General displacement and work bounds for dynamically loaded bodies

In recent years a number of writers have developed theorems which allow the evaluation of bounds on deformation properties of bodies subject to both static and dynamic loading. Some of these results have proved useful to structural designers in assessing structural performance, thereby obviating the need for a complete analysis. In this paper a general theory is described for small strains which brings together results for both quasi-static and dynamic loading, and also provides a theoretical framework within which a wide range of constitutive relationships may be discussed. The material behaviour is included through a functional property of the constitutive relationship which gives a generalization of the concept of maximum complementary work. A new result for impulsively loaded bodies is illustrated by examples involving elastic and elastic perfectly-plastic materials.