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Nonlinear coupled zigzag theory for buckling of hybrid piezoelectric plates

机译:混合压电板屈曲的非线性耦合之字形理论

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A coupled zigzag theory for hybrid piezoelectric plates, recently developed by the first author, is extended to include geometric nonlinearity in the Von Karman sense. In this theory, the potential field is approximated as piecewise linear across sublayers. The deflection approximation accounts for the transverse normal strain due to an electric field. The inplane displacements are assumed to follow a global third order variation across the thickness with a layerwise linear variation. The shear continuity conditions at the layer interfaces and the shear traction-free conditions at the top and bottom are enforced to formulate the theory in terms of only five primary displacement variables, independent of the number of layers. The coupled nonlinear equations of equilibrium and the boundary conditions are derived from a variational principle. The nonlinear theory is used to obtain the initial buckling response of symmetrically laminated hybrid plates under inplane electromechanical loading. Analytical solutions for buckling of simply supported plates under uniaxial and bi-axial inplane strains and electric potential are obtained for comparing the results with the available exact three-dimensional piezoelasticity solution. The comparison establishes that the present theory is very accurate for buckling response of hybrid plates even for highly inhomogeneous lay-ups.
机译:第一作者最近开发的混合压电板耦合之字形理论被扩展为包括冯卡曼意义上的几何非线性。在该理论中,势场近似为跨子层的分段线性。偏转近似值说明了由于电场引起的横向法向应变。假定平面内位移遵循整个厚度的整体三阶变化,并且具有逐级线性变化。层界面处的剪切连续性条件以及顶部和底部处的无剪切牵引力条件被强制用来仅用五个主要位移变量来表达该理论,而与层数无关。平衡和边界条件的耦合非线性方程是从变分原理导出的。非线性理论被用来获得对称层压复合板在平面机电载荷下的初始屈曲响应。获得了简单支撑板在单轴和双轴面内应变和电势下屈曲的解析解,以将结果与可用的精确三维压电弹性解进行比较。比较结果表明,即使对于高度不均匀的铺层,本理论对于混合板的屈曲响应也非常准确。

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