摘要
针对混凝土中氯离子扩散过程中扩散系数的非均质性导致的非线性问题,采用区域分解法并融入无网格法中的径向基函数求解思想,建立了时空一致径向基函数配点法.该方法将时间和空间区域同时分解,在相应子域上对未知函数进行径向基函数展开.针对含有Neumann边界条件的非均质扩散问题建立了Hermite型近似函数配点求解方法.该方法避免了对时间域采用差分法求解引起的迭代求解困难,对求解非均质扩散系数的问题求解具有一定优势.用Matlab语言编制了相应的求解程序,通过2个非均质扩散问题算例,验证了所提方法的正确性和有效性.所提方法为研究复杂环境下混凝土结构的耐久性问题提供了一种新的数值方法.
According to the nonlinear problem caused by heterogeneous diffusivity in the diffusion process of chloride ion in concrete, a time-space consistent collocation method is developed with the domain decomposition method and the methodology of the radial basis function （RBF） in the mesh- less method. Unknown arguments are expanded via RBFs in the corresponding sub-domain with sim- ultaneous decomposing of the time and space domain. Additionally, a Hermite collocation method of the RBF is constructed to solve the heterogeneous diffusion problem with Neumann boundary condi- tions. Compared with the finite difference process on solving time domain issues, the proposed method reduces the difficulty of iterative procedure and results in a more easy application to heteroge- neous diffusion problems. The Matlab program of the developed method is subsequently implemen- ted. Two numerical examples are performed to evaluate the accuracy and efficiency of the developed model. The examples clearly demonstrate that the developed method has more distinguished advanta- ges than the finite element method in analyzing heterogeneous diffusion problems. The proposed method provides new guidelines for the durability analysis of concrete structures.
出处
《东南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2012年第A02期346-350,共5页
Journal of Southeast University：Natural Science Edition
基金
国家重点基础研究发展计划(973计划)资助项目(2009CB623202)
高等学校博士学科点专项科研基金资助项目(20100092110049)
关键词
非均质扩散问题
区域分解法
径向基函数配点法
heterogeneous diffusion problem
domain decomposition method
collocation method ofradial basis function
