A planar heat conduction element improving temperature-related simulation accuracy

Abstract

In the numerical study of temperature field in the fields of freezing and thawing cycles in cold regions, geothermal energy and functionally graded materials, the selection of heat conduction elements of the finite element method has an important influence on the numerical calculation results. Based on the fundamental solution and heat conduction theory, the fundamental solutions of the two-dimensional heat conduction control equation were added in the temperature interpolation function of the conventional planar 4-node quadrilateral heat conduction element. A new planar heat conduction non-coordination element with the fundamental solutions was established. The element interpolation function and the stiffness matrix were derived, and the element convergence was examined. The calculation accuracy was compared among the plane heat conduction non-coordination element with the fundamental solutions, the conventional finite element method and the analytical solution. The results showed that the planar heat conduction non-coordination element with the fundamental solutions proposed in this paper is high in calculation method and precision.