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Fuzzy behavior of mechanical systems with uncertain boundary conditions. (English) Zbl 1004.74052

Summary: We discuss the problem of structures’ sensitivities to uncertain boundary conditions, and discuss the effect of uncertain prescribed displacements on static response of structures. The imprecise or uncertain prescribed displacements are treated as fuzzy quantities with known membership functions. For numerical computations, a fuzzy quantity can be approximated by sets of closed intervals with respect to specified \(\alpha\)-cuts. This transforms the problem into a set of interval equations at each \(\alpha\)-level. A numerical method is developed to solve the system of fuzzy equations. Simple stress analysis is also used to illustrate the method.

MSC:

74K99 Thin bodies, structures
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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