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The load-deformation curve is obtained for a thin tube crushed between two parallel, rigid plates. It is found that the influence of geometry changes after initial yield results in increased load-carrying capacity. In addition, the effects on the yield condition due to direct stress and shear are quantitatively discussed.

The determination of upper and lower bounds on the yield-point loads of plates are formulated as mathematical programming problems by using finite element representations for the velocity and moment fields. Results are presented for a variety of square and rectangular plate problems and are compared to other available solutions.

Reviewed by Dr. John ChristodoulidesREVIEW -The methods of elastic-plastic analysis of continua were developed in response to increased efficiency and reliability requirements on modern structural components. The fundamentals of the theory of plasticity have already been implemented in a number of available computer codes. Among the methods of plastic analysis of structures, the theory of limit analysis has already become an engineering tool. The method employs the rigid-plastic model of material behavior and it is capable fo evaluating upper and lower bounds to the ultimate load intensity that can be sustained by a structure. If variable repeated loading is present, a suitable generalization of the limit analysis is introduced, known as the shakedown theory. Initial development of the shakedown theory dates back to the thirties and the shakedown analysis of structures under variable temperature fields were initiated by Prager in the fifties. The present text is among the rare comprehensive treatments of elastic-plastic structures under cyclic mechnaical and thermal loading.The concept of elastic-plastic response under variable repeated loading and temperature is first introduced herein for a simple bar system. The possible ensuing regimes of a stabilized response or an incremental collapse process are depicted in order to enhance reader understanding of the subject matter.All the concepts of applied mechanics pertinent to the contents are illustrated before the theorems of shakedown are stated and proved. Analogies existing between shakedown analysis and limit analysis are presented. The generalized stresses and strains used traditionally in plate and shell analysis are used and the deviation of limiting interaction surfaces for variable cyclic stresses is illustrated.The solution of shakedown problems can be obtained with the aid of mathematical programming techniques. The mathematical background in the involved process is outlined and detailed examples are given for simple structural elements under cyclic mechanical and thermal loading.The book devotes considerable attention to the analysis of rotating disks at cyclic variations of angular velocity and temperature. Shakedown diagrams are derived for a number of plate and shell problems, and thus their capacity under cyclic pressure and temperature profiles is identified. Progressive thermal cycling deformation (ratchetting) and contact problems are included. Finally theoretical proof of the existence and uniqueness of the elastic stabilization (shakedown) state is given.A wealth of information concerning elastic-plastic analysis of structural components under thermal and mechanical cycling is given in this monograph. It is concise, complete and it is considered extremely valuable in its field for both research and design.