摘要
基于von Karman薄板理论建立了有间隙约束的弹性圆(环)板在径向压力作用下的轴对称过屈曲控制方程,这是一组以中面位移为基本未知量,以径向压力为参数的非线性常微分方程组.假设间隙约束位于圆板圆心处两侧且间隙值在圆板的过屈曲变形范围内,采用打靶法数值求解相应的非线性两点边值问题,获得了周边夹紧和简支圆板被约束前后的过屈曲响应.着重分析了圆板的最大挠度达到给定间隙值,受到间隙约束后的过屈曲变形和内力的变化特性,给出了有关的平衡构型和平衡路径.当板与刚性约束接触后,在板中心两侧出现了新的挠度极大值点,约束反力随着径向压力单调增加.在内周边处,接触前径向薄膜力和弯矩的代数值单调增加;接触后径向薄膜力先单调减小后增加,而弯矩一直单调减小.周边夹紧圆板在外周边处的弯矩代数值在接触前后均单调减小.
Based on von Karman＇s thin plate theory, the governing equations in terms of the displacements of the middle plane were formulated for elastic circular/annular plates under radial compression when they were constrained by space-fixed constraints in the center, which consisted of ordinary differential equations including parameter of radial compression. Using the shooting meth- od, the corresponding two-point boundary value problem for nonlinear ordinary differential equations were solved numerically and the buckling and post-buckling responses for the circular plate with simply supported and clamped edges were obtained. Characteristics of post-buckling deformation and the internal forces of the circular plate were analyzed emphatically after its largest deflection reached the fixed space and then the constraint force increased. The corresponding equilibrium paths and configurations were presented. After the plate contacted the rigid constraint, new deflection maximum points arose at two sides of the plate center. The constraining force increased monotonically with the increase of radial compression. At the inner edge, the radial force and the moment increased monotonically before contact. After contact the radial force first decreased and then increased monotonically whereas the moment decreased all the time. The moment at the outer edge of the clamped plate decreased monotonically in the process of the post-buckling.
出处
《扬州大学学报（自然科学版）》
CAS
北大核心
2013年第4期74-78,共5页
Journal of Yangzhou University：Natural Science Edition
基金
国家自然科学基金资助项目(11272278)
扬州大学科技创新培育基金(2012CXJ036)
关键词
圆(环)板
间隙约束
打靶法
过屈曲
circular/annular plate
space-constraint
shooting method
post-buckling
