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The paper describes the extension of the critical displacement method (CDM), presented by Oñate and Matias in 1996, to the instability analysis of structures with non-linear material behaviour using a simple damage model. The extended CDM is useful to detect instability points using a prediction of the critical displacement field and a secant load-displacement relationship accounting for material non-linearities. Examples of application of CDM to the instability analysis of structures using bar and solid finite elements are presented.

The subject of this paper is the computation of instability points in mechanical problems with the finite element method. The objective is to extend the application of critical point detection methods to problems with inequality constraints originating from damage and contact. A simple bilinear model is considered for the damage problems. A bilateral, frictionless contact formulation is used for the contact problems. Among the critical point detection methods the focus is laid on the critical displacement method and the extended system. At first a possible combination of both methods is evaluated by applying them to damage problems. A prediction method based on the extended system is developed to facilitate the comparison of both methods. Secondly, the extended system is used as a computation method for critical points in two‐dimensional contact problems.

An enhanced rotation-free three node triangular shell element (termed EBST) is presented. The element formulation is based on a quadratic interpolation of the geometry in terms of the six nodes of a patch of four triangles associated to each triangular element. This allows to compute an assumed constant curvature field and an assumed linear membrane strain field which improves the in-plane behaviour of the element. A simple and economic version of the element using a single integration point is presented. The implementation of the element into an explicit dynamic scheme is described. The efficiency and accuracy of the EBST element and the explicit dynamic scheme are demonstrated in many examples of application including the analysis of a cylindrical panel under impulse loading and sheet metal stamping problems.

An incompressible Finite Element Lagrangian code is presented and validated against classical experimental and numerical Eulerian results. The main distinction between an Eulerian and a Lagrangian approach is due to the convection of the mesh with the computed velocity. On one hand, the convective term is taken into account in the total derivative of the velocity, which greatly simplifies its numerical treatment. On the other hand, a constant remeshing must be performed to maintain a good element quality due to the large deformations undergone by the fluid. The classical cylinder and the thermally coupled cavity benchmarks have been chosen to perform a detailed comparison with an Eulerian code, FEFLO, and experimental results.

This paper shows the recent work of the authors in the development of a time-domain FEM model for evaluation of the seal dynamics of a surface effect ship. The fluid solver developed for this purpose, uses a potential flow approach along with a streamline integration of the free surface. The paper focuses on the free surface-structure algorithm that has been developed to allow the simulation of the complex and highly dynamic behaviour of the seals in the interface between the air cushion, and the water.; The developed fluid-structure interaction solver is based, on one side, on an implicit iteration algorithm, communicating pressure forces and displacements of the seals at memory level and, on the other side, on an innovative wetting and drying scheme able to predict the water action on the seals. The stability of the iterative scheme is improved by means of relaxation, and the convergence is accelerated using Aitken's method.; Several validations against experimental results have been carried out to demonstrate the developed algorithm. (C) 2015 Elsevier B.V. All rights reserved.

In this paper, an adjoint-based error estimation and mesh adaptation framework is developed for the compressible inviscid flows. The algorithm employs the Finite Calculus (FIC) scheme for the numerical solution of the flow and discrete adjoint equations in the context of the Galerkin finite element method (FEM) on triangular grids. The FIC scheme treats the instabilities normally generated in the numerical solution of the fluid equations through adding two stabilization terms, called streamline term and transverse term, to the original central-based discretized formulation. The non-linear system of equations resulting from the flow problem is solved implicitly using a damped Newton's method accompanied with the exact Jacobian matrix. A defect corrected scheme is implemented to iteratively solve the linear system of equations related to the adjoint problem benefiting from the transpose of the Jacobian matrix. At each iteration, the linear systems of equations resulting from the fluid and adjoint problems are solved using a preconditioned GMRES method. Having calculated the error of a specified output functional locally, an h-refinement methodology based on the element subdivision is performed to refine the candidate elements. The quality of the numerical results proves the capability of the presented approach for the adjoint-based error estimation and mesh adaptation problems in different flow regimes.

In this work we put the method proposed by van Hinsberg et al. [29] to the test, highlighting its accuracy and efficiency in a sequence of benchmarks of increasing complexity. Furthermore, we explore the possibility of systematizing the way in which the method's free parameters are determined by generalizing the optimization problem that was considered originally. Finally, we provide a list of worked-out values, ready for implementation in large-scale particle-laden flow simulations.

Este trabajo combina un elemento de sólido basado en una formulación lagrangeana total que utiliza deformaciones logarítmicas con una aproximación clásica de deformaciones transversales impuestas para láminas gruesas. El objetivo es poder utilizar el elemento para la simulación de láminas sin que bloquee por cortante. Se resume la técnica de escalamiento selectivo de masa utilizada a los fines de que la discretización en el espesor no condicione el tiempo crítico en códigos con integración explícita de las ecuaciones de movimiento. Se presentan varios ejemplos que muestran el comportamiento libre de bloqueo por corte del elemento, la influencia del escalamiento de masa y las posibilidades del elemento para el análisis de laminados en régimen no lineal material. In this work a solid finite element based on a Total Lagrangian Formulation using logarithmic strains is combined with a classical assumed strain approach of the transverse strains for thick shells. The target is to use the element for shell simulations without shear locking. The selective mass scaling technique used to avoid that the discretization across the thickness reduce the critical time in codes with explicit integration of the momentum equations is summarized. Several examples are presented showing that the element is shear-locking free, the consequences of the selective mass scaling and the possibilities of the element for the analysis of composites laminates in non-linear material regime.

The extended Delaunay tessellation (EDT) is presented in this paper as the unique partition of a node set into polyhedral regions defined by nodes lying on the nearby Voronoï spheres. Until recently, all the FEM mesh generators were limited to the generation of tetrahedral or hexahedral elements (or triangular and quadrangular in 2D problems). The reason for this limitation was the lack of any acceptable shape function to be used in other kind of geometrical elements. Nowadays, there are several acceptable shape functions for a very large class of polyhedra. These new shape functions, together with the EDT, gives an optimal combination and a powerful tool to solve a large variety of physical problems by numerical methods. The domain partition into polyhedra presented here does not introduce any new node nor change any node position. This makes this process suitable for Lagrangian problems and meshless methods in which only the connectivity information is used and there is no need for any expensive smoothing process. Fil: Calvo, Nestor Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina Fil: Idelsohn, Sergio Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina Fil: Oñate, Eugenio. Universidad Politecnica de Catalunya; España

Current work presents a monolithic method for the solution of fluid–structure interaction problems involving flexible structures and free-surface flows. The technique presented is based upon the utilization of a Lagrangian description for both the fluid and the structure. A linear displacement–pressure interpolation pair is used for the fluid whereas the structure utilizes a standard displacement-based formulation. A slight fluid compressibility is assumed that allows to relate the mechanical pressure to the local volume variation. The method described features a global pressure condensation which in turn enables the definition of a purely displacement-based linear system of equations. A matrix-free technique is used for the solution of such linear system, leading to an efficient implementation. The result is a robust method which allows dealing with FSI problems involving arbitrary variations in the shape of the fluid domain. The method is completely free of spurious added-mass effects.

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.

A local damage constitutive model based on Kachanov’s theory is used within a finite element frame and applied to the case of 2D and 3D Timoshenko beam elements. The model takes into account viscous effects, thus allowing damping to be considered in a rigorous way. A damage index based on potential energy criteria, useful in evaluating the behaviour of structures or of parts of structures, is proposed. The procedure is applied to estimate the damage produced by seismic actions in reinforced concrete building structures, whose response is computed by using a non-linear Newmark-type incremental time integration scheme. Three numerical examples are included; one of them compares results obtained by using the proposed model with results of a laboratory test. &nbsp

This paper presents a new computational technique for predicting the onset and evolution of fracture in a continuum in a simple manner combining the finite element method (FEM) and the discrete element method (DEM). Onset of cracking at a point is governed by a simple damage model. Once a crack is detected at an element side in the FE mesh, discrete elements are generated at the nodes sharing the side and a simple DEM mechanism is considered to follow the evolution of the crack. The combination of the DEM with simple 3-noded linear triangular elements correctly captures the onset of fracture and its evolution, as shown in several examples of application in two and three dimensions.

With rising environmental alarm, the reduction of critical aircraft emissions including carbon dioxides (CO2) and nitrogen oxides (NOx) is one of most important aeronautical problems. There can be many possible attempts to solve such problem by designing new wing/aircraft shape, new efficient engine, etc. The paper rather provides a set of acceptable flight plans as a first step besides replacing current aircrafts. The paper investigates a green aircraft design optimisation in terms of aircraft range, mission fuel weight (CO2) and NOx using advanced Evolutionary Algorithms coupled to flight optimisation system software. Two multi-objective design optimisations are conducted to find the best set of flight plans for current aircrafts considering discretised altitude and Mach numbers without designing aircraft shape and engine types. The objectives of first optimisation are to maximise range of aircraft while minimising NOx with constant mission fuel weight. The second optimisation considers minimisation of mission fuel weight and NOx with fixed aircraft range. Numerical results show that the method is able to capture a set of useful trade-offs that reduce NOx and CO2 (minimum mission fuel weight).

Presents a numerical strategy for the aerodynamic analysis of large buildings, with an application to the simulation of the air flow within a telescope building. The finite element formulation is presented first, and then the methodology followed to obtain significant data from the calculations is described. The quality of the ventilation of the building is defined by the average residence times, and the feasibility of this ventilation by the actions created on the instruments and the general flow pattern.

The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-006-0060-y We present a general formulation for incompressible fluid flow analysis using the finite element method. The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the Finite Calculus method using a matrix form of the stabilization parameters. This allows to model a wide range of fluid flow problems for low and high Reynolds numbers flows without introducing a turbulence model. Examples of application to the analysis of incompressible flows with moderate and large Reynolds numbers are presented.

The finite point method (FPM) is a gridless numerical procedure based on the combination of weighted least square interpolations on a cloud of points with point collocation for evaluating the approximation integrals. In the paper, details of a procedure for stabilizing the numerical solution for advective-diffusive transport and fluid flow problems using the FPM are given. The method is based on a consistent introduction of the stabilizing terms in the governing differential equations. One example showing the applicability of the FPM is given.

In this paper a meshless procedure termed ‘the finite point method’ for solving convection-diffusion and fluid flow type problems is presented. The method is based on the use of a weighted least-square interpolation procedure together with point collocation for evaluating the approximation integrals. Special emphasis is given to the stabilization of the convective terms and the Neumann boundary condition which has been found to be essential to obtain accurate results. Some examples of application to diffusive and convective transport and compressible flow problems using quadratic FP interpolations are presented.

This paper describes the latest advances on SIMPACT, a general purpose, large deformation, explicit structural dynamics code developed at the Center for Numerical Methods in Engineering (CIMNE), and its couling with FEFLO, a general purpose compressible and incompressible flow solver based on adaptive unstructured grids. Details on the codes, as well as the coupling strategy are given. Examples illustrate the possibilies the present fluid-structure coupling offers.

The final publication is available at Springer via http://dx.doi.org/10.1007/s00603-016-1133-7 This paper presents advanced computer simulation of rock cutting process typical for excavation works in civil engineering. Theoretical formulation of the hybrid discrete/finite element model has been presented. The discrete and finite element methods have been used in different subdomains of a rock sample according to expected material behaviour, the part which is fractured and damaged during cutting is discretized with the discrete elements while the other part is treated as a continuous body and it is modelled using the finite element method. In this way, an optimum model is created, enabling a proper representation of the physical phenomena during cutting and efficient numerical computation. The model has been applied to simulation of the laboratory test of rock cutting with a single TBM (tunnel boring machine) disc cutter. The micromechanical parameters have been determined using the dimensionless relationships between micro- and macroscopic parameters. A number of numerical simulations of the LCM test in the unrelieved and relieved cutting modes have been performed. Numerical results have been compared with available data from in-situ measurements in a real TBM as well as with the theoretical predictions showing quite a good agreement. The numerical model has provided a new insight into the cutting mechanism enabling us to investigate the stress and pressure distribution at the tool–rock interaction. Sensitivity analysis of rock cutting performed for different parameters including disc geometry, cutting velocity, disc penetration and spacing has shown that the presented numerical model is a suitable tool for the design and optimization of rock cutting process.

This study proposes a digital tool able to determinate, using a surface’s free form data, a CRFS (complex reciprocal frame structures) made of the aggregation of SRFU (single reciprocal frame units) on a squared grid without changing eccentricity, position and dimensions of the rods and changing only the length. This choice allows to design new structures from synclastic surfaces, even if very complex, but equipped with a fundamental technical feature of being made with equal rods that generate different SRFUs. Using different algorithms already known, the new tool creates spherical cap surface CRFS that approximate to wanted surface. The original contribution of this work in based on this last step which uses dynamic relaxation and brings the spherical CRFS to ease down on the desired non-spherical geometry, without losing the reciprocity’s bonds between the rods.

The study investigates the design and construction processes of masonry domes built without the use of centrings. In particular, it focuses on those built using a ‘compass’, i.e. an erection device that simplifies the construction process, and guarantees the bricklaying accuracy. The foundation of this research project can be found in the work of Fabrizio Carola (1931-2019) who used an erection method for masonry domes inspired by the ‘Nubian vault technique’. The design and construction processes used by Carola have been analyzed with the aim of identifying a sequence of operations, which were then simulated in a digital environment by means of recursive algorithms. Finally, the study moved to the implementation of two bespoke designed contraptions for the design of non-spherical domes. The result of this study is a computational tool which can be used to design different typologies of centring-less masonry domes and simulate their construction process.

International audience; An overview of various numerical methods developed for speeding-up computations is presented in the field of the bulk material forming under solid state, which is characterized by complex and evolving geometries requiring frequent remeshings and numerous time increments. These methods are oriented around the axis that constitutes the meshing problem. The multi-mesh method allows to optimally solve several physics involved on the same domain, according to its finite element discretization with several different meshes, for example in the cogging or cold pilgering processes. For quasi steady-state problems and problems with quite pronounced localization of deformation, such as Friction Stir Welding (FSW) or High Speed Machining, an Arbitrary Lagrangian or Eulerian formulation (ALE) with mesh adaptation shows to be imperative. When the problem is perfectly steady, as for the rolling of long products, the direct search for the stationary state allows huge accelerations. In the general case, where no process specificity can be used to solve the implicit equations, the multigrid method makes it possible to construct a much more efficient iterative solver, which is especially characterized by an almost linear asymptotic cost.

In this paper we study a simplified mathematical model representative of air-sea coupling. This model incorporates parameterizations of the turbulent boundary layers as used in realistic models. We show that even if simple equations like the one- dimensional stationary heat equation are considered the presence of parameterizations renders the problem extremly complex to study and the unicity of solutions is no longer guaranteed. We motivate and describe a coupling algorithm which ensures that a unique physically sound solution is obtained.

International audience; This paper studies numerical algorithms for the simulation of mechanical systems including rigid and flexible bodies, kinematic joints and frictionless contact conditions. The condition of impenetrability of the bodies in contact is expressed as a unilateral constraint, with the consequence that impacts and/or instantaneous changes in the velocities may arise in the dynamic response. When dynamic contacts are analyzed between elastic solids and structures, the gap velocity is necessarily discontinuous otherwise a non-physical penetration of the bodies would occur. When contacts between rigid bodies are studied, e.g., in multibody systems, impulsive reaction forces can also occur leading to an instantaneous change in the linear and angular momenta of each body. Standard schemes, such as the Newmark, HHT or generalized-α methods, are not consistent in these cases since the numerical response may artificially generate energy when a contact occurs. In order to analyze impact phenomena, nonsmooth time integration methods have been proposed in the literature and can be classified into two main groups, namely, event-driven schemes and time-stepping schemes. Event-driven schemes are accurate for the free flight smooth motions and are especially suitable for small multi-body systems with a limited number of events, but they become inefficient if frequent transitions occur in a short time. Time-stepping methods, such as Moreau–Jean scheme, have been proven to be convergent and robust even for a large number of events, and are extensively applied as the solution to nonsmooth system models.

Metamaterials are a family of artificially engineered materials consisting of an array of periodically arranged microstructures, offering unusual material properties that may not be easily found in nature. This paper will propose a new topological shape optimization method for the design of mechanical metamaterials with negative Poisson’s ratios, by integrating the numerical homogenization method with a powerful level set method. The homogenization method is used to calculate the effective properties of the microstructure, and the level set method is utilized to implement shape and topology optimization of the microstructure until the desired material properties are obtained. The proposed method can retain the unique features of the level set methods, while avoid unfavourable numerical issues occurred in the conventional level set methods. Several typical numerical examples are used to showcase the effectiveness of the proposed design method.

9788494284472; International audience; In our study we propose to solve the transient heat equation related to a thermal source moving with non uniform velocity, using the so called PGD method. The velocity will be parametrized and the coefficients involved in it included as model extra-coordinates, allowing the calculation of a general parametric solution.

ISBN 978-84-942844-7-2; International audience; This paper presents a parallel remeshing algorithm for distributed-memory architectures. It is an iterative parallel algorithm that divides the areas to be remeshed into multiple pieces which can be distributed to as many processing elements as pos-sible, in order for these pieces to be remeshed concurrently by a third-party sequential remesher. Then, remeshed pieces are reintegrated into the distributed mesh, and this pro-cess is iterated until all relevant areas of the mesh have been remeshed. Any sequential remesher can be used, provided it allows some of the mesh elements not to be modified, so as to preserve interfaces between pieces. Our method, which has been implemented in the PaMPA library, is validated by a set of experiments involving both isotropic and anisotropic meshes.

La presencia simultánea de múltiples fluidos con diferentes propiedades ocurre en numerosos problemas medioambientales, procesos industriales y situaciones de la vida diaria. Algunos ejemplos son la interacción fluido-combustible en la extracción mejorada de petróleo, mezcla de polímeros, emulsiones en productos alimentarios, formación de gotas de lluvia en nubes, inyección en motores de combustión o reactores de columna de burbujas. A pesar de que los flujos de multi-fluidos son muy frecuentes, todavía suponen un reto tanto desde el punto de vista teórico como computacional. En el caso de fluidos inmiscibles, la dinámica de la interfase entre fluidos juega un papel determinante. El éxito en la simulación de estos flujos dependerá de la capacidad del método numérico de modelar con precisión la interfase y los fenómenos que tienen lugar en ella. En este trabajo nos hemos centrado en entender la principios físicos básicos de los multi-fluidos y las dificultades que aparecen en su simulación numérica. Hemos extendido el Particle Finite Element Method (PFEM) a problemas de varios fluidos diferentes con el objetivo de explotar el hecho de que los métodos lagrangianos son especialmente adecuados para el seguimiento de todo tipo de interfases. Hemos desarrollado un esquema numérico capaz de tratar grandes saltos en las propiedades físicas (densidad y viscosidad), de incluir la tensión superficial y de representar las discontinuidades de las variables del flujo. El esquema se basa en desacoplar las variables de posición de los nodos, velocidad y presión a través de la linearización de Picard y un método de segregación de la presión que tiene en cuenta las condiciones de interfase. La interfase se ha definido alineada con la malla móvil, de forma que se mantiene el salto de propiedades físicas sin suavizar a lo largo del tiempo. Además, los grados de libertad de la presión han sido duplicados en los nodos de interfase para representar la discontinuidad de esta variable debido a la tensión superficial y a la viscosidad variable, y la malla ha sido refinada cerca de la interfase para mejorar la precisión de la simulación. Hemos aplicado el esquema resultante a diversos problemas académicos y geológicos, como el sloshingde dos fluidos, extrusión de fluidos viscosos, ascensión y rotura de una burbuja dentro de una columna de líquido, mezcla de magmas y fuentes invertidas (negatively buoyant jet)., The simultaneous presence of multiple fluids with different properties in external or internal flows is found in daily life, environmental problems, and numerous industrial processes, among many other practical situations. Examples arefluid-fuel interaction in enhanced oil recovery, blending of polymers, emulsions in food manufacturing, rain droplet formation in clouds, fuel injection in engines, and bubble column reactors, to name only a few. Although multi-fluid flows occur frequently in nature and engineering practice, they still pose a major research challenge from both theoretical and computational points of view. In the case of immiscible fluids, the dynamics of the interface between fluids plays a dominant role. The success of the simulation of such flows will depend on the ability of the numerical method to model accurately the interface and the phenomena taking place on it. In this work we have focused on understanding the basic physical principles of multi-fluid flows and the difficulties that arise in their numerical simulation. We have extended the Particle Finite Element Method to problems involving several different fluids with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking any kind of interfaces. We have developed a numerical scheme able to deal with large jumps in the physical properties, included surface tension, and able to accurately represent all types of discontinuities in the flow variables at the interface. The scheme is based on decoupling the nodes position, velocity and pressure variables through the Picard linearization and a pressure segregation method which takes into account the interface conditions. Theinterface has been defined to be aligned with the moving mesh, so that it remains sharp along time. Furthermore, pressure degrees of freedom have been duplicated at the interface nodes to represent the discontinuity of this variable due to surface tension and variable viscosity, and the mesh has been refined in the vicinity of the interface to improve the accuracy of the computations. We have applied the resulting scheme to several academic and geological problems, such as the two-fluid sloshing, extrusion of viscous fluids, bubble rise and break up, mixing of magmatic liquids and negatively buoyant jets.

International audience; Although the two-way nesting is the most usual coupling method in the ocean community, it does not address the correct problem but an approximation, and does not ensure enough regularity through the interface between the two models1. The correct approach consisting in a full coupling is more difficult and expensive than the two-way nesting, since it requires to find and implement an algorithm ensuring that the solutions in each domain satisfy the regularity conditions through the interface. The global-in-time non-overlapping Schwarz algorithm is particularly well suited for such a coupling, and can lead to improved physical results. Our work thus aims at improving the ocean coupling by determining efficient interface conditions for the usual ocean equations (the so-called 3-D primitive equations). These ones are composed of advection-diffusion equations for tracers such as temperature and salinity, and dynamics equations, which can be approximated in the 2-D case by the shallow-water equations.

International audience

In the present work, an enhanced formulation for cohesive interface that keep into account the effect of in-plane deformations of the gluing surface is proposed. Starting from this kinematical assumption an enriched formulation of interface finite element is proposed. The enriched formulation introduces also a constitutive correlation between the in-plane deformation (elongation or confinement) of the interface and the membrane state of stress. An interface damage model which accounts for the mode I and mode II and the axial deformation of the interface is proposed starting by the use of Drucker-Prager failure criterion. Simple numerical simulations are presented in order to illustrate the capabilities of the model. In particular, the effects of mortars joints in masonry substrate reinforced with FRP is investigated.

In the present paper the homogenization problem of periodic composites is investigated, in the case of a Cosserat continuum at the macro-level and a Cauchy continuum at the micro-level. In the framework of a strain-driven approach, the two levels are linked by a kinematic map based on a third order polynomial expansion. The determination of the displacement perturbation fields in the Unit Cell (UC), arising when second or third order polynomial boundary conditions are imposed, is investigated. A new micromechanical approach, based on the decomposition of the perturbation fields in terms of functions which depend on the macroscopic strain components, is proposed. The identification of the linear elastic 2D Cosserat constitutive parameters is performed, by using a Hill-Mandel-type macrohomogeneity condition. The influence of the selection of the UC is analyzed and some critical issues are outlined. Numerical examples referred to a specific composite with cubic symmetry are shown.