Scipedia: Personal Repository of Francisco Zarate

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.

New assumed strain triangles for non linear shell analysis

María Jesús Samper — Thu, 20 Dec 2018 12:25:32 +0100

A comparison between new and existing triangular finite elements based on the shell theory proposed by Juan Carlos Simo and co-workers is presented. Particular emphasis is put on the description of new triangles which show a promising behaviour for linear and non linear shell analysis.

A simple triangular element for thick and thin plate and shell analysis

María Jesús Samper — Tue, 11 Dec 2018 14:08:01 +0100

A new plate triangle based on Reissner–Mindlin plate theory is proposed. The element has a standard linear deflection field and an incompatible linear rotation field expressed in terms of the mid‐side rotations. Locking is avoided by introducing an assumed linear shear strain field based on the tangential shear strains at the mid‐sides. The element is free of spurious modes, satisfies the patch test and behaves correctly for thick and thin plate and shell situations. The element degenerates in an explicit manner to a simple discrete Kirchhoff form.

Caltep programa para el cálculo transitorio de la ecacuación de Poisson

María Jesús Samper — Mon, 22 Jul 2019 13:13:25 +0200

Esta publicación explica la utilización de un programa de elementos finitos que permita resolver la ecuación de Poisson transitoria, que rige una gran cantidad de problemas físicos como son la transición del calor a través de diversos medios, el flujo de un líquido a través de un medio permeable, problemas de magnetismo, etc.

En la publicación describe las etapas que intervienen en un programa de elementos finitos para cálculo de la ecuación de Poisson transitoria incidiendo principalmente en la metodología general de la programación de las diferentes subrutinas, así como en su aplicación a varios problemas. En la última parte de esta publicación se presentan diversos ejemplos de aplicación del programa, así como un listado completo del mismo, una descripción de sus variables más significativas y las instrucciones para la entrada de datos.

Fractures prediction in concrete structures combining the finite and discrete element methods

María Jesús Samper — Thu, 21 Feb 2019 11:02:03 +0100

This paper presents the basic concepts and application of the strategy that combines finite element methods (FEM) and discrete elements (DEM)for the study of the propagation of fractures in concrete structures. The calculation of the structure, modeled as a continuum, begins with the FEMand the DEM is used to start and grow the cracks that may appear in the structure. This methodology has been proposed by the authors in two andthree dimensions. Recently, the use of one-dimensional steel elements embedded in the continuum has been added to model the reinforcement inconcrete structures. The work presents different examples of application to the study of the breakage of parts and structures of concrete in massand armed, as well as the multiple breakage of a historic structure of masonry due to an earthquake.

Triangular element for two-dimensional elasticity with z stress and z strain constant and different from zero.

Francisco Zarate — Fri, 08 Feb 2019 15:35:03 +0100

This paper describes how to obtain a two-dimensional element of three nodes from a prismatic solid element of six nodes, assuming that the normal voltage to the triangular faces is constant and different from zero.

A numerical example is also presented where the results obtained are compared with the developed element and with three-dimensional elements, showing the good behavior of the developed element.

Pulse fracture simulation in shale rock reservoirs. DEM and FEM-DEM approaches

María Jesús Samper — Fri, 01 Feb 2019 13:00:02 +0100

In this paper we analyze the capabilities of two numerical techniques based on DEM and FEM-DEM approaches for the simulation of fracture in shale rock caused by a pulse of pressure. We have studied the evolution of fracture in several fracture scenarios related to the initial stress state in the soil or the pressure pulse peak. Fracture length and type of failure have been taken as reference for validating the models. The results obtained show a good approximation to FEM results from the literature.

A three dimensional FEM-DEM technique for predicting the evolution of fracture in geomaterials and concrete

María Jesús Samper — Thu, 31 Jan 2019 13:02:05 +0100

This paper extends to three dimensions (3D) the computational technique developed by the authors in 2D for predicting the onset and evolution of fracture in a finite element mesh in a simple manner based on combining the finite element method (FEM) and the discrete element method (DEM) approach Zarate2D. Once a crack is detected at an element edge, discrete elements are generated at the adjacent element vertexes and a simple DEM mechanism is considered in order to follow the evolution of the crack. The combination of the DEM with simple 4-noded linear tetrahedron elements correctly captures the onset of fracture and its evolution, as shown in several 3D examples of application.

Modelling and simulation of the effect loading on structures using and adaptive blending of discrete and finite element methods

Francisco Zarate — Tue, 30 Oct 2018 15:39:02 +0100

We present a new computational model for predicting the effect of blast loading on structures. The model is based in the adaptive coupling of the finite element method (FEM) and the discrete element method (DEM) for the accurate reproduction of multifracturing and failure of structures under blast loading. In the paper we briefly describe the basis of the coupled DEM/FEM technology and demonstrate its efficiency in its application to the study of the effect of blast loading on a masonry wall, a masonry tunnel and a double curvature dam.

Desarrollo y aplicación de un modelo de elementos finitos para cálculo de vigas con materiales compuestos laminados basado en la teoría de Timoshenko

Francisco Zarate — Tue, 30 Oct 2018 15:41:02 +0100

Actualmente existen programas de MAT-fem para calcular vigas de material homogéneo, según la teoría de Euler-Bernoulli o de Timoshenko. El objetivo de la presente

tesina es conseguir un nuevo programa capaz de calcular vigas de materiales compuestos con la teoría de Timoshenko.

Study of Composite Materials using Zigzag Theory on Timoshenko Beams

Francisco Zarate — Tue, 30 Oct 2018 15:43:02 +0100

This final studies work target is to contribute two new beam theories to MAT-fem [6], an educational developed program by CIMNE [5]. Until now the MAT-fem Beams program only offered the Euler-Bernoulli and Timoshenko beam theories for homogeneous materials. With this work, the Timoshenko theory for composite materials and the refined zigzag theory are added. MAT-fem Beams application works by discretizing beams into two noded elements. This work offers a beam theories opportunity of contrasting with up to four kinematic variables. Timoshenko theory for composite materials works with three kinematics variables per node and zigzag theory works with four variables. Finally, the accuracy of zigzag theory must be remarked in comparison to other classic beam theories.

Stabilized Solution of the Multidimensional Advection-Diffusion:absorption Equation using Linear Finite Elements

Francisco Zarate — Tue, 30 Oct 2018 15:35:02 +0100

A stabilized finite element method (FEM) for the multidimensional steady state advection-diffusion-absorption equation is presented. The stabilized formulation is based on the modified governing differential equations derived via the Finite Calculus (FIC) method. For 1D problems the stabilizacion terms act as a nonlinear additional diffusion governed by a single stabilization parameter. It is shown that for multidimensional problems an orthotropic stabilizing diffusion must be added along the principal directions of curvature of the solution.

Posibilidades de las nuevas tecnologías de información y comunicaciones en el sector de la construcción

Francisco Zarate — Tue, 30 Oct 2018 15:23:02 +0100

Se presenta una breve panorámica de las posibilidades de las nuevas Tecnologías de la Información y las Comunicaciones en el sector de la construcción. Tras unas reflexiones sobre el valor intrínseco de la información y las comunicaciones, se describe el impacto que está teniendo Internet en los nuevos métodos de trabajo, de comercio, de formación y, en general, de intercambio de información a todos los niveles en las actividades de los técnicos del sector de la construcción. Finalmente se especula sobre las posibilidades de las TIC para generar entornos de trabajo inteligentes que generen y gestionen conocimiento para la solución de problemas prácticos.

Rotation Free Triangular Plate and Shell Elements

Francisco Zarate — Mon, 29 Oct 2018 16:53:02 +0100

The paper describes how 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 variable. The simplest element of the two families based on combining a linear interpolation of displacements with cell centered 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.

A Simple Triangular Element for Thick and Thin Plate and Shell Analysis

Francisco Zarate — Mon, 29 Oct 2018 16:48:02 +0100

A new plate triangle based on Reissner-Mindlin plate theory is proposed. The element has a standard linear deflection field and an incompatible linear rotation field expressed in terms of the mid-side rotations. Locking is avoided by introducing an assumed linear shear strain field based on the tangential shear strains at the mid-sides. The element is free of spurious modes, satisfies the patch test and behaves correctly for thick and thin plate and shell situations. The element degenerates in a explicit manner to a simple DK form.

Contribution to the Definition of Non Deterministic Robust Optimization in Aeronautics Accounting with Variable Uncertainties

Francisco Zarate — Mon, 29 Oct 2018 16:28:02 +0100

Shape optimization is a largely studied problem in aeronautics. It can be applied to many disciplines in this field, namely efficiency improvement of engine blades, noise reduction of engine nozzles, or reduction of the fuel consumption of aircraft. Optimization for general purposes is also of increasing interest in many other fields.

Traditionally, optimization procedures were based on deterministic methodologies as in Hamalainen et al (2000), where the optimum working point was fixed. However, not considering what happens in the vicinity of the defined working conditions can produce problems like loose of efficiency and performance. That is, in many cases, if the real working point differs from the original, even a little distance, efficiency is reduced considerably as pointed out in Huyse and Lewis (2001)

Non deterministic methodologies have been applied to many fields (Papadrakakis, Lagaros and Tsompanakis, 1998; Plevris, Lagaros and Papadrakakis, 2005). One of the most extended nondeterministic methodologies is the stochastic analysis. The time consuming calculations required on Computational Fluid Dynamics (CFD) has prevented an extensive application of the stochastic analysis to shape optimization. Stochastic analysis was firstly developed in structural mechanics, several years ago. Uncertainty quantification and variability studies can help to deal with intrinsic errors of the processes or methods. The result to consider for design optimization is no longer a point, but a range of values that defines the area where, in average, optimal output values are obtained. The optimal value could be worse than other optima, but considering its
vicinity, it is clearly the most robust regarding input variability.

Uncertainty quantification is a topic of increasing interest from the last few years. It provides several techniques to evaluate uncertainty input parameters and their effects on the outcomes. This research presents a methodology to integrate evolutionary algorithms and stochastic
analysis, in order to deal with uncertainty and to obtain robust solutions.

New Rotation Free Shell Triangle for Crash-Worthiness Analysis in Parallel PC Networks

Francisco Zarate — Mon, 29 Oct 2018 16:59:02 +0100

A new three node shell triangular element with translational degree of freedom as the only nodal variables is presented. The element formulation is based on combining a standard linear finite element interpolation with a cell centered finite volume scheme. Details of the implementation of the element in an explicit dynamic code operating in parallel on networks of PC's are presented. The efficiency and applicability of the new rotation free shell triange is shown in the solution of some contact/impact and crash worthiness problem.

Discrete Element Modelling of Rock Cutting Processes Interaction with Evaluation of Tool Wear

Francisco Zarate — Mon, 29 Oct 2018 15:50:01 +0100

The document presents a numerical model of rocks and soils using spherical Discrete Elements, also called Distinct Elements. The motion of spherical elements is described by means of equations of rigid body dynamics. Explicit integration in time yields high computational efficiency. Spherical elements interact among one another with contact forces, both in normal and tangential directions. Efficient contact search scheme based on the octree structures has been implemented. Special constitutive model of contact interface taking into account cohesion forces allows us to model fracture and decohesion of materials.
Numerical simulation predicts wear of rock cutting tools. The developed numerical algorithm of wear evaluation allows us us to predict evolution of the shape of the tool caused by wear.
Results of numerical simulation are validated by comparison with experimental data.

Estudio de estimación de parámetros constitutivos en el método de elementos discretos o de partículas

Francisco Zarate — Mon, 29 Oct 2018 16:20:01 +0100

Se presenta un modelo numérico que emplea elementos discretos esféricos o también denominados elementos distintos. Este modelo se aplica en la simulación de rocas, suelos, medios granulares otros materiales. El movimiento de elementos esféricos se describe por medio de las ecuaciones de dinámica del cuerpo rígido, Se emplea en la formulación una integración explicita, la cual., brinda una buena eficiencia computacional. Los elementos esféricos interactúan recíprocamente ente si a través de las fuerzas del contacto, en la direccion normal y tangencial.

Transmisión de Calor Apuntes

Francisco Zarate — Fri, 05 Oct 2018 15:37:02 +0200

Apuntes de Clase