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An element-free computational framework for elastodynamic problems based on the IMLS-Ritz method

机译：基于IMLS-Ritz方法的弹性动力学问题的无元素计算框架

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摘要

An element-free computational framework based on the improved moving least-squares Ritz (IMLS-Ritz) method is first explored for solving two-dimensional elastodynamic problems. Employing the IMLS approximation for the field variables, discretized governing equations of the problem are derived via the Ritz procedure. Using the IMLS approximation, an orthogonal function system with a weight function is employed to construct the two-dimensional displacement fields. The resulting algebraic equation system from the IMLS-Ritz algorithm is solved without a matrix inversion. Numerical time integration for the dynamic problems is performed using the Newmark-β method. The involved essential boundary conditions are imposed through the penalty method. To examine the numerical stability of the IMLS-Ritz method, convergence studies are carried out by considering the influences of support sizes, number of nodes and time steps involved. The applicability of the IMLS-Ritz method is demonstrated through solving a few selected examples and its accuracy is validated by comparing the present results with the available solutions.
机译：为了解决二维弹性动力学问题，首先探索了一种基于改进的移动最小二乘Ritz（IMLS-Ritz）方法的无元素计算框架。利用场变量的IMLS近似，通过Ritz程序导出问题的离散控制方程。使用IMLS逼近，采用具有权函数的正交函数系统构造二维位移场。由IMLS-Ritz算法得到的代数方程组无需矩阵求逆即可求解。使用Newmark-β方法对动力学问题进行数值时间积分。涉及的基本边界条件是通过惩罚方法施加的。为了检验IMLS-Ritz方法的数值稳定性，通过考虑支撑尺寸，节点数和所涉及的时间步长的影响，进行了收敛研究。通过解决一些选定的示例，证明了IMLS-Ritz方法的适用性，并且通过将当前结果与可用解决方案进行比较来验证其准确性。

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  • 作者

    L.W. Zhang; D.M. Li; K.M. Liew;

  • 作者单位

    College of Information Technology, Shanghai Ocean University, Shanghai 201306, China;

    Department of Architecture and Civil Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR;

    Department of Architecture and Civil Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR,City University of Hong Kong Shenzhen Research Institute Building, Shenzhen Hi-Tech Industrial Park, Nanshan District, Shenzhen, China;

  • 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

    Element-free method; Improved moving least-squares; Ritz method; Elastodynamic problems;

    机译：无元素方法;改进了移动最小二乘法;丽兹法;弹性动力学问题;

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