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[EN] The superconvergent patch recovery technique with constraints (SPR-C) consists in improving the accuracy of the recovered stresses obtained with the original SPR technique by considering known information about the exact solution, like the internal equilibrium equation, the compatibility equation or the Neumann boundary conditions, during the recovery process. In this paper the SPR-C is extended to consider the equilibrium around the contact area when solving contact problems with the Cartesian grid Finite Element Method. In the proposed method, the Finite Element stress fields of both bodies in contact are considered during the recovery process and the equilibrium is enforced by means of the continuity of tractions along the contact surface., The authors would like to thank Generalitat Valenciana (PROMETEO/2016/007), the Spanish Ministerio de Economía, Industria y Competitividad (DPI2017-89816-R), the Spanish Ministerio de Ciencia, Innovación y Universidades (FPU17/03993), and Universitat Politècnica de València (FPI2015) for the financial support to this work.

Summary This paper proposes a novel Immersed Boundary Method where the embedded domain is exactly described by using its Computer-Aided Design (CAD) boundary representation with Non-Uniform Rational B-Splines (NURBS) or T-splines. The common feature with other immersed methods is that the current approach substantially reduces the burden of mesh generation. In contrast, the exact boundary representation of the embedded domain allows to overcome the major drawback of existing immersed methods that is the inaccurate representation of the physical domain. A novel approach to perform the numerical integration in the region of the cut elements that is internal to the physical domain is presented and its accuracy and performance evaluated using numerical tests. The applicability, performance, and optimal convergence of the proposed methodology is assessed by using numerical examples in three dimensions. It is also shown that the accuracy of the proposed methodology is independent on the CAD technology used to describe the geometry of the embedded domain. Copyright © 2015 John Wiley & Sons, Ltd.

This is the pre-peer reviewed version of the following article: Tur, M., Albelda, J., Nadal, E. and Rodenas, J. J. (2014), Imposing Dirichlet boundary conditions in hierarchical Cartesian meshes by means of stabilized Lagrange multipliers. Int. J. Numer. Meth. Engng, 98: 399–417, which has been published in final form at http://dx.doi.org/10.1002/nme.4629 . This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.

In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the construction of a reduced model for the stress field. Upon ensuring that the reduced stress satisfies the equilibrium in the finite element sense, the desired bounding property is obtained. The lower bound is obtained by defining a hierarchical enriched reduced model for the displacement. We show that the sharpness of both error estimates can be seamlessly controlled by adapting the parameters of the corresponding reduced order model.

This is the peer reviewed version of the following article: Rodenas, J. J., Bugeda, G., Albelda, J. and Onate, E. (2011), On the need for the use of error-controlled finite element analyses in structural shape optimization processes. Int. J. Numer. Meth. Engng., 87: 1105–1126, which has been published in final form at http://dx.doi.org/10.1002/nme.3155. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.

[EN] A new stress recovery procedure that provides accurate estimations of the discretization error for linear elastic fracture mechanic problems analyzed with the extended finite element method (XFEM) is presented. The procedure is an adaptation of the superconvergent patch recovery (SPR) technique for the XFEM framework. It is based oil three fundamental aspects: (a) the use of a singular+smooth stress field decomposition technique involving the use of different recovery methods (or each field: standard SPR for the smooth field and reconstruction of the recovered singular field using the stress intensity factor K for the singular field: (b) direct calculation of smoothed stresses at integation points using conjoint polynomial enhancement and (c) assembly of patches with elements intersected by the crack using different stress interpolation polynomials at each side of the crack. The method was validated by testing it oil problems with an exact solution in mode I, mode II, and mixed mode and oil it problem without analytical solution. The results obtained showed the accuracy of the proposed error estimator., This paper was developed within the framework of the research projects DP12007-66773-C02-01 and DPI2007-66995-C03-02 of the Ministerio de Educacion y Ciencia (Spain). Funding was also received from the Generalitat Valenciana and the Universidad Politecnica de Valencia.

[EN] The superconvergent patch recovery (SPR) technique is widely used in the evaluation of a recovered stress field sigma* from the finite element Solution sigma(fe). Several modifications of the original SPR technique have been proposed. A new improvement of the SPR technique, called SPR-C technique (Constrained SPR), is presented in this paper. This new technique proposes the use of the appropriate constraint equations in order to obtain stress interpolation polynomials in the patch sigma(p)* that locally satisfy the equations that should be satisfied by the exact Solution. As a result the evaluated expressions for sigma(p)* will satisfy the internal equilibrium and compatibility equations in the whole patch and the boundary equilibrium equation at least in vertex boundary nodes and, under certain circumstances, along the whole boundary of the patch coinciding with the boundary of the domain. The results show that the use of this technique considerably improves the accuracy of the recovered stress field sigma* and therefore the local effectivity of the ZZ error estimator., This work has been carried out within the framework of the research project DPI2004-07782-C02-02 of the Ministerio de Educación y Ciencia (Spain).The financial support of the Generalitat Valenciana and the Universidad Politécnica de Valencia is also acknowledged.

The velocity field in shape sensitivity analysis is not uniquely defined although it must meet numerous theoretical and practical criteria. These practical criteria can be used to compare the existing velocity field computation methods which meet the theoretical criteria, but only in qualitative terms. When the FEM is used in design sensitivity analysis (DSA), due to the FE discretization error, the DSA errors will depend on the design velocity field considered. This paper presents a numerical methodology for quality evaluation of design velocity field computation methods in quantitative terms based on the analysis of the DSA discretization error. The sensitivity of the squared energy norm (χm = ∂∥u∥2/∂am, am being a design variable) has been taken as the magnitude to measure the error of the DSA. For h-refinements, the squared error in energy norm (∥e(u) ∥2) and the error in χm(e(χm)) are theoretically related by a constant which is independent of the refinement degree of the FE model. The quality of the design velocity field computation methods can therefore be assessed in terms of the stability of e(χm) /∥e(u) ∥2 in sequences of meshes. An example of the use of this methodology, where six design velocity field computation methods are compared, is presented. Copyright © 2004 John Wiley & Sons, Ltd.