本文選題：板 + 初始荷載效應　； 參考：《重慶大學》2014年博士論文

【摘要】：隨著結(jié)構(gòu)設計理念和經(jīng)濟化的發(fā)展，在保證結(jié)構(gòu)安全的前提條件下，板朝輕型、高強和更薄的方向發(fā)展是今后的趨勢；而隨著板厚度的進一步減小，初始荷載效應對板的力學性能的影響則更為突出。本文采用理論分析與數(shù)值模擬相結(jié)合的方法，就初始荷載效應（包括初始豎向荷載效應和初始中面荷載效應）對板的靜、動力性能和穩(wěn)定性的非線性影響進行了較為系統(tǒng)的研究。本文取得主要研究成果如下： ①推導了考慮初始豎向荷載效應、同時考慮初始豎向荷載效應和初始中面荷載效應情況下板的靜、動力平衡微分方程；針對軸對稱情形圓形板，采用坐標變換方法，得到了圓形板考慮初始豎向荷載效應、同時考慮初始豎向荷載效應和初始中面荷載效應情況下的極坐標形式的靜、動力平衡微分方程。 ②推導了考慮初始豎向荷載效應、同時考慮初始豎向荷載效應和初始中面荷載效應情況下板的靜、動力有限元公式；提出了考慮初始豎向荷載效應的等參板單元、同時考慮初始豎向荷載效應和初始中面荷載效應的矩形板單元和等參板單元，運用MATLAB編制了相應的有限元程序；分析了初始荷載效應及相關(guān)因素對板的靜、動力性能的非線性影響。 ③解得了不同形狀板考慮初始豎向荷載效應、同時考慮初始豎向荷載效應和初始中面荷載效應的后期豎向荷載位移、基頻近似解；解得了簡支矩形板考慮初始豎向荷載效應、同時考慮初始豎向荷載效應和初始中面荷載效應的前三階頻率近似解； ④推導了考慮初始豎向荷載效應情況下板的穩(wěn)定平衡微分方程和有限元公式；解得了三種板考慮初始豎向荷載效應的屈曲臨界荷載系數(shù)近似解；分析了初始豎向荷載及相關(guān)因素對板穩(wěn)定性的影響。 ⑤板的初始荷載效應主要受初始荷載、幾何尺寸、厚度及邊界條件的影響；一般情況下，初始荷載越大、板的剛度越低、厚度越小、邊界條件約束越弱，則初始荷載效應對板的靜動力性能和穩(wěn)定性的非線性影響越明顯。
[Abstract]:With the concept of structural design and economic development, the development of light, high strength and thinner direction is the trend in the future under the premise of ensuring structural safety. With the further reduction of plate thickness, the effect of initial load effect on the mechanical properties of the plate is more sudden. This paper combines theoretical analysis with numerical simulation. In this paper, the nonlinear effects of initial load effect (including initial vertical load effect and initial middle surface load effect) on the static, dynamic and stability of the plate are studied systematically. The main research results are as follows:
The initial vertical load effect, considering the initial vertical load effect and the initial middle surface load effect, is derived. The dynamic equilibrium differential equation of the plate is considered. The circular plate is taken into consideration of the initial vertical loading effect, considering the initial vertical load effect and the initial vertical load effect. The static and dynamic equilibrium differential equations in polar coordinates under the load effect of the middle surface.
Secondly, the static and dynamic finite element formulas considering the initial vertical load effect and the initial vertical load effect and the initial middle surface load effect are derived. The isoparametric plate element, considering the initial vertical load effect, and the rectangular plate element and the isoparametric element which consider the initial vertical load effect and the initial middle surface load effect are proposed. The corresponding finite element program is compiled by MATLAB, and the nonlinear influence of initial load effect and related factors on static and dynamic performance of plate is analyzed.
Thirdly, the initial vertical load effect is considered in different shape plates, and the initial vertical load effect and the initial vertical load effect of the initial middle surface load effect are considered, and the basic frequency approximate solution is taken into consideration. The initial vertical load effect is considered by the simple supported rectangular plate, and the first three orders of the initial vertical load effect and the initial middle surface load effect are considered. Frequency approximate solution;
(4) the stable equilibrium differential equation and finite element formula of the plate under the consideration of the initial vertical load effect are derived. The approximate solution of the critical buckling load coefficient of the three kinds of plates is solved with the initial vertical load effect, and the influence of the initial vertical load and the related factors on the stability of the plate is analyzed.
The initial load effect of the plate is mainly influenced by initial load, geometric size, thickness and boundary condition. In general, the larger the initial load is, the lower the stiffness of the plate, the smaller the thickness, the weaker the boundary conditions, the more obvious the nonlinear effect of the initial load effect on the static and dynamic properties and stability of the plate.
【學位授予單位】：重慶大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：TU31

【參考文獻】

相關(guān)期刊論文 前10條

1 張濤,劉土光,趙耀,王先洲;初始缺陷加筋板的屈曲與后屈曲分析[J];船舶力學;2003年01期

2 周世軍;張家瑋;;恒載效應對拱形梁的影響分析[J];工程力學;2010年07期

3 杜國君,田雨寶;均布載荷作用下夾層圓板的載荷—頻率特征關(guān)系[J];工程力學;1997年02期

4 鄭小榮,丁雪興,何世權(quán);柔韌扁錐殼在靜載荷下的非線性振動[J];甘肅科學學報;2002年03期

5 張家瑋;;恒載效應對梁變形影響的數(shù)值分析法[J];甘肅科學學報;2009年01期

6 朱達善，錢勤，黃玉盈，朱詩頌;有初內(nèi)力的板的內(nèi)共振[J];固體力學學報;1995年02期

7 吳存利;段世慧;李新祥;;復合材料波紋板剪切載荷作用下的屈曲試驗與分析[J];航空學報;2011年08期

8 梁樞平,劉洋,楊永波,鄭文衡;梁的軸力非線性靜力問題的進一步研究[J];華中科技大學學報(自然科學版);2005年02期

9 張家瑋;周世軍;趙建昌;;考慮恒載效應的拱形梁靜力近似解[J];計算力學學報;2010年04期

10 王元清,石永久,陳宏,張勇,李少甫;現(xiàn)代輕鋼結(jié)構(gòu)建筑及其在我國的應用[J];建筑結(jié)構(gòu)學報;2002年01期

相關(guān)博士學位論文 前2條

1 劉世安;輕型薄板擋土墻振動模態(tài)理論與應用研究[D];重慶大學;2009年

2 張家瑋;初始荷載對梁力學性能非線性影響的研究[D];蘭州交通大學;2010年

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