Nonlinear Random Response of Large-Scale Sparse Finite Element Plate Bending Problems
Acoustic fatigue is one of the major design considerations for skin panels exposed to high levels of random pressure at subsonic/supersonic/hypersonic speeds. The nonlinear large deflection random response of the single-bay panels aerospace structures subjected to random excitations at various sound pressure levels (SPLs) is investigated. The nonlinear responses of plate analyses are limited to determine the root-mean-square displacement under uniformly distributed pressure random loads.
... nt computational technologies like sparse storage schemes and parallel computation are proposed and incorporated to solve large-scale, nonlinear large deflection random vibration problems for both types of loading cases: 1) synchronized in time and 2) unsynchronized and statistically uncorrelated in time. For the first time, large scale plate bending problems subjected to unsynchronized load are solved using parallel computing capabilities to account for computational burden due to the simulation of the unsynchronized random pressure fluctuations. The main focus of the research work is placed upon computational issues involved in the nonlinear modal methodologies. A nonlinear FEM method in time domain is incorporated with the Monte Carlo simulation and sparse computational technologies, including the efficient sparse Subspace Eigen-solutions are presented and applied to accurately determine the random response with a refined, large finite element mesh for the first time. Sparse equation solver and sparse matrix operations embedded inside the subspace Eigen-solution algorithms are also exploited. The approach uses the von-Karman nonlinear strain-displacement relations and the classical plate theory. In the proposed methodologies, the solution for a small number (say less than 100) of lowest linear, sparse Eigen-pairs need to be solved for only once, in order to transform nonlinear large displacements from the conventional structural degree-of-freedom (dof) into the modal dof. Moreover, the linear and nonlinear matrices are stored using sparse storage schemes in order to save computational time and memory. In case of unsynchronized load case, the time history needs to be generated and also rescaled separately for each finite element. For problems with large mesh size, the numbers of elements are high and the generation of time histories makes the problem unsolvable (in terms of computational time and/or memory requirements) for all practical purposes. By implementing parallel processing techniques, large scale structural analysis problems are solved without resorting to the use of expensive computing equipment or incurring an inordinately high computational cost that leads to a feasible solution. The reduced and coupled nonlinear equations in modal dof are inexpensively solved by the familiar Runge Kutta numerical integration scheme. Accurate responses are ensured with modal convergence, mesh convergence, and time step studies. The obtained numerical results (for synchronized load case) have also been compared favorably with results obtained from commercialized F.E. code such as Abaqus. Small, medium and large-scale single bay panel models are used to validate and evaluate the numerical performance of the present formulation and its associated computer software. Ill ACKNOWLEDGMENTS I would like to express gratitude and appreciation to my advisor Dr. Due T. Nguyen for his invaluable guidance, encouragement and advice throughout the entire course of this study. I also want