Approximate dynamic responses in random media
Complex stochastic algorithms are reduced by a stationary iterative strategy which is styled after \textit{B. A. Boley} [Q. Appl. Math. 14, 249- 257 (1956)]. Primary solutions of the thermo-elasto-dynamic system are computed for uncoupled problems. For wave propagation problems and steady harmonic responses, the lumped mass matrix representation is found to be adequate to detect random fluctuations about the mean values. The possibility of transforming stochastic problems under random loading is examined. One-dimensional finite element analysis is done for shear and bending problems of beams using the concept of equivalent random loading. Then, the stochastic differential equations are rederived for self- adjoint cases. Deterministic computer programs for dynamic problems are applied in stochastic finite element analysis with some modifications. Stochastic boundary element and stochastic finite element are formulated. The operator equation for the mean field is constructed after J. B. Keller's idea [\textit{J. B. Keller}, Proc. Symp. Appl. Math. 16, 145-170 (1964; Zbl 0202.467); ibid. 13, 227-246 (1962; Zbl 0108.147)]. The smoothing assumption permits the flux field to be deterministic for a set of deterministic model displacements. The proposed finite element technique combines methods given by \textit{V. I. Tatarski} [Wave propagation in turbulent medium (1961; Zbl 0114.419)]. The formulation may be applied to unbounded media as well, e.g. to foundation-structure interaction problems.
scientific article; zbMATH DE number 482331