pinecone/core-2020-05-10-deduplication huggingface dataset:
Linear matching method on the evaluation of plastic and creep behaviours for bodies subjected to cyclic thermal and mechanical loading

This paper extends the previous Linear Matching Method (LMM) to allow for the evaluation of plastic, creep and ratchet strains of structures subjected to a general load condition in a steady cyclic state. The constant and varying residual stress fields associated with differing mechanisms as well as the steady cyclic stress state of the whole component are obtained for further structural design and assessment. The total strain range for use in fatigue assessment, including the effects of creep and plastic strains are obtained. A typical example of 3D holed plate subjected to cyclic thermal load and constant mechanical load are assessed here in detail to verify the applicability of the proposed numerical technique. The LMM results in the paper are compared with those by ABAQUS step-bystep inelastic analyses and demonstrate that LMM have both the advantages of programming methods and the capacity to be implemented easily within a commercial finite element code, in this case, ABAQUS. The LMM provides a general-purpose technique for the evaluation of creep/ fatigue interaction
Complementarity methods for multibody friction contact problems in finite deformations

International audienceThis paper deals with the frictional contact occurring between deformable elastoplastic bodies subjected to large displacements and finite deformations. Starting from a standard slave=master formulation we have developed a symmetrical formulation with which the unilateral contact conditions and the friction law are satisfied for each body. From the continuum equations, the discretized frictional contact problem is set as a complementarity problem and solved using Lemke's mathematical programming method. The efficiency of the method is illustrated in the case of several examples
Level set X-FEM non matching meshes: application to dynamic crack propagation in elastic-plastic media

International audienceThis paper develops two aspects improving crack propagation modeling with the X-FEM method. On the one hand, it explains how one can use at the same time a regular structured mesh for a precise and efﬁcient level set update and an unstructured irregular one for the mechanical model. On the other hand, a new numerical scheme based on the X-FEM method is proposed for dynamic elastic-plastic situations. The simulation results are compared with two experiments on PMMA for which crack speed and crack path are provided
Equilibrated patch recovery error estimates: simple and accurate upper bounds of the error

This is the pre-peer reviewed version of the following article: Díez, P.; Rodenas, J.J.; Zienkiewicz, O.C. Equilibrated patch recovery error estimates: simple and accurate upper bounds of the error. "International journal for numerical methods in engineering", Març 2007, vol. 69, núm. 10, p. 2075-2098., which has been published in final form at http://www3.interscience.wiley.com/journal/112751914/abstractThis paper introduces a new recovery-type error estimator ensuring local equilibrium and yielding a guaranteed upper bound of the error. The upper bound property requires the recovered solution to be both statically equilibrated and continuous. The equilibrium is obtained locally (patch-by-patch) and the continuity is enforced by a postprocessing based on the partition of the unity concept. This postprocess is expected to preserve the features of the locally equilibrated stress field. Nevertheless, the postprocess phase modifies the equilibrium, which is no longer exactly fulfilled. A new methodology is introduced that yields upper bound estimates by taking into account this lack of equilibrium. This requires computing the L2 norm of the error or relating it with the energy norm.\ud
The guaranteed upper bounds are obtained by using a pessimistic bound of the error L2 norm, derived from an eigenvalue problem. Nevertheless, these bounds are not sharp. An additional strategy based on a more accurate assessment of the error L2 norm is introduced, providing sharp estimates, which are practical upper bounds as it is demonstrated in the numerical tests.Peer ReviewedPostprint (author’s final draft
Stabilized updated Lagrangian corrected SPH for explicit dynamic problems

This is the pre-peer reviewed version of the following article:Vidal, Y.; Bonet, J.; Huerta, A. Stabilized updated Lagrangian corrected SPH for explicit dynamic problems. "International journal for numerical methods in engineering", Març 2007, vol. 69, núm. 13, p. 2687-2710, which has been published in final form at http://www3.interscience.wiley.com/journal/112777203/abstractSmooth Particle Hydrodynamics with a total Lagrangian formulation are, in general, more robust than nite elements for large distortion problems. Nevertheless, updating the reference con¯guration\ud
may still be necessary in some problems involving extremely large distortions. However, as discussed here a standard updated formulation suffers the presence of zero energy modes that are activated\ud
and may spoil completely the solution. It is important to note that, unlike an Eulerian formulation,the updated Lagrangian does not present tension instability but only zero energy modes. Here an stabilization technique is incorporated to the updated formulation to obtain an improved method\ud
without mechanisms and capable to solve problems with extremely large distortions.Peer ReviewedPostprint (author’s final draft
A fast high-resolution algorithm for linear convection problems: particle transport method

The paper is devoted to a novel explicit technique, the particle transport method (PTM), for solving linear convection problems. While being a Lagrangian (characteristic based) method, PTM has the advantage of Eulerian methods to represent the solution on a fixed mesh. The proposed approach belongs to the class of monotone high-resolution numerical schemes, possesses the property of unconditional stability and works with structured and unstructured meshes. It is also demonstrated that the method has a linear computational complexity. The performance of the presented algorithm is tested on one- and two-dimensional benchmark problems. The numerical results confirm that the method has the 2nd-order spatial accuracy and can be significantly faster than the grid-based methods of the same order. Copyright © 2006 John Wiley & Sons, Ltd
Efficient handling of stability problems in shell optimization by asymmetric ‘worst-case’ shape imperfection

The paper presents an approach to shape optimization of proportionally loaded elastic shell structures under stability constraints. To reduce the stability-related problems, a special technique is utilized, by which the response analysis is always terminated before the first critical point is reached. In this way, the optimization is always related to a precritical structural state. The necessary load-carrying capability of the optimal structure is assured by extending the usual formulation of the optimization problem by a constraint on an estimated critical load factor. Since limit points are easier to handle, the possible presence of bifurcation points is avoided by introducing imperfection parameters. They are related to an asymmetric shape perturbation of the structure. During the optimization, the imperfection parameters are updated to get automatically the ‘worst-case’ pattern and amplitude of the imperfection. Both, the imperfection parameters and the design variables are related to the structural shape via the design element technique. A gradient-based optimizer is employed to solve the optimization problem. Three examples illustrate the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd
On the modelling of incompressibility in linear and non-linear elasticity with the master-slave approach

This is the pre-peer reviewed version of the following article: Muñoz, José J. On the modelling of incompressibility in linear and non-linear elasticity with the master-slave approach. "International journal for numerical methods in engineering", Abril 2008, vol. 74, núm. 2, p. 269-293., which has been published in final form at http://www3.interscience.wiley.com/journal/116323442/abstractThe master-slave approach is adapted to model the kinematic constraints encountered in incompressibility. The method presented here allows us to obtain discrete displacement and pressure fields for arbitrary finite element formulations that have discontinuous pressure interpolations. The resulting displacements satisfy exactly the incompressibility constraints in a weak sense, and are obtained by solving a system of equations with the minimum (independent) degrees of freedom. In linear analysis, the method reproduces the well-known stability results for inf-sup compliant elements, and permits to compute the pressure modes (physical or spurious) when they exist. By rewriting the equilibrium equations of a hyperelastic material, the method is extended to non-linear elasticity, while retaining the exact fulfilment of the incompressibility constraints in a weak sense. Problems with analytical solution in two and three dimensions are tested and compared with other solution methods.Peer ReviewedPostprint (author’s final draft
The iterated sinh transformation

A sinh transformation has recently been proposed to improve the numerical accuracy of evaluating nearly singular integrals using Gauss-Legendre quadrature. It was shown that the transformation could improve the accuracy of evaluating such integrals, which arise in the boundary element method, by several orders of magnitude. Here, this transformation is extended in an iterative fashion to allow the accurate evaluation of similar types of integrals that have more spiked integrands.    Results show that one iteration of this sinh transformation is preferred for nearly weakly singular integrals, whereas two iterations lead to several orders of magnitude improvement in the evaluation of nearly strongly singular integrals. The same observation applies when considering integrals of derivatives of the two-dimensional boundary element kernel. However, for these integrals, more iterations are required as the distance from the source point to the boundary element decreases.Full Tex
A control volume-based finite element method for plane micropolar elasticity

This paper describes the development of a numerical procedure for predicting deformations and stresses in a loaded two-dimensional membrane exhibiting micropolar or Cosserat constitutive behaviour. The procedure employs a conventional finite element (FE) mesh together with a dual mesh of interconnected control volumes, each of which must satisfy equilibrium. A series of patch tests covering a variety of simple strain states are used to validate the procedure that is then employed to predict the stress concentration in a membrane containing a small hole. The predictions provided by the procedure are compared with those given previously by FEs
NURBS-enhanced finite element method (NEFEM)

This is the pre-peer reviewed version of the following article: Sevilla, R.; Fernandez, S.; Huerta, A. NURBS-enhanced finite element method (NEFEM). "International journal for numerical methods in engineering", Octubre 2008, vol. 76, núm. 1, p. 56-83., which has been published in final form at http://www3.interscience.wiley.com/journal/117912616/abstractAn improvement to the classical finite element (FE) method is proposed. It is able to exactly represent the geometry by means of the usual CAD description of the boundary with non-uniform rational B-splines (NURBS). Here, the 2D case is presented. For elements not intersecting the boundary, a standard FE interpolation and numerical integration are used. But elements intersecting the NURBS boundary need a specifically designed piecewise polynomial interpolation and numerical integration. A priori error estimates are also presented. Finally, some examples demonstrate the applicability and benefits of the proposed methodology. NURBS-enhanced finite element method (NEFEM) is at least one order of magnitude more precise than the corresponding isoparametric FE in every numerical example shown. This is the case for both continuous and discontinuous Galerkin formulations. Moreover, for a desired precision, NEFEM is also more computationally efficient, as shown in the numerical examples. The use of NEFEM is strongly recommended in the presence of curved boundaries and/or when the boundary of the domain has complex geometric details. The possibility of computing an accurate solution with coarse meshes and high-order interpolations makes NEFEM a more efficient strategy than classical isoparametric FE.Peer ReviewedPostprint (author’s final draft
SPH with the multiple boundary tangent method

In this article, we present an improved solid boundary treatment formulation for the smoothed particle hydrodynamics (SPH) method. Benchmark simulations using previously reported boundary treatments can suffer from particle penetration and may produce results that numerically blow up near solid boundaries. As well, current SPH boundary approaches do not properly treat curved boundaries in complicated flow domains. These drawbacks have been remedied in a new boundary treatment method presented in this article, called the multiple boundary tangent (MBT) approach. In this article we present two important benchmark problems to validate the developed algorithm and show that the multiple boundary tangent\ud
treatment produces results that agree with known numerical and experimental solutions. The two benchmark problems chosen are the lid-driven cavity problem, and flow over a cylinder. The SPH solutions using the MBT approach and the results from literature are in very good agreement. These solutions involved\ud
solid boundaries, but the approach presented herein should be extendable to time-evolving, free-surface boundaries
QALE-FEM for numerical modelling of non-linear interaction between 3D moored floating bodies and steep waves

This paper presents further development of the QALE-FEM (Quasi Arbitrary Lagrangian-Eulerian Finite Element Method) based on a fully nonlinear potential theory to numerically simulate nonlinear responses of 3D moored floating bodies to steep waves. In the QALE-FEM (recently developed by the authors and applied to 2D floating bodies), the complex unstructured mesh is generated only once at the beginning of calculation and is moved to conform to the motion of boundaries at other time steps by using a robust spring analogy method specially suggested for this kind of problems, avoiding the necessity of high cost remeshing. In order to tackle challenges associated with 3D floating bodies, several new numerical techniques are developed in this paper. These include the technique for moving the mesh near body surfaces, the scheme for calculating velocity on 3D body surfaces and the ISITIMFB-M (Iterative Semi-Implicit Time Integration Method for Floating Bodies - Modified) procedure that is more efficient for dealing with the full coupling between waves and bodies. Using the newly developed techniques and methods, various cases for 3D floating bodies with motions of up to 6 degrees of freedom (DoFs) are simulated. These include a SPAR platform, a barge-type floating body and one or two Wigley Hulls in head seas or in oblique waves. For some selected cases, the numerical results are compared with experimental data available in the public domain and satisfactory agreements are achieved. Many results presented in this paper have not been found elsewhere to the best knowledge of the authors
A domain decomposition strategy to efficiently solve structures
  containing repeated patterns

This paper presents a strategy for the computation of structures with
repeated patterns based on domain decomposition and block Krylov solvers. It
can be seen as a special variant of the FETI method. We propose using the
presence of repeated domains in the problem to compute the solution by
minimizing the interface error on several directions simultaneously. The method
not only drastically decreases the size of the problems to solve but also
accelerates the convergence of interface problem for nearly no additional
computational cost and minimizes expensive memory accesses. The numerical
performances are illustrated on some thermal and elastic academic problems
Identification of random shapes from images through polynomial chaos expansion of random level-set functions

International audienceIn this paper, an efficient method is proposed for the identification of random shapes in a form suitable for numerical simulation within the eXtended Stochastic Finite Element Method (X-SFEM). The method starts from a collection of images representing different outcomes of the random shape to identify. The key-point of the method is to represent the random geometry in an implicit manner using the level-set technique. In this context, the problem of random geometry identification is equivalent to the identification of a random level-set function, which is a random field. This random field is represented on a polynomial chaos basis and various efficient numerical strategies are proposed in order to identify the coefficients of its polynomial chaos decomposition. The performance of these strategies is evaluated through some "manufactured" problems and useful conclusions are provided. The propagation of geometrical uncertainties in structural analysis using the X-SFEM is finally examined
Multi-scale domain decomposition method for large scale structural analysis with a zooming technique : Application to plate assembly

International audienceThis article is concerned with a multi-scale domain decomposition method (DDM), based on the FETI-DP solver, for large-scale structural elastic analysis and suited to problems that exhibit structural heterogeneities, such as plate assemblies in the presence of structural details. In this approach once a partition of the global fine mesh into subdomains has been performed (all subdomains possess a fine mesh) and to optimize the computational time, the fine mesh is preserved only in the zones of interest (with local phenomena due to discontinuity, hole, etc.) while the remaining subdomains are replaced by numerical homogenized coarse elements. Indeed, the multi-scale aspect is introduced by the description of subdomains with either a fine or a coarse scale mesh. As a result, an extension of the FETI-DP DDM is proposed in this article (called herein FETI-DP micro-macro) that allows the simultaneous usage of different discretizations: fine (microscopic) mesh for subdomains in zones of interest and coarse (macroscopic or homogenized) mesh for the complementary part of the structure. Using this strategy raises the problem of the determination of the stiffness of coarse subdomains, and of the incompatible finite element connection between fine and coarse subdomains. Two approaches (collocation and Mortar) are presented and compared. The article ends with patch tests and some numerical examples in 2D and 3D. The obtained numerical results exemplify the efficiency and capability of the FETI-DP micro-macro approach and reveal that the Mortar approach is more accurate, at constant cost, than the collocation approach
Smooth, second order, non-negative meshfree approximants selected by maximum entropy

This is the pre-peer reviewed version of the following article: Cyron, C.J.; Arroyo, M.; Ortíz, M. Smooth, second order, non-negative meshfree approximants selected by maximum entropy. "International journal for numerical methods in engineering", Maig 2009, vol. 79, núm. 13, p. 1605-1632, which has been published in final form at http://www3.interscience.wiley.com/journal/122373763/abstractWe present a family of approximation schemes, which we refer to as second-order maximum-entropy (max-ent) approximation schemes, that extends the first-order local max-ent approximation schemes to second-order consistency. This method retains the fundamental properties of first-order max-ent schemes, namely the shape functions are smooth, non-negative, and satisfy a weak Kronecker-delta property at the boundary. This last property makes the imposition of essential boundary conditions in the numerical solution of partial differential equations trivial. The evaluation of the shape functions is not explicit, but it is very efficient and robust. To our knowledge, the proposed method is the first higher-order scheme for function approximation from unstructured data in arbitrary dimensions with non-negative shape functions. As a consequence, the approximants exhibit variation diminishing properties, as well as an excellent behavior in structural vibrations problems as compared with the Lagrange finite elements, MLS-based meshfree methods and even B-Spline approximations, as shown through numerical experiments. When compared with usual MLS-based second-order meshfree methods, the shape functions presented here are much easier to integrate in a Galerkin approach, as illustrated by the standard benchmark problems.Peer ReviewedPostprint (author’s final draft
Design of quadrature rules for Müntz and Müntz-logarithmic polynomials using monomial transformation

A method for constructing the exact quadratures for Müntz and Müntz-logarithmic polynomials is presented. The algorithm does permit to anticipate the precision (machine precision) of the numerical integration of Müntz-logarithmic polynomials in terms of the number of Gauss-Legendre (GL) quadrature samples and monomial transformation order. To investigate in depth the properties of classical GL quadrature, we present new optimal asymptotic estimates for the remainder. In boundary element integrals this quadrature rule can be applied to evaluate singular functions with end-point singularity, singular kernel as well as smooth functions. The method is numerically stable, efficient, easy to be implemented. The rule has been fully tested and several numerical examples are included. The proposed quadrature method is more efficient in run-time evaluation than the existing methods for Müntz polynomial
Recent Advances in the Use of Separated Representations

International audienceSeparated representations based on finite sum decompositions constitute an appealing strategy for reducing the computer resources and the calculation costs by reducing drastically the number of degrees of freedom that the functional approximations involve (the number of degrees of freedom scale linearly with the dimension of the space in which the model is defined instead of the exponential growing characteristic of mesh-based discretization strategies). In our knowledge the use of separated representations is the only possibility for circumventing the terrific curse of dimensionality related to some highly multidimensional models involving hundreds of dimensions, as we proved in some of our former works. Its application is not restricted to multidimensional models, obviously separated representation can also be applied in standard 2D or 3D models, allowing for high resolution computations. Because its early life numerous issues persist, many of them attracting the Curiosity of many research groups within the computational mechanics community. In this paper we are focusing in two issues never until now addressed: (i) the imposition of non-homogenous essential boundary conditions and (ii) the consideration of complex geometries