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• Derivation of thin plate bending elements with one degree of freedom per node: a simple three node triangle

  E. Oñate, M. Cervera

  Engineering Computations (1993). Vol. 10 (6), pp. 543-561

  
  

  Abstract

  A general methodology for deriving thin plate bending elements with a single degree of freedom per node is presented. The formulation is based on the combination of a standard C0 finite element interpolation for the deflection field with an independent approximation of the curvatures which are expressed in terms of the deflection gradient along the sides using a finite volume‐like approach. The formulation is particularized for the simplest element of the family, i.e. the three node triangle with three degrees of freedom. The potential of the new element is shown through different examples of application.

  Abstract
  A general methodology for deriving thin plate bending elements with a single degree of freedom per node is presented. The formulation is based on the combination of a standard C0 [...]

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• Analysis of some partitioned algorithms for fluid-structure interaction

  R. Rossi, E. Oñate

  Engineering Computations (2010). Vol. 27 (1), pp. 20-56

  
  

  Abstract

  The field of fluid-structure interaction (FSI) has important applications ranging from the bio-medical to the civil and aeronautical engineering fields. Despite the different approaches developed over recent years the general solution of FSI problems remains however far from being closed. This paper addresses the theoretical analysis of a several partitioned solution schemes  for FSI. This is achieved by choosing a simple but representative model problem which allows to obtain analytical results. A loose coupling partitioned procedure is presented first. An iterative version of the same algorithm is presented next together with an analysis of its convergence properties and a brief discussion of a possible acceleration strategy. Finally a new iterative strategy based on solving a modified equation  is described. Some examples of application of the partitioned algorithms considered are presented including the aeroelastic analysis of a bridge.

  Abstract
  The field of fluid-structure interaction (FSI) has important applications ranging from the bio-medical to the civil and aeronautical engineering fields. Despite the different [...]

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• 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 particle finite element method for analysis of industrial forming processes

  E. Oñate, A. Franci, J. Carbonell

  Computational Mechanics (2014). Vol. 54 (1), pp. 85-107

  
  

  Abstract

  We present a generalized Lagrangian formulation for analysis of industrial forming processes involving thermally coupled interactions between deformable continua. The governing equations for the deformable bodies are written in a unified manner that holds both for fluids and solids. The success of the formulation lays on a residual-based expression of the mass conservation equation obtained using the finite calculus method that provides the necessary stability for quasi/fully incompressible situations. The governing equations are discretized with the FEM via a mixed formulation using simplicial elements with equal linear interpolation for the velocities, the pressure and the temperature. The merits of the formulation are demonstrated in the solution of 2D and 3D thermally-coupled forming processes using the particle finite element method.

  Abstract
  We present a generalized Lagrangian formulation for analysis of industrial forming processes involving thermally coupled interactions between deformable continua. The governing [...]

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