Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
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It has been found that the probability density function (PDF) of lift-off or initial speeds of wind-blown sand ejecting from a sand bed plays a central role in the research of mechanism of wind-blown sands. This article presents an approach for developing the PDF of lift-off speeds on the basis of the conventional experimental measurements of sand-flux and wind profile. After the measurements of sand-flux and wind profile in the saltation layer are conducted in a field wind tunnel, an optimization algorithm based on the experimental data is proposed by means of the multi-objective optimization and the simulation model of the quantities of saltation motion to numerically search for the PDF. Then the obtained numerical results are fitted by means of the least square method, and finally an empirical formula of the PDF is gained for the sample sand in the experiments. rived based on power series expansions of displacement components and the exact dynamic element stiffness matrix is determined using force-deformation relationships. In order to verify the accuracy of this study, the numerical solutions are presented and compared with the analytical solutions and the finite element solutions using the isoparametric beam elements. Particularly the influences of the coupled shear deformation on the vibrational behavior of non-symmetric beam on elastic foundation are investigated.