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Analysis of dynamic stress concentration problems employing spline-based wavelet Galerkin method

机译：基于样条小波Galerkin方法的动应力集中问题分析

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摘要

Two-dimensional (2D) dynamic stress concentration problems are analyzed using the wavelet Galerkin method (WGM). Linear B-spline scaling/wavelet functions are employed. We introduce enrichment functions for the X-FEM to represent a crack geometry. In the WGM, low-resolution scaling functions are periodically located across the entire analysis domain to approximate deformations of a body. High-resolution wavelet functions and enrichment functions including crack tip singular fields are superposed on the scaling functions to represent the severe stress concentration around holes or crack tips. Heaviside functions are also enriched to treat the displacement discontinuity of the crack face. Multiresolution analysis of the wavelet basis functions plays an important role in the WGM. To simulate the transients, the wavelet Galerkin formulation is discretized using a Newmark-β time integration scheme. A path independent J-integral is adopted to evaluate the dynamic stress intensity factor (DSIF). We solve dynamic stress concentration problems and evaluate DSIF of 2D cracked solids. The accuracy and effectiveness of the proposed method are discussed through the numerical examples.
机译：使用小波Galerkin方法（WGM）分析了二维（2D）动态应力集中问题。采用线性B样条缩放/小波函数。我们为X-FEM引入富集函数以表示裂纹的几何形状。在WGM中，低分辨率缩放函数在整个分析域中定期定位，以近似物体的变形。高分辨率小波函数和包括裂纹尖端奇异场的富集函数叠加在缩放函数上，以表示孔或裂纹尖端周围的严重应力集中。重金属元素的功能也得到了丰富，以治疗裂纹面的位移不连续性。小波基函数的多分辨率分析在WGM中起着重要作用。为了模拟瞬变，使用Newmark-β时间积分方案离散化小波Galerkin公式。采用与路径无关的J积分来评估动态应力强度因子（DSIF）。我们解决了动态应力集中问题，并评估了二维裂纹固体的DSIF。通过数值算例讨论了该方法的准确性和有效性。

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  • 来源
    《Engineering analysis with boundary elements》 |2015年第9期|129-139|共11页
  • 作者

    Satoyuki Tanaka; Shogo Sannomaru; Michiya Imachi; Seiya Hagihara; Shigenobu Okazawa; Hiroshi Okada;

  • 作者单位

    Graduate School of Engineering, Hiroshima University, 4-1, Kagamiyama 1-chome, Higashi-Hiroshima 739-8527, Japan;

    Graduate School of Engineering, Hiroshima University, 4-1, Kagamiyama 1-chome, Higashi-Hiroshima 739-8527, Japan;

    Graduate School of Engineering, Hiroshima University, 4-1, Kagamiyama 1-chome, Higashi-Hiroshima 739-8527, Japan;

    Department of Mechanical Engineering, Saga University, 1 Honjocho, Saga 840-8502, Japan;

    Graduate School of Engineering, Hiroshima University, 4-1, Kagamiyama 1-chome, Higashi-Hiroshima 739-8527, Japan;

    Department of Mechanical Engineering, Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda 278-8510, Japan;

  • 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

    Wavelet Galerkin method; Meshfree method; Dynamic analysis; X-FEM; Stress intensity factor;

    机译：小波Galerkin方法;无网格方法;动态分析;X-FEM;应力强度因子;

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