耦合各向异性蠕变损伤的黏弹性薄板的弯曲

Creep Deformation of Viscoelastic Plates Coupling Anisotropic Damage

设损伤张量的主方向与应力张量主方向相同,基于Schapery的耦合损伤增长的对应原理,得到考虑各向异性蠕变损伤的黏弹性本构关系.将薄壁结构沿厚度方向分层,建立层合模型,且由Kachanov的损伤演化方程描述损伤沿层中各点处2个主方向的发展.具体分析了承受均布荷载的四边简支黏弹性薄板的弯曲,给出耦合各向异性损伤黏弹性薄板蠕变弯曲问题的控制方程、边界条件以及求解方法.数值算例表明:黏弹性薄板弯曲时的材料主方向与时间基本无关;当荷载在一定范围内时由于内力的重新分布,考虑损伤后的黏弹性薄板挠度最后趋于稳态值;损伤沿厚度方向的非均匀演化引起拉弯耦合效应增加了板的变形;基于各向同性损伤模型所得板的蠕变变形大于各向异性损伤模型所给出的值.

Assuming the coincidence of principal directions of stresses tensor with that of damage tensor, the hereditary constitutive equation coupling anisotropic damage was constructed based on Schapery＇ s correspondence principle with damage growth. The thin wall structure was modeled as the lamination of finite laminas along the thickness of structure, and Kachnov＇s evolution kinetics was adopted to describe the progress of dam- age in two principal directions at any point of the laminas. The creep analysis of viscoelastic rectangular thin plates subjected to uniform transverse pressure and hinged at edges was conducted. Resulting nonlinear govern- ing equations and boundary conditions expressed in the form of deflection and in-plane displacements of plate were discretized in space domain by means of finite difference technique, and associated convolute integrations were obtained at discretized points by numerical integration, and finally, the iterative calculation of nonlinearly algebraic equations led to the numerical solution at each time step. Results have shown that the principal direc- tions of stress and damage tensor can be considered time-independent during creep deformation of plates, and the deflection approaches an asymptotic value due to the redistribution of stress when the pressures on plates lie in some extent, the coupling of tension-bending, which arises from the evolution of damage along thickness, increases the creep deflection and this effect becomes more remarkable if the loads get larger. Also, the isotropic damage model gives larger deformation than anisotropic damage model does.