STOCHASTIC STRUCTURAL DYNAMICS APPLICATION OF FINITE ELEMENT METHODS

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STOCHASTIC STRUCTURAL DYNAMICS APPLICATION OF FINITE ELEMENT METHODS

Author(s)/Editor(s): Cho W. S. To Professor of Mechanical Engineering University of Nebraska-Lincoln, US | Size: 12.84 MB| Format: PDF| Publisher: WILLY

The parallel developments of the finite element methods (FEM) in the
1950's [1, 2] and the engineering applications of the stochastic processes in the 1940's [3, 4] provided a combined numerical analysis tool for the studies of dynamics of structures and structural systems under random loadings. There are books on statistical dynamics of structures [5, 6] and books on structural dynamics with chapter(s) dealing with random response analysis [7, 8]. In addition, there are various monographs and lecture notes on the subject. However, a systematic treatment of the stochastic structural dynamics applying the FEM seems to be lacking. The present book is believed to be the first relatively in-depth and systematic treatment of the subject that applies the FEM to the field of stochastic structural dynamics.
Before the introduction to the concept and theory of stochastic quantities
and their applications with the FEM in subsequent chapters, the two FEM
employed in the investigations presented in the present book are outlined in this chapter. Specifically, Section 1.1 is concerned with the derivation of the
temporally stochastic element equation of motion applying the displacement
formulation. The consistent element stiffness and mass matrices of two beam elements, each having two nodes are derived. One beam element is uniform and the other is tapered. The corresponding temporally and spatially stochastic element equation of motion is derived in Section 1.2. The element equations of motion based on the mixed formulation are introduced in Section 1.3. Consistent element matrices for a beam of uniform cross-sectional area are obtained. This beam element has two nodes, each of which has two degrees-of-freedom (dof).
This beam element is applied to show that stiffness matrices derived from the displacement and mixed formulations are identical. The incremental variational principle and element matrices based on the mixed formulation for nonlinear structures are presented in Section 1.4. Section 1.5 deals with constitutive relations and updating of configurations and stresses. Closing remarks for this chapter are provided in Section 1.6

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