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An RMVT-based third-order shear deformation theory of multilayered functionally graded material plates

机译：基于RMVT的多层功能梯度材料板的三阶剪切变形理论

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摘要

A Reissner mixed variational theorem (RMVT)-based third-order shear deformation theory (TSDT) is developed for the static analysis of simply-supported, multilayered functionally graded material (FGM) plates under mechanical loads. The material properties of the FGM layers are assumed to obey either the exponent-law distributions through the thickness coordinate or the power-law distributions of the volume fractions of the constituents. In this theory, Reddy's third-order displacement model and the lay-erwise parabolic function distributions of transverse shear stresses are assumed in the kinematic and kinetic fields, respectively, a priori, where the effect of transverse normal stress is regarded as minor and thus ignored. The continuity conditions of both transverse shear stresses and elastic displacements at the interfaces between adjacent layers are then exactly satisfied in this RMVT-based TSDT. On the basis of RMVT, a set of Euler-Lagrange equations associated with the possible boundary conditions is derived. In conjunction with the method of variable separation and Fourier series expansion, this theory is successfully applied to the static analysis of simply-supported, multilayered FGM plates under mechanical loads. A parametric study of the effects of the material-property gradient index and the span-thickness ratio on the displacement and stress components induced in the plates is undertaken.
机译：建立了基于Reissner混合变分定理（RMVT）的三阶剪切变形理论（TSDT），用于在机械载荷下对简单支撑的多层功能梯度材料（FGM）板进行静态分析。假设FGM层的材料属性遵循厚度坐标的指数律分布或成分的体积分数的幂律分布。在该理论中，先验地假设在运动场和动力学场中假设了Reddy的三阶位移模型和横向剪应力的横向抛物线函数分布，其中横向法向应力的影响被认为是次要的，因此被忽略了。 。然后，在此基于RMVT的TSDT中完全满足了横向剪切应力和相邻层之间界面处的弹性位移的连续性条件。基于RMVT，导出了与可能的边界条件相关的一组Euler-Lagrange方程。结合变量分离和傅里叶级数展开的方法，该理论已成功地应用于简单支撑的多层FGM板在机械载荷下的静态分析。进行了材料特性梯度指数和跨度-厚度比对板中位移和应力分量影响的参数研究。

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