Variational Asymptotic Modeling of the Thermal Problem of Composite Beams

Abstract

The variational asymptotic method is used in this paper to construct models for thermal problem of composite beams under steady heat conduction. First, the original threedimensional heat conduction problem is reduced to be a two-dimensional thermal crosssectional analysis along with an optional one-dimensional heat conduction analysis. The one-dimensional heat conduction analysis exist only if the temperature is not prescribed at any point of the cross-section. Then we reduce the one-way coupled, three-dimensional thermoelasticity problem into a two-dimensional, one-way coupled thermoelastic crosssectional analysis and a one-dimensional, one-way coupled, thermoelastic beam analysis. The present theory is implemented into the computer program, VABS (variational asymptotic beam sectional analysis). Several examples are studied using the present theory and the results from VABS are compared with available analytical solutions and the threedimensional analysis using the commercial flnite element package ANSYS.