受分布载荷复合材料层合板应力分析的一般理论
GENERAL THEORY ON STRESS ANALYSIS OF LAMINATED COMPOSITE PLATE PRESSED BY DISTRIBUTED LOADING
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摘要: 为了克服经典层合板理论的缺点,提高层间应力的计算精度,提出了受分布载荷层合板应力分析的一般理论。首先根据叠加原理将层合板受力状态分解成对称和反对称状态,然后用正交完备的傅立叶级数和勒让德级数构造这两种受力状态中每一铺层与层间胶层的位移场,并应用广义势能原理确定位移场中的待定系数,从而确定层合板的位移场和应力场。另外,胶层被视为各向同性材料,并且与其它材料层具有相似的力学特性,即具有有限厚度、有限弹性常数。计算结果显示,这种解法的收敛性非常好,根据物理方程与根据平衡方程得到的层合板横向剪应力及横向正应力分布非常一致。Abstract: A general theory on stress analysis of laminated composite plate pressed by distributed loading is presented for overcoming the defect of classical plate theory and improving the precision of interfacial stress analysis. By means of the principle of superposition, the loading state of the composite laminated plate is decomposed into symmetric anti-symmetric states. The Fourier series and Legendre series are applied to describe the displacement field of each composite ply and glue layer in the above states. The principle of generalized potential energy is used to determine the unknown coefficients of the above series. In addition, the glue layers are considered to have finite thickness and finite elastic constants in this analysis. From the computational results, it can be shown that the displacements and stresses converge very well, and the distributions of transversal shearing and normal stresses obtained from the constitutive equation agree with those obtained from the equilibrium equation very well.