Nodeless variable finite element method for heat transfer analysis by means of flux-based formulation and mesh adaptation

Abstract

Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The solution accuracy is further improved by implementing an adaptive meshing technique to generate finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems are: (a) a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and (b) a transient heat conduction analysis in a long plate subjected to a moving heat source.

Adaptive nodeless variable finite elements with flux-based formulation for thermal–structural analysis

“…The nodeless variable interpolation functions, N 4 , N 5 , N 6 , vary quadratically, and are identical to those presented Ref. [5].…”

“…The first example is a steady-state conduction heat transfer in a square plate due to a highly localized surface heating [5]. The problem is analyzed by using the nodeless variable elements so that the solution error is less than 5%.…”

“…[5,7]. For the triangular nodeless variable element, the distributions of the displacement components over the element are assumed in the form:…”

“…The temperature solution accuracy is improved by incorporating an adaptive meshing technique into a nodeless variable finite element method as demonstrated in Ref. [5].…”

Nodeless variable finite element method for stress analysis using flux-based formulation

“…The objective of this paper is to develop a procedure to improve the predicted stress distribution by using an alternative finite element method. The nodeless variable finite element previously developed for heat transfer analysis [8] is extended for the stress analysis in this paper in order to increase the accuracy of the predicted displacement and stress solutions. The nodeless variable finite element uses quadratic interpolation functions to describe the displacement distribution over the element without requiring additional actual nodes.…”