Thermal stress in a trigonal crystal rod

The thermally induced stresses and strains in a freely supported long trigonal crystal rectangular rod are presented. Careful grouping of the stress, strain relationships casts the equations into the form of the usual logarithmic potential solution with new coefficients that are simple functions of the stiffness matrix elements. Then a logarithmic potential solution is used to find analytic expressions for the particular stresses. Addition of two ordinary isothermal stress fields allows the particular stresses to be corrected so that (a) the surface stresses average to zero on each lateral boundary and (b) the plane strain condition is removed and the average longitudinal stress and its moments are zero. A method to zero the residual surface stress is mentioned and numerical test cases and an example are given.