An enhanced nodal gradient finite element for non-linear heat transfer analysis

Abstract

The present work is devoted to the analysis of non-linear heat transfer problems using the recent development of consective-interpolation procedure. Approximation of temperature is enhanced by taking into account both the nodal values and their averaged nodal gradients, which results in an improved finite element model. The novel formulation possesses many desirable properties including higher accuracy and higher-order continuity, without any change of the total number of degrees of freedom. The non-linear heat transfer problems equation is linearized and iteratively solved by the Newton-Raphson scheme. To show the accuracy and efficiency of the proposed method, several numerical examples are hence considered and analyzed.

Determining of the laser heat flux for three-dimensional conduction model by the sequential method

“…When other input parameters, the boundary conditions and the laser heat intensity, are specified prior, the finite element method [10][11][12] is utilized to find the temperature field in the Ω domain. When the temperature history is measured inside the workpiece, the laser heat flux of the surface is estimated by the inverse problem.…”

Accelerating the nonlinear analysis of hyper-elastic behavior by GMDH-assisted Newton-Raphson scheme

“…In practice, the iterative Newton-Raphson (NR) scheme is the most commonly used, due to simple implementation and quadratic convergence rate. The method has been widely applied in analyses of unsaturated flow 1 , plastic deformation 2,3 , geometrical nonlinearity [4][5][6] , hyper-elastic behavior [7][8][9] , temperaturedependent heat transfer [10][11][12] and many other types of problem. It is common knowledge if the deviation between the converged solution and the "initial guess" or "starting point" is large, difficulties may occur [13][14][15] , being reflected in the large number of iterations.…”