弱粘结的斜交铺设层合圆柱壳的柱形弯曲

导出了两端简文的具有弱粘结界面的任意斜交铺设层合圆柱壳柱形弯曲问题的一个精确弹性理论解。分析中采用线性弹簧模型来表征界面的弱粘结特性。引进新的物理量改写了基本方程,导出了对应的状态空间列式,并利用变量替换技术将该状态方程转换成常系数状态方程,从而方便求解。最后给出了数值算例,并讨论了弱界面的影响。

An exact solution of angle-ply laminated cylindrical panels in cylindrical bending with imperfect interfaces

An exact elasticity analysis is presented for the cylindrical bending problem of simply-supported angle-ply laminated cylindrical panels featuring interlaminar bonding imperfections.A linear spring-layer model is adopted to describe the interfacial imperfections.New physical variables are introduced to rewrite the basic equations,and the corresponding state-space formulations are established.A variable substitution technique is then employed to transfer the state equation into the one with constant variables,of which the solution can be obtained exactly.It is shown that the effect of weak interfaces can be easily taken into consideration by integrating the so-called interfacial transfer matrix into the global transfer matrix. Numerical comparison is firstly made with other exact solution in literature for perfect angle-ply laminated cylindrical panels and good agreement is obtained,thus validating the correctness of the algebra as well as program of the present method.For an imperfect cross-ply laminated cylindrical panel,results are then compared with those obtained by an extended zig-zag shell theory.It is shown that when the compliance constants of weak interfaces increase,the shell theory becomes more and more inaccurate.Thus,for a laminated shell structure with bonding imperfections,the applicability of various two-dimensional approximate theories as well as numerical methods should be carefully clarified.The results of an unsymmetric five-layered cylindrical panel further show that the presence of weak interfaces generally reduces the transverse shear stress level at the interfaces; but for some particular values of compliance constants,the transverse shear stresses may increase at certain perfect interfaces.This will lead to a dangerous situation because high transverse shear stress is generally one of the most important causes of the interlaminar shear failure.Thus,the effect of weak interfaces should be precisely evaluated for practical laminated structures.