Using Meshless Local Natural Neighbor Interpolation Method to Solve Two-Dimensional Nonlinear Problems

被引:13
作者
Li, Q. H. [1 ]
Chen, S. S. [1 ]
Luo, X. M. [1 ]
机构
[1] East China Jiaotong Univ, Sch Civil Engn & Architecture, Nanchang 330013, Peoples R China
基金
中国国家自然科学基金;
关键词
Nonlinear heat transfer problems; meshless method; natural neighbor interpolation; backward difference method; HEAT-TRANSFER PROBLEMS; BOUNDARY-ELEMENT METHOD; BASIS COLLOCATION METHOD; PETROV-GALERKIN METHOD; FREE METHOD BEFM; CONDUCTION PROBLEMS; FREE-VIBRATION; FORMULATION; SOLIDS;
D O I
10.1142/S1758825116500691
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
Based on the meshless local natural neighbor interpolation method (MLNNI), a novel solution procedure is developed for the analysis of nonlinear steady and transient heat transfer of two-dimensional structures in this paper. Nonlinearities arising from temperature dependence of material properties and nonlinear boundary conditions have been taken into account. The present method is developed based on the natural neighbor interpolation (NNI) for constructing shape functions at scattered nodes. The three-node triangular FEM shape function is employed as the test function, which reduces the orders of integrands involved in domain integrals. Due to the delta function property of the natural neighbor shape functions, there is no need to employ special techniques to enforce the essential boundary conditions. The backward difference method is employed for the time integration scheme in transient analysis and the Newton-Raphson iterative procedure is required at each time step. Three numerical examples with different geometries and boundary conditions are presented at the end to demonstrate the validity and accuracy of the proposed method for the solution of a wide class of nonlinear steady and transient heat transfer problems.
引用
收藏
页数:20
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