黏弹性层合圆柱壳的临界轴压分析

基于经典屈曲理论，研究了轴向受压黏弹性复合材料层合圆柱壳的临界屈曲载荷.利用Boltzmann线性积分型本构关系描述铺设单层的各向异性黏弹性行为. 结合解析与数值方法，由Donnell型屈曲控制方程以及边界条件的Laplace变换导出相空间的特征方程，根据Laplace逆变换的极值定理，获得层合圆柱壳的瞬时弹性临界载荷与持久临界载荷. 针对多组铺设方式，通过数值算例重点分析了临界载荷随铺设角的变化特征，两种临界载荷的峰值点差异程度与铺设方式、几何参数以及材料类型的关系，得到了一些对黏弹性层合圆柱壳的优化设计有参考价值的结论.

ANALYSIS OF CRITICAL AXIALLY COPMRESSIVE LOADS FOR VISCOELASTIC LAMINATED CIRCULAR CYLINDRICAL SHELLS

The critical buckling loads of viscoelastic laminatedcircular cylindrical shells under axial compression are investigated withinthe theory of classic buckling. Boltzmann hereditary linear constitutiverelationship is used to model the viscoelastic behavior of lamina. Bothgoverning equations of Donnell type and boundary conditions in phase domainare obtained by Laplace transformation. The deflections and in-plane forcefunctions are expressed in series form of separate variables with circumferentialpart in trigonometric functions. The generalized eigenvalue problemin phase domain of determining the critical axial load is studied by means ofthe differential scheme with respect to the axial coordinate. Applying thetheorems of asymptotic value and initial value for Laplace inversetransformation, we obtain, respectively, the formulation of transientelastic critical loads and durable critical loads. The focus of thispaper is on the investigation of these criticed loads. Boron fibre/epoxy andgraphite fibre/epoxy materials are used in the analysis. Numericalresults indicate that, in the cases of both symmetrical and antisymmetricalply-up configuration, transient elastic critical loads and durablecriticalloads see similar trends of variation with ply angle and reach theirmaximum values at a respective ply angle of little difference regardless ofboundary conditions at two ends. It may be observed, however, that the plyangles corresponding to the peak values of these two types of critical loaddiffer by $5^{circ} sim 10^{circ}$ in the arbitrary ply-up mode and thisdifference is dependent on the stacking sequence, the geometric parametersand the type of material as well. The conclusions drawn in the paper canexpect to be applicable to the optimal design of laminated circularcylindrical shells concerning the capability in delayedbuckling.