| Summary: | 碩士 === 中華大學 === 機械工程學系碩士班 === 98 === Problem of nonlinear large-deflection of an elastically-bossed and clamped symmetrically layered isotropic circular plate under pretension due to uniform lateral load is studied. Based on von-Karman large deflection plate theory, the thus obtained nonlinear governing equations were formulated in a non-dimensional form in terms of lateral slope and radial force resultant. The small defection condition is considered first by neglecting the arising nonlinear terms, yielding a linear differential equation for the lateral slope. The reduced linear problem of large-deflection is solved by employing the recurrence relations between Modified Bessel functions as well as the boundary conditions at the clamped end and interface continuity condition between the central boss and the annular plate. The associated linear analytical solution was found to be expressible in terms of the first and the second kind of Modified Bessel functions, rather than just the first kind for a single–layered flat plate. A finite difference method is employed incorporating an iteration scheme in solving the nonlinear problem, by taking the obtained linear solution as the initial value.
For a nearly monolithic single-layered plate with a tiny central boss under a small initial tension, the results correlate well with those available for a single-layer plate, thus the prevent approach was validated. Increasing the thickness ratio between the central boss and annular plate, the central boss will gradually illustrate a rigid behavior and has an apparent influence upon the structural responses of the entire plate. Meanwhile, the range of lateral pressure and initial tension for the existence of plate behavior will also be stretched. In other words, the onset of nonlinear behavior will be delayed to occur with increasing initial tension or lateral pressure magnitude. Moreover, the edg-zone effect of the plate tends to exasperate, as the lateral pressure and initial tension proceeds or the size and thickness of the central boss increases. On the other hand, the influence due to difference in layer moduli appears to be insignificant. The pressure sensitivity of plate increases as the central elastic boss illustrates a rigid behavior but decreases as the magnitude of initial tension is increased.
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