Scipedia: Eugenio Oñate's Journal Papers

Advances in FE explicit formulation for simulation of metalforming processes

María Jesús Samper — Fri, 18 Jan 2019 12:21:24 +0100

This paper presents some advances of finite element explicit formulation for simulation of metal forming processes. Because of their computational efficiency, finite element programs based on the explicit dynamic formulation proved to be a very attractive tool for the simulation of metal forming processes. The use of explicit programs in the sheet forming simulation is quite common, the possibilities of these codes in bulk forming simulation in our opinion are still not exploited sufficiently. In our paper, we will consider aspects of bulk forming simulation.

We will present new formulations and algorithms developed for bulk metal forming within the explicit formulation. An extension of a finite element code for the thermomechanical coupled analysis is discussed. A new thermomechanical constitutive model developed by the authors and implemented in the program is presented.

A new formulation based on the so-called split algorithm allows us to use linear triangular and tetrahedral elements in the analysis of large plastic deformations characteristic to forming processes. Linear triangles and tetrahedra have many advantages over quadrilateral and hexahedral elements. Linear triangles and tetrahedra based on the standard formulations exhibit volumetric locking and are not suitable for large plastic strain simulation. The new formulation allows to overcome this difficulty.

New formulations and algorithms have been implemented in the finite element code Stampack developed at the International Centre for Numerical Methods in Engineering in Barcelona. Numerical examples illustrate some of the possibilities of the finite element code developed and validate new algorithms.

Combination of the critical displacement method with a damage model for structural instability analysis

María Jesús Samper — Fri, 04 Jan 2019 12:07:16 +0100

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.

A scalar damage model with a shear retention factor for the analysis of reinforced concrete structures: theory and validation

María Jesús Samper — Mon, 07 Jan 2019 13:57:07 +0100

A local isotropic single parameter scalar model that can simulate the mechanical behaviour of quasi-brittle materials, such as concrete, is described. The constitutive law needs the mechanical characteristics and the fracture energy of concrete to be completely defined. The damage parameter is obtained directly from the value of an equivalent effective stress in order to reduce the computing effort. Due to the unique damage parameter, this model is suitable for the study of quasi-static problems involving monotonically increasing loads. The problem of localisation and mesh dependency have been partially overcome by using an enhanced local method in which a characteristic internal length related to the mesh dimension is employed instead of the characteristic fracture length. In this work, the model was enriched further with the introduction of a shear retention factor that accounts for the friction between the two surfaces of a crack. These new features assure a real improvement of the damage model, maintaining nevertheless its simplicity and low computing cost and making it suitable for the practical solution of large scale problems. Several numerical simulations of experimental tests, concerning fracture tests on concrete specimens and beams failing in shear, have been performed for the validation of the model. The main results from the numerical analyses are described and compared with the experimental ones.

A finite point method for elasticity problems

María Jesús Samper — Mon, 07 Jan 2019 13:45:56 +0100

The basis of the finite point method (FPM) for the fully meshless solution of elasticity problems in structural mechanics is described. A stabilization technique based on a finite calculus procedure is used to improve the quality of the numerical solution. The efficiency and accuracy of the stabilized FPM in the meshless analysis of simple linear elastic structural problems is shown in some examples of applications.

Rotation‐free triangular plate and shell elements

María Jesús Samper — Wed, 12 Dec 2018 12:50:18 +0100

The paper describes how the finite element method and the finite volume method can be successfully combined to derive two new families of thin plate and shell triangles with translational degrees of freedom as the only nodal variables. The simplest elements of the two families based on combining a linear interpolation of displacements with cell centred and cell vertex finite volume schemes are presented in detail. Examples of the good performance of the new rotation‐free plate and shell triangles are given.

Shape variable definition with C0 , C1 and C2 continuity functions

María Jesús Samper — Fri, 23 Nov 2018 14:27:28 +0100

The present paper proposes a new technique for the definition of the shape design variables in 2D and 3D optimisation problems. It can be applied to the discrete model of the analysed structure or to the original geometry without any previous knowledge of the analytical expression of the CAD defining surfaces. The proposed technique allows the surface continuity to be preserved during the geometry modification process to be defined a priori. This capability allows for the definition of shape variables suitable for every kind of discipline involved in the optimisation process (structural analysis, fluid-dynamic analysis, crash analysis, aerodynamic analysis, etc.).

An anisotropic elastoplastic constitutive model for large deformation analysis of fibre reinforced composites

María Jesús Samper — Tue, 20 Nov 2018 13:32:06 +0100

In this work a generalized anisotropic elastoplastic constitutive model in large deformation is presented. It is used for the analysis of fiber-reinforced composite materials in the frame of the finite element method. Mixing theory is applied to simulate the behavior of the composite material. The elastic anisotropic behavior is simulated with classical elasticity theory, while that of a non-proportional anisotropic solid is simulated by means of the proposed generalized anisotropic elastoplastic model. The approach assumes the existence of a real anisotropic space and of a fictitious isotropic space where a mapped fictitious problem is solved. Both spaces are related by means of a linear transformation using a fourth order tensor incorporating complete information on the real anisotropic material. Details of the numerical implementations of the model into a non-linear, large deformations finite element solution scheme are provided. Examples of application showing the performance of the model for the analysis of fiber-reinforced composite materials are given.

A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation

María Jesús Samper — Tue, 20 Nov 2018 13:22:17 +0100

A stabilized finite element formulation for incompressible viscous flows is derived. The starting point are the modified Navier-Stokes equations incorporating naturally the necessary stabilization terms via a finite increment calculus (FIC) procedure. Application of the standard finite element Galerkin method to the modified differential equations leads to a stabilized discrete system of equations overcoming the numerical instabilities emanating from the advective terms and those due to the lack of compatibility between approximate velocity and pressure fields. The FIC method also provides a natural explanation for the stabilization terms appearing in all equations for both the Navier-Stokes and the simpler Stokes equations. Transient solution schemes with enhanced stabilization properties are also proposed. Finally a procedure for computing the stabilization parameters is presented.

Desarrollos y aplicaciones de modelos de fractura en la escuela de ingenieros de caminos de Barcelona

María Jesús Samper — Wed, 20 Nov 2019 11:44:53 +0100

El artículo es una panorámica de los aspectos teóricos y algunas aplicaciones prácticas de los modelos de fractura desarrollados por diversos grupos en la Escuela de Ingenieros de Caminos de Barcelona (EICB) durante los últimos quince años para el análisis no lineal de estructuras. La motivación fundamental para el desarrollo de estos modelos se centra en el análisis de la seguridad de estructuras de hormigón en masa y armado. La mayor parte de los modelos se basan en la teoría de daño continuo y utilizan el método de los elementos finitos para la solución numérica. Los modelos de daño se han extendido y aplicado también con éxito al análisis de diversas estructuras de edificios históricos. Los desarrollos más recientes de estos modelos en la EICB incluyen la predicción de fenómenos de localización en estructuras de hormigón y el análisis del comportamiento no lineal de estructuras con materiales compuestos. De todos estos modelos se presentan en el artículo unas breves pinceladas, las aplicaciones más relevantes y las referencias donde pueden encontrarse los detalles sobre cada caso.

A finite point method for incompressible flow problems

María Jesús Samper — Tue, 22 Jan 2019 11:47:07 +0100

A stabilized finite point method (FPM) for the meshless analysis of incompressible fluid flow problems is presented. The stabilization approach is based in the finite increment calculus (FIC) procedure developed by Oñate [14]. An enhanced fractional step procedure allowing the semi-implicit numerical solution of incompressible fluids using the FPM is described. Examples of application of the stabilized FPM to the solution of two incompressible flow problems are presented.

Numerical aerodynamic analysis of large buildings using a finite element model with application to a telescope building

María Jesús Samper — Mon, 21 Jan 2019 12:06:00 +0100

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.

A simple method for automatic update of finite element meshes

María Jesús Samper — Thu, 17 Jan 2019 12:35:57 +0100

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

Finite element solution of free‐surface ship‐wave problems

María Jesús Samper — Wed, 12 Dec 2018 12:37:40 +0100

An unstructured finite element solver to evaluate the ship‐wave problem is presented. The scheme uses a non‐structured finite element algorithm for the Euler or Navier–Stokes flow as for the free‐surface boundary problem. The incompressible flow equations are solved via a fractional step method whereas the non‐linear free‐surface equation is solved via a reference surface which allows fixed and moving meshes. A new non‐structured stabilized approximation is used to eliminate spurious numerical oscillations of the free surface.

Solving structural optimization problems with genetic algorithms and simulated annealing

María Jesús Samper — Wed, 12 Dec 2018 12:24:32 +0100

In this paper we study the performance of two stochastic search methods: Genetic Algorithms and Simulated Annealing, applied to the optimization of pin‐jointed steel bar structures. We show that it is possible to embed these two schemes into a single parametric family of algorithms, and that optimal performance (in a parallel machine) is obtained by a hybrid scheme. Examples of applications to the optimization of several real steel bar structures are presented.

A homogeneous constitutive model for masonry

María Jesús Samper — Wed, 12 Dec 2018 12:14:16 +0100

Masonry has been a broadly used material since the beginning of human life. Despite its popularity, the analysis of masonry structures is a complex task due to the heterogeneity and the non‐linear material behaviour. The need for reliable analysis procedures capable of predicting damage evolution and failure in historical structures in order to design efficient repair and maintenance has motivated the work of many structural analysts in this field. Here the finite element method has emerged as one of the most powerful procedures for linear and non‐linear analysis of masonry structures. The main problem pending is the development of accurate and efficient constitutive models capable of predicting the behaviour of masonry in the non‐linear range and this has been the motivation of this work.

The constitutive model presented is based on the homogenized anisotropic elastoplasticity previously developed by the authors. The effect of anisotropy is introduced by means of fictitious isotropic stress and strain spaces. The material properties in the fictitious isotropic spaces are mapped into the actual anisotropic space by means of a consistent fourth‐order tensor. The advantage of the model is that the classical theory of plasticity can be used to model the non‐linear behaviour in the isotropic spaces.

Details of the model for masonry structures and its implementation in a general non‐linear finite element code are given. Examples of application to the analysis of some masonry structures are presented, showing the efficiency of the model.

A large strain explicit formulation for composites

María Jesús Samper — Wed, 12 Dec 2018 11:58:30 +0100

A geometrically non‐linear formulation for composites and the resulting explicit dynamic finite element algorithm are presented. The proposed formulation assumes that small elastic and large plastic strains, being the anisotropy considered using tensors which map the model variables at each time step into an equivalent isotropic space, where the integration of the rate constitutive equations is performed. The evolution of the internal variables is calculated in the auxiliary spaces, taking into account the material non‐linear behaviour, and the results mapped back to the real stress space. The updating of the mapping tensors for each new spatial configuration allows the treatment of general anisotropic materials under large strain and can be extended to treat multiphase composite materials using the mixing theory. The behaviour of the composite is dictated by the mechanical response of each substance, and the resultant model allows a fully non‐linear analysis combining different material models, such as damage in one compounding substance, elastoplastic behaviour in the other, while a third substance behaves elastically.

A generalized streamline finite element approach for the analysis of incompressible flow problems including moving surfaces

María Jesús Samper — Fri, 23 Nov 2018 14:47:06 +0100

In the present work a generalized streamline finite element formulation able to deal with incompressible flow problems is presented. In the finite element framework, this technique allows the use of equal order interpolation for the unknowns of the problem: velocity and pressure. In this context, stable and convergent solutions can be obtained without requiring tuning parameters defined outside this model. The tracking of moving surfaces is also included in the numerical model. This formulation has been checked in 21) and 3D tests.

Un modelo de optimización estocástica aplicado a la optimización de estructuras de barras prismáticas

Scipedia content — Fri, 16 Jun 2017 10:32:25 +0200

Se presenta de forma general una familia de algoritmos de busqueda estocastica en forma parametrizada que puede ser utilizada para resolver problemas de optimizacion combinatoria. Esta familia incluye los ya conocidos algoritmos de optimizacion: algoritmos geneticos, estrategias evolutivas y recocido simulado. Ademas se incluye una nueva tecnica propuesta por los autores del trabajo que combina el recocido simulado en paralelo con seleccion. Se muestra el buen comportamiento del algoritmo propuesto y se aplica en la optimizacion de una armadura para una nave industrial en acero sujeta a cargas laterales, utilizando como informacion un catalogo de secciones transversales. Tambien se estudia en forma optima la estructura de un puente considerando efectos de compresion en el diseño de los elementos estructurales. Los autores del trabajo estan aplicando esta tecnica para realizar optimizacion de un gran numero de problemas de ingenieria civil y de mecanica.

Structural shape sensitivity analysis for nonlinear material models with strain softening

María Jesús Samper — Fri, 26 Apr 2019 11:54:51 +0200

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 example

A general procedure for deriving stabilized space–time finite element methods for advective–diffusive problems

María Jesús Samper — Fri, 12 Apr 2019 10:53:52 +0200

A procedure to derive stabilized space–time finite element methods for advective–diffusive problems is presented. The starting point is the stabilized balance equation for the transient case derived by Oñate [Comput. Methods Appl. Mech. Eng., 151, 233–267 (1998)] using a finite increment calculus approach. A description of the new stabilization method and a procedure for computing the stabilization parameter of the space–time solution is given. The efficiency of the stabilization approach is shown in the solution of some transient advective–diffusive problems, including the non‐linear Burger's equation.