Institute of Fundamental Technological Research

The problem of optimum selection and distribution of prestressing forces in a shell structure subjected to different loads is solved within membrane theory. The range of admissible prestressing tensors at a shell point is deter mined and the selection of optimum prestressing is described. The problem is discretized, linearized, and reduced to that of linear mathematical programming. A method of tracing cable trajectories is given. Graph theory approach is applied to form design combinations of elementary loads when these are related by logical conditions. An outline is given of the computation of a prestressed secondary containment of a nuclear reactor.

The paper provides a survey of the present state and basic trends of the theory. Following topics are dealt with: basic definitions (grain, phase, etc.), field of research (in particular, macroscopic constitutive equations), fundamental assumptions. Apart from some special methods (e.g. dilute suspensions, fluctuating inhomogeneities), main attention is focused on (1) variational approach (approximate solutions, closing inequalities for effective quantities), (2) probabilistic approach (exact solutions in the form of series according to correlation functions of increasing order). Problems are mainly tackled in the context of the theory of elasticity, other fields of applications, however, being also pointed out. Some possible future trends are discussed, especially the wave problem, theory of micro- and macro-plasticity, relations to chemical physics of manufacturing of materials.