摘要
研究了上下表面粘贴压电层的功能梯度材料Timoshenko梁在升温及电场作用下的过屈曲行为。在精确考虑轴线伸长和一阶横向剪切变形的基础上,建立了压电功能梯度Timoshenko层合梁在热-电-机械载荷作用下的几何非线性控制方程。其中,假设功能梯度的材料性质沿厚度方向按照幂函数连续变化,压电层为各向同性均匀材料。采用打靶法数值求解所得强非线性边值问题,获得了在均匀电场和横向非均匀升温场内两端固定Timoshenko梁的静态非线性屈曲和过屈曲数值解。并给出了梁的变形随热、电载荷及材料梯度参数变化的特性曲线。结果表明,通过施加电压在压电层产生拉应力可以有效地提高梁的热屈曲临界载荷,延缓热过屈曲发生。由于材料在横向的非均匀性,即使在均匀升温和均匀电场作用下,也会产生拉-弯耦合效应。但是对于两端固定的压电-功能梯度材料梁,在横向非均匀升温下过屈曲变形仍然是分叉形的。
Post-buckling of functionally graded material Timoshenko beams with surface-bonded piezoelectric layers subjected to temperature rise and electric field is studied. By accurately considering the axial extension and transverse shear deformation in the sense of theory of Timoshenko beam, geometrically nonlinear governing equations, for functionally graded beams subjected to thermo-electro-mechanical loadings were formulated. In the analysis, it was assumed that the material properties of the beam vary continuously as a power function of the thickness coordinate and that the piezoelectric layers are isotropic and homogenous. By using a shooting method, the obtained nonlinear boundary value problem was numerically solved and buckling and post-buckling response of the beams with the both ends fixed and subjected to transversely non-uniform heating and uniform electric field were presented. Characteristic curves of the post-buckling deformation of the beam varying with thermal load, the electrical load, and the power law index are plotted. Numerical results show that the tensional force produced in the piezoelectric layers by the voltage can efficiently increase the critical buckling temperature and defer the therreal post-buckling to occur. Due to being transversely non-uniform in the material properties, there exists tension-bending coupling effects in the beam even in uniform temperature rise in the thickness direction. However, for the piezoelectric-FGM beam with the two ends fixed the post-buckling is also bifurcation form under transversely non-uniform temperature rise.
出处
《计算力学学报》
EI
CAS
CSCD
北大核心
2010年第6期1067-1072,共6页
Chinese Journal of Computational Mechanics
基金
国家自然科学基金(10872083)
教育部博士点基金(200807310002)资助项目
关键词
功能梯度材料
TIMOSHENKO梁
压电层合粱
打靶法
过屈曲
functionally od
thermal graded material
Timoshenko beam
laminated piezoelectric beam
shoot methbuckling
buckling voltage
作者简介
李世荣（1957-），男，教授（E—mail：lisr@lut．cn，srli@yzu．edu．cn）．
