This work presents a limit-analysis formulation for the Hybrid Virtual Element Method (HVEM). The key features of the approach are the use of an energy norm for the VE projection and a high-order, divergence-free stress interpolation. Unlike classical VEM formulations, HVEM eliminates the need for stabilization terms, thereby avoiding issues related to the choice of stabilization parameters. The method effectively avoids volumetric locking and spurious hardening effects observed in stabilized VEM approaches. The self-equilibrated assumed stress field is suitable for a limit analysis based on the static theorem. Plastic admissibility is tested in a sufficiently large number of control points inside the element domain. The limit-analysis problem is solved through a proximal point formulation, allowing it to be rewritten in a pseudo elasto-plastic form. Numerical experiments demonstrate the accuracy of HVEM even on coarse meshes and its high convergence rate in predicting collapse loads.

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Limit Analysis of 2D Problems Using a Hybrid Virtual Element Formulation

  • Francesco S. Liguori,
  • Antonio Madeo,
  • Sonia Marfia,
  • Giovanni Garcea,
  • Elio Sacco

摘要

This work presents a limit-analysis formulation for the Hybrid Virtual Element Method (HVEM). The key features of the approach are the use of an energy norm for the VE projection and a high-order, divergence-free stress interpolation. Unlike classical VEM formulations, HVEM eliminates the need for stabilization terms, thereby avoiding issues related to the choice of stabilization parameters. The method effectively avoids volumetric locking and spurious hardening effects observed in stabilized VEM approaches. The self-equilibrated assumed stress field is suitable for a limit analysis based on the static theorem. Plastic admissibility is tested in a sufficiently large number of control points inside the element domain. The limit-analysis problem is solved through a proximal point formulation, allowing it to be rewritten in a pseudo elasto-plastic form. Numerical experiments demonstrate the accuracy of HVEM even on coarse meshes and its high convergence rate in predicting collapse loads.