【正文】 ed piezoelectric shells. International Journal of Solids and Structures, 2002, 39 (20): 53255344[41]Shen H. S. Thermal postbuckling behavior of functionally graded cylindrical shells with temperaturedependent properties. International Journal of Solids and Structures, 2004, 41 (7): 19611974[42]Sofiyev A. H. Dynamic buckling of functionally graded cylindrical thin shells under nonperiodic impulsive loading. ACTA Mechanica, 2003, 165 (34): 151163[43]Shen H. S. Postbuckling analysis of axially, loaded functionally graded cylindrical panels in thermal environments. International Journal of Solids and Structures, 2002, 39 (24): 59916010[44]Yang J., Kitipornchai S., Liew K. M. Nonlinear analysis of the thermoelectro mechanical behaviour of shear deformable FGM plates with piezoelectric actuators. International Journal for Numerical Methods in Engineering, 2004, 59 (12): 16051632[45]Chen W. Q., Bian Z. G., Lv C. F., Ding H. J. 3D free vibration analysis of a functionally graded piezoelectric hollow cylinder filled with pressible fluid. International Journal of Solids and Structures, 2004, 41(34): 947–964[46]Sankar . An elasticity solution for functionally graded beams. Composites Science and Technology, 2001, 61(5): 689696[47]Sankar, ., Taeng J. T. Thermal stresses in functionally graded beams. AIAA Journal, 2002, 40(6): 12281232[48]Venkataraman S., Sankar B. V. Analysis of Sandwich Beams with Functionally Graded Core, AIAA, 2001, 1: 752759[49]Venkataraman S., Sankar B. V. Elasticity solution for stresses in a sandwich beam with functionally graded core這將使我受用終身！在這里我要對指導教師表達衷心的敬意與謝意。 作者簽名： 日期： 畢業(yè)論文（設(shè)計）授權(quán)使用說明本論文（設(shè)計）作者完全了解**學院有關(guān)保留、使用畢業(yè)論文（設(shè)計）的規(guī)定，學校有權(quán)保留論文（設(shè)計）并向相關(guān)部門送交論文（設(shè)計）的電子版和紙質(zhì)版。 圖表整潔，布局合理，文字注釋必須使用工程字書寫，不準用徒手畫3）畢業(yè)論文須用A4單面打印，論文50頁以上的雙面打印4）圖表應(yīng)繪制于無格子的頁面上5）軟件工程類課題應(yīng)有程序清單，并提供電子文檔1）設(shè)計（論文）2）附件：按照任務(wù)書、開題報告、外文譯文、譯文原文（復印件）次序裝訂3）其它 第35頁 共35頁。：任務(wù)書、開題報告、外文譯文、譯文原文（復印件）。學?？梢怨颊撐模ㄔO(shè)計）的全部或部分內(nèi)容。據(jù)我所知，除文中已經(jīng)注明引用的內(nèi)容外，本論文（設(shè)計）不包含其他個人已經(jīng)發(fā)表或撰寫過的研究成果。 Journal of Applied Mechanics, ASME, 2004, 71(3): 421424[51]Shi Z. F. General solution of a density functionally gradient piezoelectric cantilever and its applications. Smart Material and Structures, 2002, 11(1): 122129[52]Shi Z. F., Chen Y. Functionally graded piezoelectric cantilever beam under load. Archive of Applied Mechanics, 2004, 74(34): 237–247附 錄由邊界條件(10),(11)及(9)的第一式,求得A=Pbk1H1h2H1(h2), B=q2k1H1h2H1(h2)C1=Pbλ330k1H0h2H0(h2) C4=q2λ330k1H0h2H0(h2)C7=ak1H1h2H0h2H1h2H0(h2),C8=qk1H0h2H0h2H1h2H1h2H1h2H0h2+ h2H1h2H0h2H1h2H0(h2)C10=Pbk1H1h2H0h2H1h2H0(h2),其中k1=H1h2H1(h2)H0h2H0(h2)+H0h2H0(h2)H1h2H1(h2)+H1h2H0h2H1h2H0(h2)h由邊界條件(12)和(13)得到C0=0, C3=0, C2=Aλ330, C5=Bλ330C6=d150λ330+d310λ110λ110G0h2G0(h2)C4T1h2T1h2+C5T0h2T0(h2)d1502λ110C7C9=d150λ330+d310λ110λ110G0h2G0(h2)C1T1h2T1(h2)+C2T0h2T0(h2)d150λ110C10,C12=d1502C4λ330T1h2+2C5λ330T0h2+C7G0(h2)2λ110C4d310T1h2+C5d310T0h2+C6G0(h2)由邊界條件(9),求得C13=A1H1h2H1(h2)A2H0h2H0(h2)Mbk0H0h2H0(h2)λ330k2,C14=A1H2h2H2(h2)+A2H1h2H1(h2)+Mbk0H1h2H1(h2)λ330k2,其中A1=a12C4λ330H11h2H11(h2)+2C5λ330H01h2H01(h2)+C8h+a22C4λ330N1h2N1(h2)+2C5λ330N0h2N0(h2)+C7G01h2G01(h2)+2a3C4d310N1h2N1(h2)+C5d310N0h2N0(h2)+C6G01h2G01(h2)+s130λ33013C4λ330H3h2H3(h2)+C5λ330H2h2H2(h2)d330λ33013C4d310H3h2H3h2+C5d310H2h2H2(h2)+C12d310H0h2H0(h2),A2=a12C4λ330H111h2H111(h2)+2C5λ330H011h2H011(h2)+C7h312+a22C4λ330N11h2N11(h2)+2C5λ330N10h2N10(h2)+C7G011h2G011h2+2a3C4d310N11h2N11(h2)+C5d310N01h2N01(h2)+C6G011h2G011(h2)+s130λ33013C4λ330H4h2H4(h2)+C5λ330H3h2H3(h2)d330λ33013C4d310H4h2H4(h2)+C5d310H3h2H3(h2)+C12d310H1h2H1(h2),k2=H1h2H1(h2)2H2h2H2(h2)H0h2H0(h2)由邊界條件(14)，求得：a=C13l+C1l22k0+C4l33k0 ，d=s330s130a1k0+d330a4k02C4λ330Y10+2C5λ330Y00+C7G10+C8G00k0(s130a2+d330a5)2C4λ330T10+2C5λ330T00+C7G0(0)+2(s130a3+d330a6)C4d310T10+C5d310T00+C6G0(0)C13l22C1l33k0C4l44k0e=l33k0C5l22k0C2+ls4402C4λ330T10+2C5λ330T00+C7G0(0)+2d150C4d310T10+C5d310T0+C6G0(0)C14+s440C1λ330T10+C2λ330T00+C10G0(0)+d150C1d310T10+C2d310T00+C9G0(0)致 謝本文在陳老師的多次指導下終于完稿，感激之情，溢于言表。所采用的方法還可用于求解其他邊界條件下的功能梯度壓電梁問題。上述這些特征在建立功能梯度壓電梁的簡化理論時可以考慮。m1 s11 s13 s33 s44 d31 d33 d15 λ11 λ33 135 300 525 下面給出了梁的一些物理量隨坐標z的變化情況，由此可見，無論是功能梯度壓電梁（α≠0）還是均質(zhì)壓電梁(α=0)，位移ω沿厚度方向幾乎不發(fā)生變化，近似為常量。h2處， Dz=0 (13) 固定端位移邊界條件：在z=0 x=l處 u=w=0, ?w?x=0 (14)引入艾利應(yīng)力函數(shù)U(x,z),滿足σx=?2U?z2 σz=?2U?x2 τzx=?2U?z?x (15)將(5)，(7)和(15)式代入電平衡方程(2)，得到d15?3U?x2?zλ11?2φ?x2+??zd31?2U?z2+??zd33?2U?x2??zλ33?φ?z=0 (16)將(4)，(7)和(15)式代入應(yīng)變協(xié)調(diào)方程(8)，得到?2?z2s11?2U?z2+s13?2U?x2+??zs44?3U?x2?z+s13?4U?x2?z2+s33?4U?x4=?2?z2d31?φ?z+d33?3φ?x2?z??z(d15?2φ?x2) (17)彎曲應(yīng)力σx主要是由彎矩產(chǎn)生的，切應(yīng)力τzx主要是由剪力產(chǎn)生的，而擠壓應(yīng)力σz主要是由荷載q產(chǎn)生的，現(xiàn)因q為常數(shù)，可以假設(shè)僅僅是y的函數(shù) 即σz=fz于是有 ?2U?x2=f(z) 而 ?U?x=xfy+f1(y) 假設(shè) U=x2fz+xf1z+f2(z)