A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry ...A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional （2D） problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method （FEM） shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.展开更多
According to the axisymmetric heat conduction of monolayer cylinder, a general method was deduced to calculate the axisymmetric temperature of linear heat conduction multilayer cylinder. Four types of boundary conditi...According to the axisymmetric heat conduction of monolayer cylinder, a general method was deduced to calculate the axisymmetric temperature of linear heat conduction multilayer cylinder. Four types of boundary conditions were summarized and formulas for each type were derived. Then, a general calculating program was developed. Four temperature formulas could be expressed by a uniform equation, and the intermediate interface temperatures of axisymmetrical linear conduction multilayer cylinder satisfied tridiagonal linear and nonlinear systems of equations, which could be solved with the pursuit method and the Newton＇s method, respectively. With the calculating program, the temperature at any point of linear heat conduction multilayer cylinder could be obtained.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11002054)the Foundation of Hunan Educational Committee(Grant No.12C0059).
文摘A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional （2D） problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method （FEM） shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.
基金Item Sponsored by National Natural Science Foundation of China (50474014)Provincial Key Technologies Research and Development Program of Liaoning of China(2008216005)
文摘According to the axisymmetric heat conduction of monolayer cylinder, a general method was deduced to calculate the axisymmetric temperature of linear heat conduction multilayer cylinder. Four types of boundary conditions were summarized and formulas for each type were derived. Then, a general calculating program was developed. Four temperature formulas could be expressed by a uniform equation, and the intermediate interface temperatures of axisymmetrical linear conduction multilayer cylinder satisfied tridiagonal linear and nonlinear systems of equations, which could be solved with the pursuit method and the Newton＇s method, respectively. With the calculating program, the temperature at any point of linear heat conduction multilayer cylinder could be obtained.
