Convex models of uncertainty in applied mechanics. (English) Zbl 0703.73100

Studies in Applied Mechanics, 25. Amsterdam etc.: Elsevier. xvii, 221 p. Dfl. 185.00; $ 94.75 (1990).
Probabilistic modelling in mechanics is discussed in the first chapter. Also simple examples of structural reliability and sensitivity problems are presented. Quotations are collected from some authors, they are not in favour of probabilistic methods. Convexity concept is suggested as an alternative of the probabilistic approach when the solution is uncertain. Elementary mathematics of convex regions, functions and sets is reminded. Uniformly bounded functions, functions with bounded derivatives or envelope, functions of bounded energy or frequency are taken for the convex modelling. They are exemplified in two vast areas: - uncertain excitations because of vehicle vibrations, seismic actions as well as measurements of damped vibrations, - geometric imperfections of beams and shells under dynamic compressive forces. Various response parameters are analyzed such as maximum deflection, duration of overloading, averaged displacement along the bar, buckling in effect of impact loading, bounded imperfections of thin shells and their knockdown factors. Partial differential equations are formulated in both areas and analytical solutions or approximate estimates are derived.
Reviewer: J.Murzewski


74S30 Other numerical methods in solid mechanics (MSC2010)
74H50 Random vibrations in dynamical problems in solid mechanics
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74K15 Membranes
74G60 Bifurcation and buckling
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
90C15 Stochastic programming
49Q12 Sensitivity analysis for optimization problems on manifolds