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首页> 外文会议>2014 9th International Microsystems, Packaging, Assembly and Circuits Technology Conference: Challenges of Change - Shaping the Future, 16th International Conference on Electronic Materials and packaging >Linear analytical study of large deflection of simply supported and elastically-bossed plate under pretension
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Linear analytical study of large deflection of simply supported and elastically-bossed plate under pretension

机译：预应力作用下简支弹性凸板大挠度的线性分析研究

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摘要

A simplified linear problem of large deflection of a pre-tensioned and elastically bossed plate due to lateral load is studied. von Karman's plate theory of large deflection is employed and extended to a simply supported and symmetrically-layered case with an elastic boss. The governing equations reduce to a modified Bessel equation for the lateral slope, by neglecting the arising nonlinear terms. The analytical solutions were developed by imposing the end support condition and the interface continuity, leading to modified Bessel functions of both the first and the second kinds, in contrast to only the first kind for a flat plate. The recurrence relations of the modified Bessel functions were then employed to derive the lateral deflection and curvature. The central deflection of the bossed plate is further evaluated to study the transition behavior. The approach was implemented with typical silicon-based materials commonly used for a sensing device, for various radial sizes and thicknesses of the center boss and a wide range of pretension, as a parametric study. For a monolithic plate with a narrow and shallow boss under a slight pretension, the solutions agree well with those of classical plate approach under free pretension, thus the presented approach is validated. For typically bossed plates, no edge effect arises around the support end and the geometrical responses show that, the plate mode in low pretension may shift to a membrane mode in a comparatively high pretension. Compared to the available clamped-ended problem, the present study reveals a relatively lower pretension for the plate to change to a membrane mode. The center boss geometry shows an apparent influence upon the structural responses but is limited to a low pretension regime. In this case, a bigger radial size for the center boss may slightly extend the magnitude of pretension for the bossed plate to retain a plate behavior. For a pretension beyond a moderate threshold magnitude, the responses- tend to be unified, implying that the pretension effect dominates those of the center boss.
机译：研究了简化的线性问题，该问题是由于侧向载荷而导致的预张紧且弹性凸台的大挠度。冯·卡曼（von Karman）的大挠度板理论被采用，并扩展到具有弹性凸台的简单支撑且对称分层的表壳。通过忽略出现的非线性项，控制方程简化为横向斜率的修正贝塞尔方程。通过施加端部支撑条件和界面连续性来开发分析解决方案，从而导致第一和第二种类型的Bessel功能都得到了修改，与之相比，第一种和第二种是针对平板的。然后，使用修改后的Bessel函数的递归关系得出侧向挠度和曲率。进一步评估了凸台板的中心挠度，以研究过渡行为。作为一种参数研究，该方法是使用通常用于传感设备的典型硅基材料来实现的，该材料具有各种径向尺寸，中心凸台的厚度以及广泛的预应力。对于在预紧力作用下具有窄而浅的凸台的整体板，其解决方案与在自由预紧力下的经典板方法非常吻合，因此可以验证所提出的方法。对于典型的凸台板，在支撑端周围不会出现边缘效应，并且几何响应表明，低预应力下的板模式可能会转变为较高预应力下的膜模式。与可用的夹紧端问题相比，本研究表明板改变成膜模式的相对较低的预紧力。中心凸台的几何形状显示出对结构响应的明显影响，但仅限于低预应力状态。在这种情况下，中心凸台的较大径向尺寸可能会略微扩大凸台板的预张力大小，以保持板的性能。对于超过适中阈值幅度的预应力，响应趋于统一，这意味着预应力效应主导中心凸台的响应。

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