轴对称问题中的耦合多项式基的径向点插值法  

A radial point interpolation meshless method with polynomial basis for axi-symmetric solids

作　　者：贾延[1] 刘长武[2] 

机构地区：[1]北方民族大学信息与计算科学学院,宁夏银川750021 [2]四川大学水利水电学院,四川成都610065

出　　处：《合肥工业大学学报（自然科学版）》2012年第12期1714-1718,共5页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(50879049);宁夏自然科学基金资助项目(NZ11138);北方民族大学自主科研基金资助项目(2011ZQY027)

摘　　要：文章采用耦合多项式基的径向点插值法分析轴对称问题,得到固体力学中轴对称问题的无网格离散方程,依据厚壁圆筒的受力特点对其进行简化,建立了无网格数值模型;研究了其受均匀外压时的径向应力和环向应力分布以及径向位移分布,对其计算结果进行分析,并与有限元计算结果进行对比,取得了令人满意的结果;验证了耦合多项式基的径向点插值法在工程轴对称问题中的应用可行性。数值算例结果表明,该方法计算精度较高、稳定性好,具有很好的应用前景。A radial point interpolation meshless method with polynomial basis is applied to solving axi-symmetric problem. The meshless discrete equation of axi-symmetric problem of solid mechanics is obtained. Numerical calculation of the thick wall cylinder is carried out by means of the meshless method, and the meshless numerical model is established. The distribution of radial displacement and the distribution of radial stress and circumferential stress under uniform external pressure are researched. The numerical results are analyzed and compared with those of the finite element method. They show good agreement and verify the feasibility of the application of proposed method in engineering axi-symmetric problem. The numerical results show that this method has high accuracy, good stability and good application prospects.

关 键 词：无网格法 点插值法 径向基函数 轴对称问题 厚壁圆筒 有限元法 

分 类 号：O242[理学—计算数学] O343[理学—数学]