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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A finite element framework for continua with boundary energies. Part I: The two-dimensional case
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A finite element framework for continua with boundary energies. Part I: The two-dimensional case

机译：具有边界能的连续体的有限元框架。第一部分：二维情况

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摘要

This contribution deals with the implications of boundary potential energies on the two-dimensional deformations of solids in the framework of the finite element method. Common modelling in continuum mechanics takes exclusively the bulk into account, nevertheless, neglecting possible contributions from the boundary. However, boundary effects sometimes play a dominant role in the material behavior, the most prominent example being surface tension. Within this contribution the boundary potentials are allowed, in general, to depend not only on the boundary deformation but also on the boundary deformation gradient and the spatial boundary tangent. For the finite element implementation, a suitable curvilinear converted coordinate system attached to the boundary is defined and corresponding geometrical and kinematical derivations completely based on a tensorial representation are carried out. Afterwards, the discretization of the generalized weak formulation, including boundary potentials, is performed and eventually numerical examples are presented to demonstrate the boundary effects due to different proposed material models.
机译：在有限元方法的框架内，这种贡献涉及边界势能对固体二维变形的影响。连续力学中的通用建模只考虑了大部分，却忽略了边界的可能贡献。但是，边界效应有时在材料行为中起主要作用，最突出的例子是表面张力。在该贡献范围内，通常允许边界电势不仅取决于边界变形，还取决于边界变形梯度和空间边界切线。对于有限元实现，定义了附加到边界的合适的曲线转换坐标系，并完全基于张量表示进行了相应的几何和运动学推导。然后，对包括边界势的广义弱公式进行离散化处理，并最终通过数值例子说明了由于提出的不同材料模型而产生的边界效应。

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  • 来源
  • 作者

    A. Javili; P. Steinmann;

  • 作者单位

    Lehrstuhl fuer Technische Mechanik, Universitaet Erlangen-Nuernberg, Egerlandstrasse 5, D-91058 Erlangen, Germany;

    Lehrstuhl fuer Technische Mechanik, Universitaet Erlangen-Nuernberg, Egerlandstrasse 5, D-91058 Erlangen, Germany;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    boundary potentials; surface tension;

    机译：边界电位;表面张力;

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