Optimum Synthesis of Prestressed Structures

The concept of reversed deformation is described. By using this technique, it is shown that any prestressed indeterminate structure can be designed without solving compatibility equations. The shape of the fully stressed structure and the stresses in the members are chosen prior to design. This approach is particularly suitable for the design of highly redundant and nonlinear structures on the basis of permissible stress criterion. The method is illustrated with examples of both skeletal and shell structures. Variational equations for minimum weight are stated. The notions of neutral lines and regular and irregular panels are introduced, and optimum solutions are given for various types of prestressed plates and beam grids (grillages). The concept is compared with other optimum design methods.