and a Euler flow were derived together with a strategy for the adaptive remeshing. The sensitivity analysis is derived for a full potential flow coupled with a boundary layer model, and a new error estimator is employed

Conclusions of the FractalComs Project: exploring the limits of fractal electrodynamics for the future telecommunication technologies

After two years of basic research on fractal electrodynamics, the FractalComs consortium presents the conclusions of the FractalComs Project (http://www.tsc.upc.es/fractalcoms/). They state the performance limits (fundamental and technological) of pre-fractal shaped miniature devices compared with conventional ones. Many miniature antennas and devices have been designed, analyzed and/or measured, the most outstanding being the two-arm square spiral antennas and the Hilbert superconductor resonators for miniature filters.

A C++ object-oriented programming strategy for the implementation of the finite element sensitivity analysis for a non-linear structural material model

Abstract The Finite Element Method (FEM) has become the most popular numerical method for solving a wide variety of complex engineering problems. However, from the programming point of view, when a FEM program has a lot of computational capabilities it is very difficult to maintain and enlarge the program codes. Recently the object-oriented programming paradigm has become a powerful method for overcoming such difficulties. This paper contains the description of an open environment for the FEM, written in C++, with explanations about how the sensitivity analysis and the non-linear material behaviour (damage models) have been taken into account.