Large Deflections of Structures Subjected to Heating and External Loads

The method of direct formulation of the stiffness matr ix 1 3 is extended to include the effects of nonuniform heating and large deflections. The purpose is to develop an analytical tool for the treatment of actual structures. In the solution of aeroelastic problems the relations between forces and deflections must be determined. The usual stiffness matrix formulation of this relationship is limited to small temperature changes and small deflections. For large temperature changes additional terms are required. Also the problem becomes geometrically nonlinear when large deflections are involved. To overcome the inherent difficulties of the nonlinear problem for practical structures either an iterative or a step-bystep procedure must be used. The force-deformation relations necessary for this step-by-step or iterative approach are derived for an axially loaded member and for a plate element including the effects of thermal strains.