Documents published in Scipedia

• Solution on square domains of reaction-convection-diffusion equations using spectral stochastic finite element and streamline upwind Galerkin Petrov

  D. Garzón-Alvarado, A. Ramírez-Martínez, C. Daza

  Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería (2017).

  
  

  Abstract

  In this paper we have developed the numerical solution of two problems of diffusion-convection (DC), using the finite element method of Streamline Upwind Petrov-Galerkin (SUPG). The parameters that define the behavior of the equations are modeled as stochastic fields, specifically, are used: the convective velocity, diffusion and heat capacity as values of random type. Therefore, we have included SUPG method to DC, with dominant convection, with the stochastic spectral finite element method. Each parameter was described by Karhunen-Loève expansion, while the unknown is represented by the polynomial expansion of the chaos. The objectives of the paper are: 1. To study the influence of stochastic fields in solving problems with SUPG DC and 2. Get the solution of each expansion unknown variable. The results show the versatility of the method for solving different physical problems due to the generality of the statistical description of the solution and the richness in the representation of the areas where there is the greater variability in response. The patterns shown in the unknown uncertainty depends on the dynamics of diffusion, convective velocity and the type of solution used.

  Abstract
  In this paper we have developed the numerical solution of two problems of diffusion-convection (DC), using the finite element method of Streamline Upwind Petrov-Galerkin (SUPG). [...]

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• Optimum sizing of launching nose of prestressed concrete bridges

  A. Fontán, S. Hernández, A. Baldomir, J. Díaz

  Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería (2017).

  
  

  Abstract

  The design of the launching nose of an incrementally launched bridge determines its constructive process and, therefore, also its dimensions. The optimization of the launching nose can raise as a first step to improve the design of a launched bridge. The conventional design process of a launching nose is based on trial and error method to reduce bending moment of prestressed concrete deck at the foremost support during launch. In this way, there is no guarantee that the obtained solution is the best among all the possible solutions since they all depend on the experience and intuition of a designer, and they are also restricted by a limited number of possible iterations. Given that launched bridges constitute an important constructive typology, all the available capacities of design innovation should be incorporated, among which it can be found numerical optimization. This research work proposes an objective and rigorous formulation to optimize a launching nose of launched bridge under real constraints that a bridge designer can encounter in practice. Comparing the results obtained by conventional process and that by optimization techniques, it can be verified that some of the assumptions, considered in classical design methods of a launching nose, are not based on any theoretical foundation. This fact demonstrates the utility of numerical optimization to improve a design.

  Abstract
  The design of the launching nose of an incrementally launched bridge determines its constructive process and, therefore, also its dimensions. The optimization of the launching [...]

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• A Solid finite element with an improvement in the transverse shear behavior for shell analysis

  F. Flores, E. Oñate

  Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería (2017).

  
  

  Abstract

  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.

  Abstract
  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 [...]

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• Turing patterns formation on surfaces under deformation: A total lagrangian method approach

  C. Duque-Daza, A. Ramirez, D. Garzón-Alvarado

  Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería (2017).

  
  

  Abstract

  In this work we have developed several numerical examples of reaction-diffusion equations with growing domain. For this purpose we have used the Schnakenberg reaction model with parameters in space Turing. Therefore numerical tests are performed on the appearance of Turing patterns on surfaces that have high deformation rate. For the solution of reaction diffusion equations is presented a solution method on surfaces in three dimensions using the finite element method under the use of the total Lagrangian formulation. The results show that the formation of Turing patterns depends on the features of surface deformation and the rate at which change in position of each point of the domain. These results can explain some phenomena of change of pattern on the surface of the skin of animals that exhibit characteristic spots.

  Abstract
  In this work we have developed several numerical examples of reaction-diffusion equations with growing domain. For this purpose we have used the Schnakenberg reaction model [...]

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• Numeric validation of the cyclic behaviour of interior connections in waffle-flat-plate structures

  J. Donaire-Ávila, A. Benavent-Climent

  Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería (2017).

  
  

  Abstract

  Several approaches are investigated to model interior reinforced concrete waffle-flat-plate-column connections. A model is proposed that provides very good results with reasonable low computational cost. The proposed model is validated with the experimental results obtained on a 3/5 scale specimen, subjected to quasi-static in cyclic loads up to collapse. To this end, the non-linear advanced theory of reinforced concrete is applied on a three-dimensional finite element model and non-linear analysis are conducted. Both fiber and layer elements are used for the one-dimensional and bi-dimensional components respectively. The main results of the simulation were: (i) the capacity curve obtained through out a push-over analysis with displacement control, (ii) the hysteretic curves of the slab, and (iii) the crack patterns. A very good agreement is found between numerical and experimental results.

  Abstract
  Several approaches are investigated to model interior reinforced concrete waffle-flat-plate-column connections. A model is proposed that provides very good results with reasonable [...]

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• Developement of a computational tool for the analysis of reinforced concrete membrane elements

  R. Souza

  Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería (2017).

  
  

  Abstract

  Reinforced concrete elements subjected to membrane forces, i.e., elements subjected to in-plane shear and axial stresses are very common for modeling complex structures such as aircraft hangars, nuclear power plants, offshore oil platforms and long-span bridges. While the design of reinforcement for membrane elements is well adressed the same can not be said regarding the analysis of performance of these elements. Into this context, the present paper aims at providing a numerical tool developed in the Matlab platform, taking into account the “Modified Compression Field Theory”. In order to certificate the performance of the proposed tool, extensive numerical results were compared with experimental results available in the literature. The obtained results revealed that the proposed tool is very confident for the analysis of reinforced concrete membrane elements.

  Abstract
  Reinforced concrete elements subjected to membrane forces, i.e., elements subjected to in-plane shear and axial stresses are very common for modeling complex structures such [...]

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• A numerical model for the simulation of precipitates dissolution of hardened aluminium alloys using neural networks

  C. Saracibar, R. López, B. Ducoeur, M. Chiumenti, B. Meester

  Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería (2017).

  
  

  Abstract

  The motivation of this work is the modeling of the hardening precipitate and hardness evolutions of fully hardened heat treatable aluminium alloys during friction stir welding (FSW) and/or heat treatment processes. The model used is based on the kinetics of dissolution of precipitates model for hardened aluminium alloys given by Myhr and Grong (1991). This model contains a single independent variable, the time, and a single state variable, the volume fraction of hardening precipitates. A key point of this model is the identification of the effective activation energy for precipitates dissolution and the master curve defining the model, which was given by a look-up table. The goal of this work is to find an estimation of the effective activation energy and to model the dissolution rate of hardening precipitate in aluminium alloys using neural networks, avoiding the use of look-up tables. For this purpose a new and more convenient parametrization of the master curve is defined, a neural networks class is proposed, an objective functional is defined and a variational problem including independent parameters is solved. The novel methodology has been applied to different aluminium alloys, including the AA 6005A T6, AA 7449 T79 and AA 2198 T8. Experimental tests have been carried out for those aluminium alloys in order to get the HV1 hardness after isothermal heat treatments at different temperatures and for different treatment time durations. The effective activation energy for hardening precipitates dissolution and the master curve of the model have been obtained, using different network architectures, for the aluminium alloys considered in this work.

  Abstract
  The motivation of this work is the modeling of the hardening precipitate and hardness evolutions of fully hardened heat treatable aluminium alloys during friction stir welding [...]

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• Switching implicit-explicit numerical technique for nonlinear unstable structures

  J. Curiel-Sosa, D. Owen

  Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería (2017).

  
  

  Abstract

  Simulation problems involving non-linear materials imply in numerous cases divergence of the implicit method which use return mapping algorithms for modelling of the nonlinear response. A switching implicit-explicit numerical technique in the context of Finite Element Methods is presented in this paper. Implicit/explicit mesh partitions are not considered whatsoever. Formulation for application to nonlinear hyperelastic materials and nonlinear elastic-plastic materials is provided. Furthermore, the response of the solid subjected to large deformations is presented and is embedded in the proposed technique. Numerical tests for nonlinear problems (geometric and/or material) showed the accurateness of the technique.

  Abstract
  Simulation problems involving non-linear materials imply in numerous cases divergence of the implicit method which use return mapping algorithms for modelling of the nonlinear [...]

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• Steel compression design: the bucklings weigth

  J. Cervera, J. Ortiz, M. Vázquez, A. Aznar

  Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería (2017).

  
  

  Abstract

  The verification of the slender compressed members of a structure is a well formulated and codified problem. However, the non-linearity of the design process, combined with the no linearity of the physical problem requires an iterative process to define the piece that solves a given problem. This paper demonstrates an identity relationship between seemingly different problems, based on which we develop a theoretical approach and a simple procedure to determine, without iteration and with little margin for error, the piece needed for a given problem. The paper provides a statistical model to check that the provided procedure is safe and effective in the 98% of the problems in buildings —pillars and bars from trusses—. The presented approach therefore greatly facilitates decisions in this area.

  Abstract
  The verification of the slender compressed members of a structure is a well formulated and codified problem. However, the non-linearity of the design process, combined with [...]

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• A mortar contact algorithm for three-dimensional elasticity problems

  F. Cavalieri, V. Fachinotti, A. Cardona

  Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería (2017).

  
  

  Abstract

  In this paper we propose a mortar algorithm for the study of contact mechanics in three dimensional elasticity problems. The projection surface used for integrating the equations is selected through a local cartesiana base defined in each contact element. In this way, some difficulties in the algorithm implementation as well as in the linearization of the equations are avoided. The proposed examples show that the algorithm satisfies the patch tests. Finally, we use the algorithm in an industrial application, the contact of an internal combustion engine valve with its seat.

  Abstract
  In this paper we propose a mortar algorithm for the study of contact mechanics in three dimensional elasticity problems. The projection surface used for integrating the equations [...]

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