A comparison between new adaptive remeshing strategies based on point wise stress error estimation and energy norm error estimation

Traditionally, the most commonly used mesh adaptive strategies for linear elastic problems are based on the use of an energy norm for the measurement of the error, and a mesh refinement strategy based on the equal distribution of the error between all the elements. However, little attention has been paid to the study of alternative error norms and alternative refinement strategies. This paper studies the feasibility of using alternative mesh refinement strategies based on — the use of the classical error energy norm and an optimality criterion based on the equal distribution of the density of error, — the use of alternative error norms based on measurements of the point wise error contained in the main magnitudes that control the equilibrium problem and/or the material constitutive equations such as the stresses (e.g. the Von Mises stress). The feasibility of using all the described strategies is demonstrated through the solution of a benchmark example. This example is also used for comparison between the described refinement criteria

A new adaptive remeshing scheme based on the sensitivity analysis of the SPR point wise error estimation

This paper presents a formulation for the obtainment of the sensitivity analysis of a point wise error estimator with respect to the nodal coordinates using the adjoint state method. The proposed point wise error estimator is based on the SPR method. The numerical accuracy of the presented sensitivity analysis has been tested by perturbing a mesh. The capability of the presented sensitivity analysis for the detection of pollution error has also been tested. A new adaptive remeshing strategy based on the sensitivity analysis of the point wise error estimation has been developed and tested. This strategy produces very cheap meshes for the accurate evaluation of stresses at specific points

Optimum aerodynamic shape design for fluid flow problems including mesh adaptivity

This paper presents 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 (Bugeda and Oñate, Int. J. Numer. Methods Fluids, 20, 915–924 (1995)). In that paper, the sensitivity analysis corresponding to both an incompressible potential flow and a Euler flow were derived together with a strategy for the adaptive remeshing. In the present paper, the sensitivity analysis is derived for a full potential flow coupled with a boundary layer model, and a new error estimator is employed

Shape sensitivity analysis for structural problems with non‐linear material behaviour

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 non‐linear constitutive material model. Depending on the type of non‐linear behaviour two different approaches are proposed. First, a new direct (non‐incremental) formulation is proposed for material models characterized by the fact that the stresses at any time t can be expressed in terms of the strains at the same time t and, in some cases, the strains at a specific past time tu (tu<t). This is the case of elasticity (linear as well as non‐linear), perfect plasticity and damage models. Second, a more classical incremental approach is proposed for general plasticity cases. A special strategy is also proposed for material models with strain softening. The quality and reliability of the proposed approaches are assessed through their application in different examples

Control of the finite element discretization error during the convergence of structural shape optimization algorithms

[EN] This work analyzes the influence of the discretization error contained in the Finite Element (FE) analyses of each design configuration proposed by structural shape optimization algorithms over the behaviour of the algorithm. If the FE analyses are not accurate enough, the final solution will neither be optimal nor satisfy the constraints. The need for the use of adaptive FE analysis techniques in shape optimum design will be shown. The paper also proposes the use of the algorithm described in [1] in order to reduce the computational cost associated to the adaptive FE analysis of each geometrical configuration when evolutive optimization algorithms are used.¿The authors have been sponsored by the Spanish Ministerio de Ciencia e Innovación through the projects DPI2008-05250 (first author) and DPI2007-66773-C02-01 (second and third authors). The second and third authors have also been sponsored by the Generalitat Valenciana and the Universidad Politécnica de Valencia.Bugeda, G.; Ródenas, J.; Albelda Vitoria, J.; Oñate, E. (2009). Control of the finite element discretization error during the convergence of structural shape optimization algorithms. International Journal for Simulation and Multidisciplinary Design Optimization. 3(3):363-369. https://doi.org/10.1051/ijsmdo/2009012S3633693

Multilevel Monte-Carlo methods applied to the stochastic analysis of aerodynamic problems

This paper demonstrates the capabilities of the Multi-Level Monte Carlo Methods (MLMC) for the stochastic analysis of CFD aeronautical problems with uncertainties. These capabilities are compared with the classical Monte Carlo Methods in terms of accuracy and computational cost through a set of benchmark test cases. The real possibilities of solving CFD aeronautical analysis with uncertainties by using MLMC methods with a reasonable computational cost are demonstrated.Postprint (published version

Robust design methods in aerospace engineering

This document is an introduction to some important methodologies that have been developed in robust design in aerospace engineering. After describing the concept of robustness and uncertainty, multipoint, minimax, expected value, second order second moment and Taguchi methods are mentioned. At the end of this report, Game Theory, as one of the approach for multi objective optimization problems has been introduced

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

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

Numerical differentiation for local and global tangent operators in computational plasticity

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

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 timet u (t u<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 exampl