Patent ID: 8600710
Filing Date: 2013-12-03
Classification: G06F

Abstract:
1. A method of modeling thermal problems using a non-dimensional finite element method, comprising a computer executing the steps of: (a) establishing a steady state heat conduction equation in three dimensions for an orthotropic material as  wherein the orthotropic material has three surfaces having surface areas S  holds for S  holds for S (b) establishing a scalar functional quantity Π=U+Ω  wherein V represents volume; (c) establishing a set of non-dimensional parameters  where θ is non-dimensional temperature, (d) expressing the scalar functional quantity for no internal heat generation in matrix form as:  where [  where Bi  and non-dimensional specified heat flux (e) minimizing a dimensionless scalar functional quantity given as Π=Π/hT (f) calculating an element stiffness matrix as [  and (g) calculating an element load vector as {