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Mathematical models for the analysis and optimization of elastoplastic structures. Transl. from the Russian by L. W. Longdon. (English) Zbl 0616.73079
Ellis Horwood Series in Engineering Science. Chichester: Ellis Horwood Ltd.; New York etc.: Halsted Press: a division of John Wiley & Sons. 121 p.; $ 39.95 (1983).
The author starts with the following assumptions: (a) All loads are quasistatic, i.e. dynamic effects and inertia forces are ignored. (b) The material is isotropic and perfectly plastic, or linearly elastic. (c) At plastic failure, limit deformations are ”small”. All structures are discretized. He derives the basic (matrix) equations relating the velocity and force fields that are analogues of discrete elastic models when dissipation is taken into account. Next, he determines the limit load parameters corresponding to plastic failure. He considers both static and kinematic formulations derived from duality for the corresponding programming problems. Monotone increasing and cyclic loads are considered in detail. Solutions of specific examples are offered in the final chapter.
This monograph is of primary interest to structural engineers concerned with the mathematical programming approach to structural design. In the opinion of the reviewer it is only of marginal interest to applied mathematicians.

MSC:
74P99 Optimization problems in solid mechanics
74-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids
74R20 Anelastic fracture and damage
90C05 Linear programming