Prestress for Maximum Strength

The problem of designing prestress to maximize elastic capacity is treated analytically. Our formulation models structures comprised of a one-material elastic continuum, subject to a single deterministic load configuration. The equations needed to predict the optimal prestress design are derived. They are shown to comprise necessary and sufficient conditions for global maximum strength in the unconstrained design problem. The theory is demonstrated on the design of prestress for a thick-walled cylinder. INTRODUCTION FREQUENTLY the structural function of a structure or machine part might be enhanced through the installation of an appropriate initial stress state. Indeed, prestress is primary to structural integrity for some material composites, such as prestressed concrete. Otherwise, for a structure made of either a single material or a composite, structural response is almost always sensitive to initial stress state. At least theoretically, the option to use prestress in design exists in proportion to this sensitivity. Yet among topics in structural mechanics, there appears to be relatively little literature on basics in the design of prestress. Some of the literature on particular design problems is listed in [l] and [2]. An unusual application of structural prestress is treated in [3], while [4] presents a method to evaluate optimal prestress. A formulation is given in [5] for problems in the design of prestress to extremize the Euler load. Optimal prestress relative to plastic collapse and relative to elastic capacity are related through theorems stated recently by Nagtegaal [6]. This paper provides an analytical formulation for problems arising in the design of prestress to maximize carrying capacity. The results apply to structures made of a single material, where the structure experiences just one (deterministic) loading environment. The development leading to these results is otherwise general; it is written in the next section for an elastic continuum but the argument is similar for any structural element or system where prestress might be used to increase elastic capacity. It also proves possible to predict the collapse load for von Mises yield condition, simply by interpreting in an appropriate way the outcome of our investigation for elastic structures. An example is given to indicate how the theory of this paper may be used to predict an optimal prestress configuration. However, no attempt is made to otherwise consider the technical situations where prestress might be employed to practical advantage. Nor