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hermal buckling of functionally graded circular plates based on higher order shear deformation plate theory. European Journal of Mechanics ASolids, 2004, 23 (6): 10851100[29]Najafizadeh M. M., Heydari H. R. An exact solution for buckling of functionally graded circular plates based on higher order shear deformation plate theory under uniform radial pression. International Journal of Mechanical Sciences, 2008, 50(3): 603612[30]Shen HuiShen. Postbuckling of FGM plates with piezoelectric actuators under thermoelectromechanical loadings. International Journal of Solids and Structures, 2005, 42(23): 61016121[31]Shen HuiShen. Thermal postbuckling behavior of shear deformable FGM plate with temperaturedependent properties. International Journal of Mechanical Sciences, 2007, 49(4): 466478[32]Shen HuiShen. Nonlinear thermal bending response of FGM plates due to heat conduction. Composites Part B: Engineering, 2007, 38(2): 201215[33]Shen HuiShen, Li ShiRong. Postbuckling of sandwish plates with FGM face sheets and temperaturedependent properties. Composites Part B: Engineering, 2007, 39(2): 332344[34]Woo J., Meguid S. A. Nonlinear analysis of functionally graded plates and shallow shells. International Journal of Solids and Structures, 2001, 38 (4243): 74097421[35]Woo J., Meguid S. A. Thermomechanical postbuckling analysis of moderately thick functionally graded plates and shallow shells. International Journal of Mechanical Sciences, 2005, 47(8): 11471171[36]Yang J., Kitipornchai S., Liew K. M. Large amplitude vibration of thermoelectromechanically stressed FGM laminated plates. Computer Methods in Applied Mechanics and Engineering, 2003, 192(3536): 38613885[37]Qian L. F., Batra R. C., Chen L. M. Static and dynamic deformations of thick functionally graded elastic plates by using higherorder shear and normal deformable plate theory and meshless local PetrovGalerkin method. Composites Part B: Engineering, 2004, 35(68): 685697[38]Loy C. T., Lam K. Y, Reddy J. N. Vibration of functionally graded cylindrical shells. International Journal of Mechanical Sciences , 1999, 41 (3): 309324[39]Ng T. Y., Lam K. Y., Liew K. M., et al. Dynamic stability analysis of functionally graded cylindrical shells under periodic axial loading. International Journal of Solids and Structures , 2001, 38 (8): 12951309[40]Wu X. H., Chen C. Q., Shen Y. P., et al. A high order theory for functionally graded 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。假設(shè)所有電彈性材料常數(shù)沿厚度方向按同一函數(shù)規(guī)律變化,獲得了功能梯度壓電梁在上表面受均布壓力、自由端受集中力及集中力矩聯(lián)合作用問題的力電耦合場。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。對于功能梯度壓電梁(α≠0),σx厚度方向呈非線性變化,而位移u沿厚度方向保持為線性分布,但在z=0處,當(dāng)α≠0時,位移μ并不為零。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(biāo)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。N1 壓電常數(shù)/1012Ch2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) (18) φ=x2f3z+xf4z+f5(z) (19)引入如下符號 Hiz=0zzidzF(z)