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• A unified approach for the analysis of bridges, plates and axisymmetric shells using the linear mindlin strip element

  E. Oñate, B. Suarez

  Computers and Structures (1983). Vol. 17 (3), pp. 407-426

  
  

  Abstract

  In this paper a finite strip formulation which allows to treat bridges, axisymmetric shells or plate structures of constant transverse cross section in an easily and unified manner is presented. The formulation is based on Mindlin's shell plate theory. One dimensional finite elements are used to discretize the transverse section and Fourier expansions are used to define the longitudinal/circumferential behavior of the structure. The element used is the simple two noded strip element with just one single integrating point. This allows to obtain all the element matrices in an explicit and economical form. Numerical examples for a variety of straight and curve bridges, axisymmetric shells and plate structures which show the efficiency of the formulation and accuracy of the linear strip element are given.

  Abstract
  In this paper a finite strip formulation which allows to treat bridges, axisymmetric shells or plate structures of constant transverse cross section in an easily and unified [...]

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• 2D particle contact-based meshfree method in CDEM and its application in geotechnical problems

  C. Feng, S. Li, E. Oñate

  Engineering Computations (2015). Vol. 32 (4), pp. 1080-1103

  
  

  Abstract

  Purpose   – Continuum-based discrete element method is an explicit numerical method, which is a combination of block discrete element method (DEM) and FEM. When simulating large deformation problems, such as cutting, blasting, water-like material flowing, the distortion of elements will lead to no convergence of the numerical system. To solve the convergence problem, a particle contact-based meshfree method (PCMM) is introduced in. The paper aims to discuss this issue.   Design/methodology/approach   – PCMM is based on traditional particle DEM, and use particle contacts to generate triangular elements. If three particles are contact with each other, the element will be created. Once elements are created, the macroscopic constitutive law could be introduced in. When large deformation of element occurs, the contact relationship between particles will be changed. Those elements that do not meet the contact condition will be deleted, and new elements that coincide with the relationship will be generated. By the deletion and creation of elements, the convergence problem induced by element distortion will be eliminated. To solve FEM and PCMM coupled problems, a point-edge contact model is introduced in, and normal and tangential springs are adopted to transfer the contact force between particles and blocks.   Findings   – According to the deletion and recreation of elements based on particle contacts, PCMM could simulate large deformation problems. Some numerical cases (i.e. elastic field testing, uniaxial compression analysis and wave propagation simulation) show the accuracy of PCMM, and others (i.e. soil cutting, contact burst and water-like material flowing) show the rationality of PCMM.   Originality/value   – In traditional particle DEM, contact relationships are used to calculate contact forces. But in PCMM, contact relationships are adopted to generate elements. Compared to other meshfree methods, in PCMM, the element automatic deletion and recreation technique is used to solve large deformation problems.

  Abstract
  Purpose   – Continuum-based discrete element method is an explicit numerical method, which is a combination of block discrete element method (DEM) [...]

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• Validation of the particle finite element method (PFEM) for simulation of free surface flows

  A. LARESE, R. Rossi, E. Oñate, S. Idelsohn

  Engineering Computations (2008). Vol. 25 (3-4), pp. 385-425

  
  

  Abstract

  Purpose – The purpose of this paper is to evaluate the possibilities of the particle finite element method for simulation of free surface flows. Design/methodology/approach – A numerical simulation of a number of examples for which experimental data are available is performed. The simulations are run using the same scale as the experiment in order to minimize errors due to scale effects. Some examples are chosen from the civil engineering field: a study of the flow over a flip bucket is analyzed for both 2D and 3D models, and the flow under a planar sluice gate is studied in 2D. Other examples, such as a 2D and 3D “dam break” with an obstacle are taken from the smooth particle hydrodynamics literature. Findings – Different scenarios are simulated by changing the boundary conditions for reproducing flows with the desired characteristics. Different mesh sizes are considered for evaluating their influence on the final solution. Originality/value – Details of the input data for all the examples studied are given. The aim is to identify benchmark problems for future comparisons between different numerical approaches for free surface flows.

  Abstract
  Purpose – The purpose of this paper is to evaluate the possibilities of the particle finite element method for simulation of free surface flows. Design/methodology/approach [...]

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• Non‐linear explicit dynamic analysis of shells using the BST rotation‐free triangle

  E. Oñate, P. Cendonya, J. Canet

  Engineering Computations (2002). Vol. 19 (6), pp. 662-706

  
  

  Abstract

  The paper describes the application of the simple rotation‐free basic shell triangle (BST) to the non‐linear analysis of shell structures using an explicit dynamic formulation. The derivation of the BST element involving translational degrees of freedom only using a combined finite element–finite volume formulation is briefly presented. Details of the treatment of geometrical and material non linearities for the dynamic solution using an updated Lagrangian description and an hypoelastic constitutive law are given. The efficiency of the BST element for the non linear transient analysis of shells using an explicit dynamic integration scheme is shown in a number of examples of application including problems with frictional contact situations.

  Abstract
  The paper describes the application of the simple rotation‐free basic shell triangle (BST) to the non‐linear analysis of shell structures using an explicit dynamic formulation. [...]

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• A residual correction method based on finite calculus

  E. Oñate, R. Taylor, O. Zienkiewicz, J. Rojek

  Engineering Computations (2003). Vol. 20 (5-6), pp. 629-658

  
  

  Abstract

  In this paper, a residual correction method based upon an extension of the finite calculus concept is presented. The method is described and applied to the solution of a scalar convection‐diffusion problem and the problem of elasticity at the incompressible or quasi‐incompressible limit. The formulation permits the use of equal interpolation for displacements and pressure on linear triangles and tetrahedra as well as any low order element type. To add additional stability in the solution, pressure gradient corrections are introduced as suggested from developments of sub‐scale methods. Numerical examples are included to demonstrate the performance of the method when applied to typical test problems.

  Abstract
  In this paper, a residual correction method based upon an extension of the finite calculus concept is presented. The method is described and applied to the solution of a scalar [...]

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• Direct computation of instability points with inequality constraints using the FEM

  H. Tschöpe, P. Wriggers, E. Oñate

  Engineering Computations (2003). Vol. 20 (5-6), pp. 611-628

  
  

  Abstract

  The subject of this paper is the computation of instability points in mechanical problems with the finite element method. The objective is to extend the application of critical point detection methods to problems with inequality constraints originating from damage and contact. A simple bilinear model is considered for the damage problems. A bilateral, frictionless contact formulation is used for the contact problems. Among the critical point detection methods the focus is laid on the critical displacement method and the extended system. At first a possible combination of both methods is evaluated by applying them to damage problems. A prediction method based on the extended system is developed to facilitate the comparison of both methods. Secondly, the extended system is used as a computation method for critical points in two‐dimensional contact problems.

  Abstract
  The subject of this paper is the computation of instability points in mechanical problems with the finite element method. The objective is to extend the application of critical [...]

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• Direct computation of instability points with inequality constraints using the FEM

  H. Tschöpe, P. Wriggers, E. Oñate

  Engineering Computations (2003). Vol. 20 (5-6), pp. 611-628

  
  

  Abstract

  The subject of this paper is the computation of instability points in mechanical problems with the finite element method. The objective is to extend the application of critical point detection methods to problems with inequality constraints originating from damage and contact. A simple bilinear model is considered for the damage problems. A bilateral, frictionless contact formulation is used for the contact problems. Among the critical point detection methods the focus is laid on the critical displacement method and the extended system. At first a possible combination of both methods is evaluated by applying them to damage problems. A prediction method based on the extended system is developed to facilitate the comparison of both methods. Secondly, the extended system is used as a computation method for critical points in two‐dimensional contact problems.

  Abstract
  The subject of this paper is the computation of instability points in mechanical problems with the finite element method. The objective is to extend the application of critical [...]

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• The extended Delaunay tessellation

  N. Calvo, S. Idelsohn, E. Oñate

  Engineering Computations (2003). Vol. 20 (5-6), pp. 583-600

  
  

  Abstract

  The extended Delaunay tessellation (EDT) is presented in this paper as the unique partition of a node set into polyhedral regions defined by nodes lying on the nearby Voronoï spheres. Until recently, all the FEM mesh generators were limited to the generation of tetrahedral or hexahedral elements (or triangular and quadrangular in 2D problems). The reason for this limitation was the lack of any acceptable shape function to be used in other kind of geometrical elements. Nowadays, there are several acceptable shape functions for a very large class of polyhedra. These new shape functions, together with the EDT, gives an optimal combination and a powerful tool to solve a large variety of physical problems by numerical methods. The domain partition into polyhedra presented here does not introduce any new node nor change any node position. This makes this process suitable for Lagrangian problems and meshless methods in which only the connectivity information is used and there is no need for any expensive smoothing process.

  Abstract
  The extended Delaunay tessellation (EDT) is presented in this paper as the unique partition of a node set into polyhedral regions defined by nodes lying on the nearby Voronoï [...]

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• Numerical modelling and simulation of frictional contact using a generalised coulomb law

  A. Heege, P. Alart, E. Oñate

  Engineering Computations (1995). Vol. 12 (7), pp. 641-656

  
  

  Abstract

  A consistent formulation for unilateral contact problems including frictional work hardening or softening is proposed. The approach is based on an augmented Lagrangian approach coupled to an implicit quasi‐static Finite Element Method. Analogous to classical work hardening theory in elasto‐plasticity, the frictional work is chosen as the internal variable for formulating the evolution of the friction convex. In order to facilitate the implementation of a wide range of phenomenological models, the friction coefficient is defined in a parametrised form in terms of Bernstein polynomials. Numerical simulation of a 3D deep‐drawing operation demonstrates the performance of the methods for predicting frictional contact phenomena in the case of large sliding paths including high curvatures.

  Abstract
  A consistent formulation for unilateral contact problems including frictional work hardening or softening is proposed. The approach is based on an augmented Lagrangian approach [...]

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• An anisotropic elastoplastic model based on an isotropic formulation

  S. Oller, S. Botello, J. Canet, E. Oñate

  Engineering Computations (1995). Vol. 12 (3), pp. 245-262

  
  

  Abstract

  This paper shows a generalization of the classic isotropic plasticity theory to be applied to orthotropic or anisotropic materials. This approach assumes the existence of a real anisotropic space, and other fictitious isotropic space where a mapped fictitious problem is solved. Both spaces are related by means of a linear transformation using a fourth order transformation tensor that contains all the information concerning the real anisotropic material. The paper describes the basis of the spaces transformation proposed and the expressions of the resulting secant and tangent constitutive equations. Also details of the numerical integration of the constitutive equation are provided. Examples of application showing the good performance of the model for analysis of orthotropic materials and fibre‐reinforced composites are given.

  Abstract
  This paper shows a generalization of the classic isotropic plasticity theory to be applied to orthotropic or anisotropic materials. This approach assumes the existence of [...]

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