預應力下對稱疊層圓板之非線性大撓曲分析

Nolinear Large Deflection Analysis of Symmetric Isotropic Layered Plate under Initial Tension

陳春福(Cun-Fu Chen) ； 尤靖棋(Jin-Chi Yiou)

《中國航空太空學會學刊》 37卷2期 (2005/06) Pp. 127-134

https://doi.org/10.6124/TAASRC.200506_37(2).03

摘要

本文係探討夾固式對稱疊層均向圓型板件在預拉伸及均勻面壓作用下之非線性大撓曲問題，求解方法係以馮卡門大撓曲(von-Karman Large Deflection)板理論爲基礎，並考量對稱疊層之情況。其簡化之線性問題可得一表爲修正貝索函數(Modified Bessel functions)的解析解，而非線性問題則藉由一有限差分法配合一修正之數值迭代技巧以求解。在各式面壓及預拉伸力條件下，擬單一材質板件之解發現與文獻之單層均向板件結果幾近相同，而典型疊層件之解則顯示，面壓與預拉伸力均能明顯影響板件之行爲。此外，層間模數比之影響則在低面壓及低拉伸力情況下較爲顯著。

關鍵字

預拉伸力 ； 馮卡門大撓曲理論 ； 修正貝索函數 ； 有限差分法

並列摘要

The nonlinear problem of large-deflection of a clamped and symmetrically layered isotropic circular plate due to uniform lateral loading is studied. The governing equations were developed based on von-Karman's large deflection theory including a symmetrically-layered consideration. Neglecting the arising nonlinear term, the simplified linear problem was considered first and the associated analytical solution was found to be expressible in terms of modified Bessel functions. The nonlinear problem was then solved using a finite difference method incorporating a modified numerical iteration scheme.
The results for a quasi-monolithic plate were found to correlate well with those available for a single layered isotropic plate, following the implementation for various lateral loads and pretensions. For a typical three-layered symmetric laminate, both the lateral load and pretension are found to have a significant influence upon the nonlinear structural responses of the layered plate. On the other hand, the effect due to the deviation in the layer moduli seems to be apparent only when the lateral load is moderate and when the pretension is notable.

並列關鍵字

Initial tension ； Von-Karman large deflection theory ； Modified bessel function ； Finite difference method