基于Reddy简化高阶剪切理论的复合材料对称角铺设矩形板横向弯曲一般解析解

采用复数级数法求解基于Reddy简化高阶剪切理论的复合材料对称角铺设矩形板横向弯曲问题。将待定位移函数展开为复数级数,代入该弯曲问题控制偏微分方程组,确定特征根和挠度待定常数与其他位移函数待定常数之间关系式。首次给出了该弯曲问题实数形式的一般解析解。将该一般解析解代入矩形板弯曲边界条件和角点条件,根据正弦级数的正交性建立关于挠度函数待定常数的线性代数方程组,求解此线性代数方程组可确定挠度函数待定常数。建立了该问题解析求解模式。将Reddy高阶剪切理论解析解与经典理论、一阶剪切理论解析解进行对比计算,验证了一般解析解,并给出数值算例。

General Analytical Solutions for Transverse Bending Problem of Symmetrical Angle-ply Laminated Rectangular Plate Based on Reddy Simplified High Order Shear Deformation Theory

The complex series method (CSM) is applied to slove the transverse bending problem of symmetrical angle-ply laminated rectangular plate based on Reddy simplified high order shear deformation theory. The underdetermined displacement functions can be expanded into the complex series and these complex series are substituted into the system of partial differential equation which governs this bending problem.The characteristic root and the relationship between the undersolved coefficients of deflection and those of other displacements can be determined. The general analytical solution in real form for this problem is presented for the first time. The general analytical solution can be substituted into the boundary conditions and the corner conditions in the rectangular laminates in transverse bending .The system of linear algebraic equations for the undersolved coefficients of deflection is conducted by the orthogonality of sine series and the undersolved coefficients of deflection can be determined by solving this system of linear algebraic equations.The analytical method for this bending problem is conducted .The computations using the general analytical solutions of this bending problem based on Reddy simplified high order shear deformation theory are carried out to compare between those of classical laminated plate theory and the first-order shear deformation theory.The general analytical solutions based on Reddy simplified high order shear deformation theory are tested and verified. Some numerical results are presented.