无网格动力法中质量矩阵构造方法研究

发布时间：2018-06-07 12:41

本文选题：无网格法 + 一致质量矩阵　；参考：《西安理工大学学报》2017年01期

【摘要】：无网格动力法中质量矩阵的构造对计算结果的精度有着重要影响。本文就无网格动力法中质量矩阵的构造方法,给出了一致质量矩阵和集中质量矩阵的数学表达式,运用MATLAB软件编制了基于不同质量矩阵的无网格动力法计算程序,对无约束矩形板不同质量矩阵构造下的频率和振型进行了对比计算。结果表明:采用集中质量矩阵时,结果受节点划分的影响较大,只有节点划分足够密集时,结果才趋于精确值;而采用一致质量矩阵时,结果受节点划分的影响较小,说明了一致质量矩阵在无网格动力法质量矩阵构造中的优越性。
[Abstract]:The construction of mass matrix plays an important role in the meshless dynamic method. In this paper, the method of constructing mass matrix in meshless dynamic method is discussed. The mathematical expressions of consistent mass matrix and lumped mass matrix are given, and the calculation program of meshless dynamic method based on different mass matrices is compiled by using MATLAB software. The frequencies and modes of unconstrained rectangular plates with different mass matrices are calculated and compared. The results show that when the lumped mass matrix is adopted, the results are greatly affected by the nodal partitioning, only when the nodal partitioning is dense enough, the results tend to be accurate, but when the uniform mass matrix is used, the results are less affected by the nodal partitioning. The superiority of uniform mass matrix in the construction of mass matrix of meshless dynamic method is explained.
【作者单位】：西安理工大学土木建筑工程学院;
【基金】：国家自然科学基金资助项目(51308455) 陕西省教育厅自然科学专项基金资助项目(15JK1522) 西安市建设科技计划资助项目(SJW2015-21) 西安理工大学科技创新计划资助项目(2015CX019)
【分类号】：O241

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