FINITE ELEMENT ANALYSIS OF SYSTEM STOCHASTICITY (NEUMANN, MONTE CARLO)

The first part of this dissertation deals with the response variability of an axially loaded prismatic bar which is subjected to static loads of a deterministic nature. The response variability arises from the spatial randomness of the elastic modulus of the bar. The problem is analyzed using the finite element method along with a Neumann expansion of the stillness matrix in order to obtain an analytic expression for the covariance matrix of the response displacement vector. The finite element size necessary to obtain sufficiently accurate values of the stochastic response parameters is examined thoroughly.; The second part deals with the stochastic finite element analysis of a wave propagation problem, consisting of a statically determinate rod having an elastic modulus varying randomly along its length and loaded with a deterministic dynamic axial load. Monte Carlo simulation techniques are used in order to analyze the system. This part has two purposes: first to find the statistical distribution functions the response quantities of the system will follow and second to examine how the input parameters of the problem affect the response variability of the system.; The third part deals with the stochastic finite element analysis of a nonlinear structural dynamic problem, consisting of a linearly elastic beam lying on a nonlinear foundation and loaded with a deterministic transverse dynamic load. The beam can be simply-supported or fixed at both ends. Monte Carlo simulation techniques are used in order to analyze the system. This part has the same two purposes as the second one.; Finally, the fourth part deals with the stochastic finite element analysis of nonlinear structural dynamic problems, consisting of a linearly elastic plate lying on a nonlinear foundation and loaded with a deterministic uniform transverse dynamic load. The plate can be simply-supported or fixed all-around. The stochasticity of the problem arises from the spatial randomness of the elastic modulus of the plate and/or from the spatial randomness of a coefficient controlling the degree of nonlinearity of the foundation. Monte Carlo simulation techniques are used in order to analyze the system. This part has again the same two purposes as the second and third ones. (Abstract shortened with permission of author.)...