WAVELET-BASED MODEL FOR STOCHASTIC-ANALYSIS OF BEAM STRUCTURES

A wavelet-based model for stochastic analysis of beam structures is pr esented. In this model, the random processes representing the stochast ic material and geometric properties are treated as stationary Gaussia n processes with specified mean and correlation functions. Using the K arhunen-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 line ar sums of compactly supported orthogonal wavelets, and the integral e igenvalue problem is converted to a finite dimensional eigenvalue prob lem. The energy-principle-based finite element approach is used to obt ain the equilibrium and boundary conditions, Neumann expansion of the stiffness matrix is used to write the nodal displacement vector in ter ms 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 te chniques.