Stochastic Field Theory in Materials Engineering

Abstract

This paper consists of three chapters. The first one deals with the problem of simulating a stochastic process or field using the spectral representation method. The stochastic process or field is simulated according to its prescribed power spectrum. The simulation is performed very efficiently using the Fast Fourier Transform technique. In the second chapter, a probabilistic model for the spatial variation of the strength of materials used for laminated orthotropic composites is introduced. The principal idea lies in the interpretation that the material strength can be idealized as a two-dimensional stochastic field. Under such an assumption, the strength of laminated orthotropic composite plates in uniaxial tension is found to follow a Weibull distribution function. Another conclusion is the demonstration of the statistical size effect. Finally, in the third chapter, a methodology is introduced to perform both the response variability and reliability analysis of plates subjected to plane stress or plane strain. A stochastic finite element approach based on the concept of weighted integrals is utilized. The variability response function of the system is established in closed form. Then, the response variability is calculated by a first-order Taylor expansion, while the safety index is computed using an advanced first-order second-moment approach.