摘要
为了解决含裂纹结构中因材料特性和载荷的不确定性因素给结构设计及计算带来的困难,基于区间数学理论,结合了摄动法、内积空间及无网格伽辽金法,提出基于局部正交的区间无网格伽辽金法。该方法在计算过程中只需节点信息,无需单元信息,采用局部加权正交基函数作为基函数,其导数形式简单且具有通式,又可避免矩阵A(x)求逆,编程简单,并推导出区间局部正交无网格平衡方程,利用区间参数摄动法求解平衡方程,还详细推导出区间J积分公式,并将其应用到含裂纹结构的不确定性问题中,通过算例验证了本方法的正确性和有效性。
In order to solve the problem that some structural parameters have errors or uncertainties which are caused by manufacture,installation,measurement or computation in structural analysis and design,an interval local orthogonal element-free Galerkin method（ILOEFGM）is proposed.Based on the interval mathematics,inner product space,perturbation theory,element-free Galerkin method（EFGM）are employed to deduce ILOEFGM equilibrium equations,and the parameter perturbation of interval number is used to solve the ILOEFGM equilibrium equations.As an application of the method,a numerical example based on the problem for plane with cracks is given.The calculated results show that the method is effective.
出处
《重庆大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2013年第7期127-132,共6页
Journal of Chongqing University
基金
吉林省科技厅基金项目(201205011
201215048)
关键词
区间参数
内积空间
区间分析
区间局部正交无网格伽辽金法
interval parameters
inner product space
interval analysis
interval local orthogonal element-free Galerkin method
