Abstract
A wavelet-based model for stochastic analysis of beam structures is presented. In this model, the random processes representing the stochastic material and geometric properties are treated as stationary Gaussian processes with specified mean and correlation functions. Using the Karhunen-Loeve expansion, the process is represented as a linear sum of orthonormal eigenfunctions with uncorrelated random coefficients. The correlation and the eigenfunctions are approximated as truncated linear sums of compactly supported orthogonal wavelets, and the integral eigenvalue problem is converted to a finite dimensional eigenvalue problem. The energy-principle-based finite element approach is used to obtain the equilibrium and boundary conditions. Neumann expansion of the stiffness matrix is used to write the nodal displacement vector in terms of random coefficients. The expectation operator is applied to the nodal displacements and their squares to obtain the mean and standard deviation of the displacements. Studies show that the results obtained using this method compare well with Monte Carlo and semianalytical techniques.
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