A closed-form solution for thermal stresses of structures using generalized variational principles

An energy-based method for thermal stresses of various statically indeterminate structures is presented. Using the Lagrange multiplier method, internal forces of statically indeterminate structures are investigated. A new functional from unconditional generalized variational principles is presented. Based on the variational method, a general matrix solution for internal forces and thermal stresses of statically indeterminate structures is established. Several types of structures including the rivet, truss, and bilayer cantilever beam are considered. Compared with the traditional methods, the accuracy and universality of the present model are confirmed. This work provides a convenient and unified method to solve the thermal stresses of various statically indeterminate structures.