The development of irregular elements for differential quadrature element method steady-state heat conduction analysis

A new numerical approach for solving steady-state heat conduction problems by using the irregular elements of the differential quadrature element method (DQEM) is proposed. The mapping technique is used to transform the governing partial differential equation, the natural transition condition of two adjacent elements and the Newmann boundary condition defined on the irregular physical element into the parent space. The differential quadrature technique is used to discretize the transformed relation equations defined on the regular element in the parent space. Various techniques for selecting and implementing the constraint conditions, at element corners, are proposed. A global algebraic equation system can be obtained by assembling all of the discretized relation equations. Numerical procedures are summarized and the related computer code is developed. Numerical results are presented. They demonstrate the developed DQEM steady-state heat conduction analysis model.