[The articles of this volume will not be indexed individually.]
This volume contains the papers that were presented at the first international conference on computational stochastic mechanics, held at Corfu, Greece, 17-19 September 1991; it is dedicated to Dr. Masanobu Shinozuka, a well-known expert in structural reliability, structural dynamics, and lifeline earthquake engineering, who contributed in a great measure to the appearance of this field of research.
Computational stochastic mechanics is indeed a very recent scientific field; its birth is due to the development of computational hardware and of mechanical techniques, too. Now, computational stochastic mechanics is the most suitable frame for the study of a very large class of complex, actual mechanical systems.
This book, edited by P. D. Spanos (Rice University, USA), and C. A. Brebbia (Wessex Institute of Technology, U.K.), represents the first attempt at an overview of the results – both theoretical and practical - - in this field, the authors being well-known and highly-appreciated experts.
Papers are grouped together on sections as follows:
1. Theoretical reliability analysis.
(“On excursion of non-homogeneous vector-valued Gaussian random fields”, “Fitting-adaptive importance sampling in reliability analysis”, “Exceedance probabilities under various combinations of rare events”, “Skewness and kurtosis of safety margin”, “A curve-fitting method of combined distribution in probabilistic modeling of random variables”, “On procedures to calculate the reliability of structural systems under stochastic loading”, “The sensitivity analysis of stochastic hysteretic dynamic systems”, “Solution of random eigenvalue problem by crossing theory and perturbation”, “SORM analysis using quasi-Newton optimization”, “Method of stochastic linearization revised and improved”, “Maximal Lyapunov exponent for a stochastically perturbed codimension two bifurcation”, “Updating of a model and its uncertainties utilizing dynamic test data”).
The papers in this section present a large variety of theoretical analysis methods: scalarizations for the failure surfaces, event combination methods, use of combined distributions, sensitivity analysis, some techniques for the calculus of the failure probability, stochastic linearization theory, study of asymptotic stability, choice of optimal parameters for structural models.
2. Damage analysis.
(“Identification of structural dynamic systems by sequential prediction error method”, “Computer and test aided modelling and its application to identify structural damage”, “The effect of model uncertainty on the accuracy of global nondestructive damage detection in structures”, “Evaluation of maximum softening as a damage indicator for reinforced concrete under seismic excitation”).
The following methods are used: estimation of the modal parameters of a structural dynamical system, test and computer modelling for identification of structural damage, theory of damage localization.
3. Applied reliability analysis.
(“Empirical formulae to presume the resistance performance of high speed crafts models”, “Computational experience with damage-tolerant optimization of structural systems”, “On the effect of stochastic imperfections on the buckling strength of certain structures”, “Chaos, stochasticity and stability of a nonlinear oscillator with control”).
Papers in this section are dealing with computational modelling techniques and tests for actual systems such as: technique of principal component analysis, damage tolerant optimum design, treatment of the stochastic nature of structural imperfections, analysis of global stability of the systems.
4. Theoretical random vibrations.
(“Stochastic response of nonlinear multi-degrees-of-freedom (MDOF) structures subjected to combined random loads”, “Moment equations approach to nonstationary responses of a nonlinear system subjected to nonwhite random excitation”, “The path integral solution technique applied to the random vibration of hysteretic systems”, “Non-stationary probabilistic response of linear systems under non-Gaussian input”, “Stochastic linearization for the response of MDOF systems subjected to external and parametric Gaussian excitations”, “Equivalent linearization of a newly introduced general hysteretic model”, “A method for solving the diffusion equation with random coefficients”, “Response statistics of nonlinear systems under variations of excitation bandwidth”, “Stochastic equivalent linearization of nonlinear complex structures”, “Numerical solution of Fokker-Planck equation for first passage probabilities”, “Approximative analysis of nonstationary random vibrations of MDOF systems”).
The papers in this section try to propose new theoretical models and methods (adapted to numerical calculus) for various systems: cumulant truncation technique for Fokker-Planck equation, recurrence algorithms for moment equations, path integral solution technique, stochastic equivalent linearization and Gaussian closure, Monte Carlo simulations for hysteretic models, finite element method for transient Fokker-Planck equation, approximation for the mean square response.
5. Stochastic finite element concept.
(“First order reliability analysis using stochastic finite element methods”, “Analysis of two-dimensional stochastic systems by the weighted integral method”, “Non-conservatively loaded stochastic columns”).
There are presented some results on stochastic finite element methods. New theoretical methods, discussed by the authors, are used in numerical examples.
6. Fatigue/fracture.
(“Inspection strategy for deteriorating structures based on cost minimization approach”, “Probabilistic approach to cumulative damage of car components”, “Stochastic two-dimensional fatigue crack growth analysis including the effect of crack coalescence”, “Stochastic fatigue damage in welded cruciforms”, “Statistical evaluation of the distribution of crack propagation fatigue life by simulating the crack growth process”, “Filter technique for stochastic crack growth”).
The crack growth processes are especially discussed; they are analyzed using stochastic crack growth models, Rayleigh approximation technique, and response surface technique.
7. Monte Carlo simulations.
(“Probabilistic seismic response of a steel frame structure using Monte Carlo simulation”, “Galerkin method to analyze systems with stochastic flexural rigidity”, “Monte Carlo simulation of beams on Winkler foundation”, “Simulation of multi-variate stationary and nonstationary random processes: A recent development”, “Optimality in the estimation of a MA system from a long AR model”, “Random fields. Digital simulation and applications in structural mechanics”).
Authors set up theoretical approaches to the considered systems on the basis of nonlinear and linear seismic analyses, the Bubnov-Galerkin approximation, the direct boundary element approach, FFT simulation schemes and autoregressive modelling. Numerical examples illustrate the theoretical developments.
8. Earthquake engineering applications.
(“Stochastic estimation of orientation error in buried seismometers”, “Strains in long dams due spatially correlated random ground motions”, “Seismic reliability assessment of redundant structural systems”, “Seismic ground strain simulations for pipeline response analysis”, “Parametric study of the stochastic seismic response of simple nonlinear structures”, “Applications of stochastic-adaptive filters in earthquake engineering”, “Study of propagation and amplification of seismic waves in Caracas Valley with reference to the July 29, 1967 earthquake response”, “Seismic response of stochastic ground”, “An efficient treatment of model uncertainties for the dynamic response of structures”, “Evaluation of response statistics of moment resisting steel frames under seismic excitation”).
Some of the theoretical methods used herein are: maximum cross- correlation method, maximum coherence method, substructuring method, Markov chain description, spectral representation method, time-dependent autoregressive-moving average, stochastic adaptive filtering, Bayesian probabilistic approach. There are also presented very interesting comments on seismological information.
9. Materials.
(“On wave front propagation in random nonlinear media”, “A stochastic approach to the rheology of fibrous systems”, “Stability of composite structures with random material imperfections”).
This section deals with a new type of approach to some classes of materials that can be treated as “random media”. One way of studying these structures is modelling their evolution as a Markov diffusion process, and another is stability analysis using a Lyapunov type method.
10. Applied random vibrations.
(“Thermally forced random vibrations of thick plates”, “Random vibration of the rigid block”, “Response of non-linear trusses with spatial variability under random excitations”, “Nonlinear effects on TLP springing response and reliability”, “Disordered periodic structures”, “Response statistics of nonlinear coupled oscillator under parametric excitation”, “Random field interpolation between point by point measured properties”, “Application of dynamic response analysis in calculation of natural frequencies”).
The models and methods of analyses are: method of evolutionary power spectrum, Fokker-Planck equation describing Markovian processes (solved both in the approximation of the Gaussian closure and of the non-Gaussian closure), stochastic equivalent linearization method, first-order reliability methods, models for randomly disordered structures, and stochastic interpolation method.
11. Applied stochastic finite element analysis.
(“Stochastic eigenvalue analysis by SFEM code “SAINT” ”, “A probabilistic postbuckling analysis of composite shells”, “An efficient SFEM algorithm for nonlinear structures”, “Stochastic methods for systems with uncertain properties under plane stress/strain”).
All the papers in this section demonstrate by their results the advantages of using the new method of study called “Stochastic finite element method” (SFEM). The authors also used perturbation analysis, reliability analysis, and numerical simulation for testing the theoretical results.
12. Flow Related Applications and Chaotic Dynamics.
(“Nonlinear response and sonic fatigue of high speed aircraft”, “Necessary condition for homoclinic chaos induced by additive noise”).
The first paper presents an analytical model for nonlinear response and for solving the corresponding equations using a Galerkin method. The second one analyses the occurrence of homoclinic chaos in forced systems, additively perturbed.
Conclusions.
The papers in this book give a detailed up-to-date overview of the recently born domain of computational stochastic mechanics. This complex interdisciplinary field of research uses modern mathematical and engineering analysis tools as well as the extraordinary power of modern numerical calculus. It offers the most generous, flexible frame for the analysis of the behaviour of a wide variety of mechanical systems.
This book is very well-proportioned: it presents new theoretical approaches, new methods and models in this field as well as the concrete ways to apply them to various actual mechanical systems; it contains many experimental data examples as well as the ways to approach them theoretically.
We strongly recommend this interesting and useful book to anyone who has modern mechanics or connected domains as fields of interest.