Stochastic mechanics

The properties of many physical systems and/or the actions on these systems exhibit notable random ¯uctuations that cannot be captured by deterministic models. Examples are used to demonstrate the need for probabilistic models to represent systems and inputs depending on uncertain parameters. The displacement, stress, strain, damage, and other output measures of these systems are stochastic so that their properties cannot be obtained by the deterministic methods of classical solid mechanics. The methods of stochastic mechanics are needed for solution. Following an introduction and a section on elementary concepts of probability theory, the four possible combinations of deterministic/stochastic system and input are examined in separate sections. The case of deterministic systems and inputs is discussed to demonstrate the potential of the stochastic methods for solving classical problems of solid mechanics. The case of deterministic operators and random inputs is focused on random vibration problems because these problems constitute a major topic of stochastic mechanics. The last two sections deal with problems de®ned by stochastic operators and deterministic or stochastic inputs. All the sections on stochastic mechanics review some of the most notable past accomplishments, outline current research trends on both analytical and numerical solutions, and illustrate some of these research trends by simple example