On the complex potentials for a body with holes in doubly periodic plane

First, the complex variable method in planethermoelasticity for harmonic temperature change field is discussed, and thegeneral expression of the complex potentials in a finite multi-connectedregion under harmonic temperature change is derived. Then, based on theanalysis for the expression and multivalue property of the doubly-periodicanalytic function (the real part of which is given) and its object function,the general expression of the two complex potentials in plane elasticity fora body with a doubly periodic set of holes under doubly-periodic harmonictemperature change is obtained. Finally, the conclusion that the heatstresses vanish in two special cases is deduced.