前屈曲耦合变形时功能梯度圆板的屈曲行为

Buckling behavior of functionally graded circular plates with pre-buckling coupled deformations

基于经典板非线性理论,给出功能梯度板临界载荷的耦合前屈曲二级线性理论.假设功能梯度材料性质只沿板厚度方向,并按成分百分比的幂指数函数形式变化.推导问题的基本理论方程,分析指出前屈曲耦合变形对功能梯度板稳定性有着不可忽略的影响并给出不同外因素作用下是否会发生屈曲现象的判断方法.研究结果表明,对于有耦合挠度的功能梯度板的失稳问题,现行求解临界力的方法可能给出完全不真实的解.原则上要按非线性或本文给出的二级理论求解,须计及耦合前屈曲及边界条件的影响.

Based on classical nonlinear plate theory, a second-order linear theory was given for the coupled pre-buckling functionally graded plates under critical loads. The material properties were assumed to vary as a power function of the content of material composition in normal direction of the plate. The governing equations were derived and it was pointed out by analysis that the pre-buckling coupled deformation had nonnegligible influences on plate stability. Thus, a method was given for identifying the occurrence of true bifurcation buckling due to different external influencing factors. The investigation result showed that cur- rent method for determining instability of a functionally graded plate with coupled deflection might give a false solution. In principle, the solution should be based on nonlinear or second-order linear theory given in this paper, taking the influence of pre-buckling coupled deformation and boundary condition into consideration.