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首页> 外文学位 >Analysis by meshless local Petrov-Galerkin method of material discontinuities, pull-in instability in MEMS, vibrations of cracked beams, and finite deformations of rubberlike materials.
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Analysis by meshless local Petrov-Galerkin method of material discontinuities, pull-in instability in MEMS, vibrations of cracked beams, and finite deformations of rubberlike materials.

机译：通过无网格局部Petrov-Galerkin方法分析材料的不连续性，MEMS中的拉入不稳定性，裂纹梁的振动以及橡胶状材料的有限变形。

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摘要

The Meshless Local Petrov-Galerkin (MLPG) method has been employed to analyze the following linear and nonlinear solid mechanics problems: free and forced vibrations of a segmented bar and a cracked beam, pull-in instability of an electrostatically actuated microbeam, and plane strain deformations of incompressible hyperelastic materials. The Moving Least Squares (MLS) approximation is used to generate basis functions for the trial solution, and for the test functions. Local symmetric weak formulations are derived, and the displacement boundary conditions are enforced by the method of Lagrange multipliers. Three different techniques are employed to enforce continuity conditions at the material interfaces: Lagrange multipliers, jump functions, and MLS basis functions with discontinuous derivatives. For the electromechanical problem, the pull-in voltage and the corresponding deflection are extracted by combining the MLPG method with the displacement iteration pull-in extraction algorithm. The analysis of large deformations of incompressible hyperelastic materials is performed by using a mixed pressure-displacement formulation. For every problem studied, computed results are found to compare well with those obtained either analytically or by the Finite Element Method (FEM). For the same accuracy, the MLPG method requires fewer nodes but more CPU time than the FEM.
机译：无网格局部Petrov-Galerkin（MLPG）方法已用于分析以下线性和非线性固体力学问题：分段杆和裂梁的自由振动和强迫振动，静电致动微束的拉入不稳定性以及平面应变不可压缩的超弹性材料的变形。移动最小二乘（MLS）逼近用于生成试验解决方案和测试函数的基础函数。推导了局部对称的弱公式，并通过拉格朗日乘子法来施加位移边界条件。三种不同的技术用于在材料界面上强制执行连续性条件：拉格朗日乘数，跳转函数和具有不连续导数的MLS基本函数。对于机电问题，通过将MLPG方法与位移迭代引入提取算法相结合来提取引入电压和相应的挠度。使用混合压力位移公式对不可压缩的超弹性材料的大变形进行了分析。对于研究的每个问题，发现计算结果都可以与通过分析或有限元方法（FEM）获得的结果进行比较。为了达到相同的精度，与FEM相比，MLPG方法需要更少的节点，但需要更多的CPU时间。

著录项

  • 作者

    Porfiri, Maurizio.;

  • 作者单位

    Virginia Polytechnic Institute and State University.;

  • 授予单位 Virginia Polytechnic Institute and State University.;
  • 学科 Engineering Mechanical.
  • 学位 Ph.D.
  • 年度 2006
  • 页码 163 p.
  • 总页数 163
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 机械、仪表工业;
  • 关键词

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