COLLECTIONS

Documents published in Scipedia

• A study of mesh optimality criteria in adaptive finite element analysis

  E. Oñate, G. Bugeda

  Engineering Computations (1993). Vol. 10 (4), pp. 307-321

  
  

  Abstract

  The concepts of solution error and optimal mesh in adaptive finite element analysis are revisited. It is shown that the correct evaluation of the convergence rate of the error norms involved in the error measure and the optimal mesh criteria chosen are essential to avoid oscillations in the refinement process. Two mesh optimality criteria based on: (a) the equal distribution of global error, and (b) the specific error over the elements are studied and compared in detail through some examples of application.

  Abstract
  The concepts of solution error and optimal mesh in adaptive finite element analysis are revisited. It is shown that the correct evaluation of the convergence rate of the error [...]

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

  E. Oñate, H. Tschöpe, P. Wriggers

  Engineering Computations (2001). Vol. 18 (3-4), pp. 642-662

  
  

  Abstract

  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.

  Abstract
  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 [...]

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• Free vibration analysis of plates, bridges and axisymmetric shells using a thick finite strip method

  B. Suarez, J. Canet, E. Oñate

  Engineering Computations (1988). Vol. 5 (2), pp. 158-164

  
  

  Abstract

  A unified approach for the vibration analysis of curved or straight prismatic plates and bridges and axisymmetric shells using a finite strip method based in Reissner—Mindlin shell theory is presented. Details of obtaining all relevant strip matrices and vectors are given. It is also shown how the use of the simple linear two node strip with reduced integration leads to direct explicit forms of all relevant matrices. Examples of application which show the accuracy of the linear strip for free vibration analysis of structures are presented.

  Abstract
  A unified approach for the vibration analysis of curved or straight prismatic plates and bridges and axisymmetric shells using a finite strip method based in Reissner—Mindlin [...]

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• A constitutive model for cracking of concrete based on the incremental theory of plasticity

  E. Oñate, S. Oller, J. Oliver, J. Lubliner

  Engineering Computations (1988). Vol. 5 (4), pp. 309-319

  
  

  Abstract

  A constitutive model based on classical plasticity theory for non‐linear analysis of concrete structures using finite elements is presented. The model uses the typical parameters of non‐associated plasticity theory for frictional materials and a modified Mohr‐Coulomb yield surface is suggested. Onset and amount of cracking at a point are controlled by the values of the effective plastic strain and thus it can be studied by a posteriori postprocessing of numerical results. The accuracy and objectivity of the model is checked out with some examples of application.

  Abstract
  A constitutive model based on classical plasticity theory for non‐linear analysis of concrete structures using finite elements is presented. The model uses the typical parameters [...]

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• A stabilized mixed implicit Material Point Method for non-linear incompressible solid mechanics

  I. Iaconeta, A. LARESE, R. Rossi, E. Oñate

  Computational Mechanics (2019). Vol. 63 (6), pp. 1243–1260

  
  

  Abstract

  In this work a stabilized mixed formulation for the solution of non-linear solid mechanics problems in nearly-incompressible conditions is presented. In order to deal with high material deformation, an implicit Material Point Method is chosen. Such choice allows avoiding the classical limitations of the Finite Element Method, e.g., element tangling and extreme mesh distortion. The proposed mixed formulation, with displacement and pressure as primary variables, is tested through classical benchmarks in solid and geo-mechanics where a Neo-Hookean, a J2 and a Mohr-Coulomb plastic law are employed. Further, the stabilized mixed formulation is compared with a displacement-based formulation to demonstrate how the proposed approach gets better results in terms of accuracy, not only when incompressible materials are simulated, but also in the case of compressible ones.

  Abstract
  In this work a stabilized mixed formulation for the solution of non-linear solid mechanics problems in nearly-incompressible conditions is presented. In order to deal with [...]

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• A new formulation for air-blast fluid–structure interaction using an immersed approach. Part I: basic methodology and FEM-based simulations

  Y. Bazilevs, K. Kamran, G. Moutsanidis, D. Benson, E. Oñate

  Computational Mechanics (2017). Vol. 60 (1), pp. 83-100

  
  

  Abstract

  In this two-part paper we begin the development of a new class of methods for modeling fluid–structure interaction (FSI) phenomena for air blast. We aim to develop accurate, robust, and practical computational methodology, which is capable of modeling the dynamics of air blast coupled with the structure response, where the latter involves large, inelastic deformations and disintegration into fragments. An immersed approach is adopted, which leads to an a-priori monolithic FSI formulation with intrinsic contact detection between solid objects, and without formal restrictions on the solid motions. In Part I of this paper, the core air-blast FSI methodology suitable for a variety of discretizations is presented and tested using standard finite elements. Part II of this paper focuses on a particular instantiation of the proposed framework, which couples isogeometric analysis (IGA) based on non-uniform rational B-splines and a reproducing-kernel particle method (RKPM), which is a Meshfree technique. The combination of IGA and RKPM is felt to be particularly attractive for the problem class of interest due to the higher-order accuracy and smoothness of both discretizations, and relative simplicity of RKPM in handling fragmentation scenarios. A collection of mostly 2D numerical examples is presented in each of the parts to illustrate the good performance of the proposed air-blast FSI framework.

  Abstract
  In this two-part paper we begin the development of a new class of methods for modeling fluid–structure interaction (FSI) phenomena for air blast. We aim to develop accurate, [...]

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• Numerically stable formulas for a particle-based explicit exponential integrator

  P. Nadukandi, E. Oñate

  Computational Mechanics (2015). Vol. 55 (5), pp. 903-920

  
  

  Abstract

  Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.

  Abstract
  Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential [...]

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• A reduced-order model based on the coupled 1D-3D finite element simulations for an efficient analysis of hemodynamics problems

  E. Soudah, R. Rossi, S. Idelsohn, E. Oñate

  Computational Mechanics (2014). Vol. 54 (4), pp. 1013-1022

  
  

  Abstract

  A reduced-order model for an efficient analysis of cardiovascular hemodynamics problems using multiscale approach is presented in this work. Starting from a patient-specific computational mesh obtained by medical imaging techniques, an analysis methodology based on a two-step automatic procedure is proposed. First a coupled 1D-3D Finite Element Simulation is performed and the results are used to adjust a reduced-order model of the 3D patient-specific area of interest. Then, this reduced-order model is coupled with the 1D model. In this way, three-dimensional effects are accounted for in the 1D model in a cost effective manner, allowing fast computation under different scenarios. The methodology proposed is validated using a patient-specific aortic coarctation model under rest and non-rest conditions.

  Abstract
  A reduced-order model for an efficient analysis of cardiovascular hemodynamics problems using multiscale approach is presented in this work. Starting from a patient-specific [...]

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• A contact algorithm for shell problems via Delaunay-based meshing of the contact domain

  K. Kamran, R. Rossi, E. Oñate

  Computational Mechanics (2013). Vol. 52 (1), pp. 1-16

  
  

  Abstract

  The simulation of the contact within shells, with all of its different facets, represents still an open challenge in Computational Mechanics. Despite the effort spent in the development of techniques for the simulation of general contact problems, an all-seasons algorithm applicable to complex shell contact problems is yet to be developed. This work focuses on the solution of the contact between thin shells by using a technique derived from the particle finite element method together with a rotation-free shell triangle. The key concept is to define a discretization of the contact domain (CD) by constructing a finite element mesh of four-noded tetrahedra that describes the potential contact volume. The problem is completed by using an assumed-strain approach to define an elastic contact strain over the CD.

  Abstract
  The simulation of the contact within shells, with all of its different facets, represents still an open challenge in Computational Mechanics. Despite the effort spent in the [...]

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• Modelling of tunnelling processes and rock cutting tool wear with the particle finite element method

  J. Puigbó, E. Oñate, B. Suarez

  Computational Mechanics (2013). Vol. 52 (3), pp. 607-629

  
  

  Abstract

  Underground construction involves all sort of challenges in analysis, design, project and execution phases. The dimension of tunnels and their structural requirements are growing, and so safety and security demands do. New engineering tools are needed to perform a safer planning and design. This work presents the advances in the particle finite element method (PFEM) for the modelling and the analysis of tunneling processes including the wear of the cutting tools. The PFEM has its foundation on the Lagrangian description of the motion of a continuum built from a set of particles with known physical properties. The method uses a remeshing process combined with the alpha-shape technique to detect the contacting surfaces and a finite element method for the mechanical computations. A contact procedure has been developed for the PFEM which is combined with a constitutive model for predicting the excavation front and the wear of cutting tools. The material parameters govern the coupling of frictional contact and wear between the interacting domains at the excavation front. The PFEM allows predicting several parameters which are relevant for estimating the performance of a tunnelling boring machine such as wear in the cutting tools, the pressure distribution on the face of the boring machine and the vibrations produced in the machinery and the adjacent soil/rock. The final aim is to help in the design of the excavating tools and in the planning of the tunnelling operations. The applications presented show that the PFEM is a promising technique for the analysis of tunnelling problems.

  Abstract
  Underground construction involves all sort of challenges in analysis, design, project and execution phases. The dimension of tunnels and their structural requirements are [...]

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