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• Volumetric constraint models for anisotropic elastic solids

  C. Felippa, E. Oñate

  (2002). Research Report, Nº PI216

  
  

  Abstract

  We study three “incompressibility flavors” of linearly-elastic anisotropic solids that exhibit volumetric constraints: isochoric, hydroisochoric and rigidtropic. An isochoric material deforms without volume change under any stress system. An hydroisochoric material does so under hydrostatic stress. A rigidtropic material undergoes zero deformations under a certain stress pattern. Whereas the three models coalesce for isotropic materials, important differences appear for anisotropic behavior. We find that isochoric and hydroisochoric models under certain conditions may be hampered by unstable physical behavior. Rigidtropic models can represent semistable physical materials of arbitrary anisotropy while including isochoric and hydroisochoric behavior as special cases.

  Abstract
  We study three “incompressibility flavors” of linearly-elastic anisotropic solids that exhibit volumetric constraints: isochoric, hydroisochoric and rigidtropic. [...]

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• A finite element formulation for the geometrically non linear analysis of shells

  E. Oñate, J. Oliver

  (1986). Finite element methods for plate and shell structures, T.J.R. Hughes, E. Hinton (Ed.) Pineridge Press, Vol. 2: Formulations and algorithms, pp. 83-101

  
  

  Abstract

  A finite element formulation for the analysis of geometrically nonlinear shell problems is presented. Degenerated 3D elasticity elements are used for the finite element discretization of the shell. Large rotation effects are taken into account in the nonlinear large displacement kinematic description. The shell formulation is derived in detail using a Total Lagrangian approach and explicit forms of the relevant finite element matrices are given. In the last part of the chapter the obtention of the alternative Updated Lagrangian formulation is presented.

  Abstract
  A finite element formulation for the analysis of geometrically nonlinear shell problems is presented. Degenerated 3D elasticity elements are used for the finite element discretization [...]

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• A simple method for automatic adaption of finite element meshes to changes in the boundary shape

  G. Chiandussi, G. Bugeda, E. Oñate

  (2001). Innovative Tools for Scientific Computation in Aeronautical Engineering, J. Periaux, P. Joly, O. Pironneau and E. Oñate (Eds.), pp. 149-167, CIMNE, Barcelona, Spain

  
  

  Abstract

  A simple method to automatically update the finite element mesh of the analysis domain is proposed for cases when the shape of the domain in modified. The method considers the mesh as a fictitious elastic body subjected to prescribed displacement at selected boundary points. The mechanical properties of each mesh element are appropriately selected in order to minimize the deformation and the distortion of the mesh elements. Different selection strategies have been used of remeshing in the solution of shape optimization problems and reduces the number of the remeshing step in the solution of coupled fluid-structure interaction problems

  Abstract
  A simple method to automatically update the finite element mesh of the analysis domain is proposed for cases when the shape of the domain in modified. The method considers [...]

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• Fractura elastoplástica: Modelos elastoplásticos para la simulación numérica de procesos de fractura

  J. Oliver, S. Oller, E. Oñate

  (1988). Métodos Numéricos Aplicados a la Mecánica de Fractura, J. Oliver et al (Eds.), CIMNE, Barcelona, pp. 27-60

  
  

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• A finite element formulation for the geometrically non linear analysis of shells using a total lagrangian approach

  J. Oliver, E. Oñate

  (1988). Computational Methods for Non Linear Problems, C. Taylor (Ed.) Pineridge Press, pp. 29-55

  
  

  Abstract

  A total Lagrangian formulation for the large displacement large rotation: analysis of shells using finite elements is presented. Different expressions for the strain matrix obtained using various displacement interpolation forms are discussed and details of the obtention of the tangent stiffness matrix are given. Simplifications of the general 3D shell formulation for 2D shells are also presented together with some examples of applications.

  Abstract
  A total Lagrangian formulation for the large displacement large rotation: analysis of shells using finite elements is presented. Different expressions for the strain matrix [...]

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• Mindlin finite strip and axisymmetric finite element shell analysis

  E. Oñate, B. Suárez, E. Hinton

  (1984). Finite Elements Software for Plates and Shells, Hinton E. y Owen D.R.J. (Eds.), Pineridge Press, 1984

  
  

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• Stress, strain and energy splittings for anisotropic elastic solids under volumetric constraints

  C. Felippa, E. Oñate

  (2002). Research Report, Nº PI217

  
  

  Abstract

  We define stress and strain splittings appropriate to linearly elastic anisotropic materials with volumetric constraints. The treatment includes rigidtropic materials, which develop no strains under a stress pattern that is a null eigenvector of the compliance matrix. This model includes as special case incompressible materials, for which the eigenvector is hydrostatic stress. The main finding is that pressure and volumetric strain must be redefined as effective quantities. Using this idea, an energy decomposition that exactly separates deviatoric and volumetric energy follows.

  Abstract
  We define stress and strain splittings appropriate to linearly elastic anisotropic materials with volumetric constraints. The treatment includes rigidtropic materials, [...]

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• A study of optimal membrane triangles with drilling freedoms

  C. Felippa

  (2002). Research Report, Nº PI218

  
  

  Abstract

  This article compares derivation methods for constructing optimal membrane triangles with corner drilling freedoms. The term “optimal” is used in the sense of exact inplane pure-bending response of rectangular mesh units of arbitrary aspect ratio. Following a comparative summary of element formulation approaches, the construction of an optimal 3-node triangle using the ANDES template is shown to be unique if energy orthogonality constraints are enforced a priori. Two other formulation are examined and compared with the optimal model. Retrofitting the conventional LST (Linear Strain Triangle) element by midpoint-migrating by congruential transformations is shown to be unable to produce an optimal element while rank deficiency is inevitable. Use of the quadratic strain field of the 1988 Allman triangle, or linear filtered versions thereof, is also unable to reproduce the optimal element. Moreover, these elements exhibit aspect ratio lock. These predictions are verified on benchmark examples.

  Abstract
  This article compares derivation methods for constructing optimal membrane triangles with corner drilling freedoms. The term “optimal” is used in the sense of [...]

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• A template tutorial: panels, families, clones, winners and losers

  C. Felippa

  (2002). Research Report, Nº PI219

  
  

  Abstract

  The article has a dual historical and educational theme. It is a tutorial on finite elements templates for two-dimensional structural problems. The exposition focused on the four-node plane stress element of flat rectangular geometry, called here the “rectangular panel” for brevity. This is one of two oldest two-dimensional structural elements, soon to reach its gold anniversary. On the other hand, the concept of finite element templates is a recent development. Interweaving the old and the new throws historical perspective into the “golden age” of discovery of finite elements. Templates provide a framework in which diverse element development methods can be fitted, compared and traced back to the sources. On the technical side templates have the virtue of facilitating the unified implementation of back to the sources. On the technical side templates have the virtue of facilitating the unified implementation of element families as well as the construction of custom elements. As an illustration of customization power, the Appendix presents the construction of a four noded bending optimal trapezoid that has eluded FEM investigators for several decades.

  Abstract
  The article has a dual historical and educational theme. It is a tutorial on finite elements templates for two-dimensional structural problems. The exposition focused on the [...]

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• Principis d'acústica, d'aeroacústica i breu introducció a l'aeroacústica computacional de fluixos subsònics

  O. Guasch

  (2002). Research Report, Nº PI220

  
  

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