Structural Optimization with Uncertainties
search in optimal design has grown in connection with the rapid development of
aeronautical and space technologies, shipbuilding, and design of precision machin-
ery. A special field in these investigations is devoted to structural optimization with
incomplete information (incomplete data). The importance of these investigations
is explained as follows. The conventional theory of optimal structural design as-
sumes precise knowledge of material parameters, including damage characteristics
and loadings applied to the structure. In practice such precise knowledge is seldom
available. Thus, it is important to be able to predict the sensitivity of a designed
structure to random fluctuations in the environment and to variations in the material
properties.
This monograph is devoted to the exposition of new ways of formulating and
solving problems of structural optimization with incomplete information. We recall
some research results concerning the optimum shape and structural properties of
bodies subjected to external loadings. We study optimal design with incomplete in-
formation, accounting for the interaction between the structure and its environment,
properties of materials, existence of initial damages and damage accumulation. This
study is devoted to overcoming mathematical difficulties caused by local function-
als. Most of the attention of the book is devoted to the minimax approach using worst
case scenario, i.e. the guaranteed approach. But a probabilistic approach that does
not guarantee the result is also described in the monograph, because it gives more
“optimistic” results. Also, a mixed probabilistic-guaranteed approach is discussed
and applied.
solving problems of structural optimization with incomplete information. We recall
some research results concerning the optimum shape and structural properties of
bodies subjected to external loadings. We study optimal design with incomplete in-
formation, accounting for the interaction between the structure and its environment,
properties of materials, existence of initial damages and damage accumulation. This
study is devoted to overcoming mathematical difficulties caused by local function-
als. Most of the attention of the book is devoted to the minimax approach using worst
case scenario, i.e. the guaranteed approach. But a probabilistic approach that does
not guarantee the result is also described in the monograph, because it gives more
“optimistic” results. Also, a mixed probabilistic-guaranteed approach is discussed
and applied.
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