正交层板弯曲问题的一种半解析法
A SEMI-ANALYTICAL METHOD FOR THE BENDING OF CROSS-PLY LAMINATES
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摘要: 本文提出了一个完全满足对称正交层合板弯曲基本方程的挠度级数表达式,并导出了相应的位移、变形及内力的显表达式。边界条件则用离散型最小二乘法近似满足。由于所用级数较简单且具备完备性,因而推导与计算都较简单,对于各种边界条件下的单连通板,它都能逼近其精确解。文中的例子表明,本方法往往用较少的待定系数及配点,就可获得相当好的结果。Abstract: A series expression of deflection is presented which exactly satisfies the foundation equation of bending of symmetric crass-ply laminates,and the corresponding expressions of displacements,deformations and internal forces are derived in explicit form.The simplicity of the series makes all the derivation and the expressions simple.In general cases,the boundary conditions of the laminate can not be satisfied exactly by the series presented,but they can be satisfied approximately by the use of the discrete least squares.Because the series is proved to be complete in mathematics,if the laminate only occupies simply connected region and the number of boundary collocations is large enough,the series may approximate the exact solution of bending problem of symmetric cross-ply laminates under various boundary conditions including the cases that the edges are clamped,simply supported,and/or free.For nonsymmetric cross-ply laminates with many layers,the coupling between extension and bending is after negligible and the method can be still used as an approximation.A widely applicable program implemented with the use of micro-computer IBM.PC/XT has been written and certain laminates with different layes have been calculated.
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