Article,
Application of the finite element method to heat conduction analysis
Nuclear Engineering and Design, 4 (3): 276--286 (1966)
Abstract
A variational principle is applied to the transient heat conduction
analysis of complex solids of arbitrary shape with temperature and
heat flux boundary conditions. The finite element discretization
technique is used to reduce the continuous spatial solution into
a finite number of time-dependent unknowns. The continuum is divided
into subregions (elements) in which the temperature field variable
is approximated by Rayleigh-Ritz polynomial expansions in terms of
the values of the temperatures at prescribed boundary points of the
subregions. These temperatures at the node points act as generalized
coordinates of the system and, being common to adjacent subregions,
enable appropriate continuity requirements to be satisfied over the
entire continuum. The variational principle yields Euler equations
of the Lagrangian form which result in the development of an equivalent
set of first order, ordinary differential equations in terms of the
nodal temperatures. A unique method of numerical solution of these
equations is introduced which is stable and requires a minimum of
computer effort. Elements of various shapes and their associated
temperature fields are discussed for one, two and three-dimensional
bodies. The method is developed in detail for two-dimensional bodies
which are idealized by systems of triangular elements. The development
of a digital computer program is discussed and several examples are
given to illustrate the validity and practicality of the method.
� 1966.
