On the Refined First-Order Shear Deformation Plate Theory of Kûrmûn Type
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摘要: 依据Mindlin-Reissner理论,着重研究一阶剪切板的Kûrmûn型精化理论,并推导出仅以挠度和应力函数为未知变量的广义Kûrmûn型大挠度方程,适用于复合材料上复合构造剪切板的非线性分析.在当前板的精化理论中,消去的两个转角以隐含形式作用于板的整体变形.这一工程理论适用于各种计及横向剪切复合材料板、正交各向异性中厚板和夹层板等的线性和非线性分析.容易发现,针对具体的工程应用,由该方程可直接获得相应的退化形式,并且与文献所载的一致.Abstract: A new refined first-order shear-deformation plate theory of the Karman type is presented for engineering applications and a new version of the generalized Karman large deflection equations with deflection and stress functions as two unknown variables is formulated for nonlinear analysis of shear-deformable plates of composite material and construction, based on the Mindlin/Reissner theory. In this refined plate theory two rotations that are constrained out in the formulation are imposed upon overall displacements of the plates in an implicit role. Linear and nonlinear investigations may be made by the engineering theory to a class of shear-deformation plates such as moderately thick composite plates, orthotropic sandwich plates, densely stiffened plates, and laminated shear-deformable plates. Reduced forms of the generalized Karman equations are derived consequently, which are found identical to those existing in the literature.
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Key words:
- composite /
- shear deformation plates /
- Kûrmûn equations
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[1] Zhang J W.A simplified perturbation solution to the large deflection Karman equations of orthotropic composite plates in axial compression and lateral pressure[J].Ingenieur-Archiv(Arch Appl Mech),199 1,61(3):174~182. [2] Zhang J W,Shen H S.Postbuckling of orthotropic rectangular plates in biaxial compression[J].ASCE J Engng Mech,1991,117(5):1158~1170. [3] 张建武.复合构造剪切板的屈曲与后屈曲性态研究[J].力学学报,1994,26(2):176~182. [4] 张建武,林忠钦.复合材料剪切板的后屈曲及其Karman型精化理论[J].上海交通大学学报,1994,28(4):115~120. [5] 沈惠申.中厚板的弹性屈曲和后屈曲[J].应用数学和力学,1990,11(4):341~350. [6] Reissner E.On the theory of bending of elastic plates[J].J M ath Phys,1944,23:184~191. [7] Mindlin R D.Influence of rotatory inertia and shear on fluctuat motions of isotropic elastic plates[J].ASME J Appl Mech,1951,18:31~38. [8] Reddy J N.A simple higher-order theory for laminated composite plates[J].J Appl Mech,1984,51:745~752. [9] Reddy J N,Phan N D.Stability and vibration of isotropic,orthotropic and laminated plates according to a higher-order shear deformation theory[J].J Sound Vibration,1985,98:157~170. [10] Kyoung Woo-Min,Kim Chun-Gon.Delamination buckling and growth of composite laminated plates with transverse shear deformation[J].Journal of Compostie Materials,1995,29(15):2047~2068. [11] Bogdanovich A E,Deepak B P.Three-dimensional analysis of thick composite plates with multiple layers[J].Composites Part B,Engineering,1997,28B(4):345~357. [12] Alwan A M.Large deflection of sandwich plates with orthotropic core[J].AIAA J,1964,2(2):1820~1822.
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