Deterministic and Stochastic Sensitivity in Computational Structural Mechanics

摘要

A theory and computational methods for deterministic and stochastic sensitivityanalysis of time-independent and time-varying system are provided. Discussions are restricted to multi-degrees of freedom linear-elastic 3D structures with fixed global configuration. On the basis of the displacement finite element modeling and a stochastic Hamiltonian's variational principle, two proposed new problems of computational mechanics are formulated for static and dynamic response sensitivity. A new form of response functionals is introduced in terms of a convolution of a time signal sequence enabling the dynamic sensitivity response to be dealt with at any particular instant. To eliminate the secularity appearing in the perturbation solutions, time-varying forcing functions are assembled into complex-valued series and the fast Fourier transform is employed to remove the resonant parts. To handle large finite element systems at acceptable computation cost, the two-fold superposition technique involving modal analysis and transformation from a correlated space to an uncorrelated space of random variables is presented. A complete algorithm was worked out and implemented into the microcomputer program POLSAP, a finite element code for deterministic and stochastic analysis of statics, minimum-weight optimization, buckling load, eigenpair, forced-vibration, eigen value sensitivity, static and dynamic response sensitivity of truss-beam-shell structures. A number of numerical results are presented.