摘要
结合径向基点插值函数和弹性材料修正后的H-R(Hellinger-Reissner)变分原理,推导了Hamilton正则方程的无网格列式。以Multiquadric(MQ)、Gaussian(EXP)和薄板样条(TPS)为基函数,研究了Hamilton体系下无网格方法的收敛性、精确性以及基函数无量纲形状参数对计算结果的影响规律。该文的工作使得无网格有限元法的优越性与弹性力学Hamilton正则方程的半解析法得到了有机的结合,为Hamilton正则方程提出了一种无网格半解析方法。
Meshless formulistic of Hamilton canonical equation was derived by combining the modified Hellinger-Reissner variational principle for elastic material and the radial point interpolation functions in this paper. Based on the shape functions of Multiquadric （MQ）, Gaussian （EXP） and thin plane spine （TPS）, the maximum displacements in z direction of the single laminated plates were obtained by the meshless formulistic of Hamilton canonical equation. All of the numerical results were compared with those of ANSYS, demonstrating that the meshless formulistic of Hamilton canonical equation is reliable. As an application of the present method, the convergence of this meshless formulistic and the effects of the dimensionless shape parameters on the maximum displacement were investigated through numerical examples of single laminated plates clamp supported on four sides. This study introduced the advantages of meshless finite element method into semi-analytic solution of Hamilton canonical equation, and a new semi-analytic method was presented for Hamilton canonical equation.
出处
《工程力学》
EI
CSCD
北大核心
2011年第10期46-51,85,共7页
Engineering Mechanics
基金
国家自然科学基金民航联合研究基金项目(60979001)
中国民航大学校内科研基金项目(2011KYE07)
