On the thermal problem for composite beams using a finite element semi-discretisation

Abstract The paper deals with steady state thermo-elastic problems in beam-like structures and it is composed of three theoretical sections. The first part presents a two-dimensional finite element procedure to compute the temperature distribution within a beam cross section subjected to prescribed boundary conditions. It allows the beam cross section to be modelled taking into account any kind of thermal anisotropy or inhomogeneity. The second part is devoted to the structural thermo-elastic problem in a beam having arbitrary non-homogeneous, anisotropic material properties over the cross section but constant along the axis; the extension of a well-known semi-discretisation procedure to take into account anisotropic thermal expansion coefficients is presented. In this way it is possible to compute strains and stresses related to temperature distributions on the cross section computed, using the method outlined in the first part of the paper. The third part describes the procedure to evaluate thermal equivalent loads suitable for a three dimensional frame analysis. Some examples are presented and the results are compared either with their theoretical counterparts or with numerical results obtained from a full three-dimensional finite element analysis.