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A Ritz type solution with exponential trial functions for laminated composite beams based on the modified couple stress theory

机译：基于修正耦合应力理论的层状组合梁具有指数试验功能的Ritz型解

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摘要

This paper proposes novel Ritz functions for the size-dependent analysis of micro laminated composite beams with arbitrary lay-ups. Displacement field is based on a higher-order deformation beam theory and size effect is captured by the modified couple stress theory. Lagrange's equations are used to obtain the governing equations of motion. The present beam model, which can recover the classical one by neglecting the material length scale parameter, is used to predict the size-dependent responses of micro composite beams. The results indicate that the present study is efficient for bending, vibration and buckling problems of micro composite beams. Some new results are given to serve as benchmarks for future studies.
机译：本文提出了新颖的Ritz函数，用于任意叠合的微型层压复合梁的尺寸相关分析。位移场基于高阶变形梁理论，而尺寸效应则由改进的耦合应力理论捕获。拉格朗日方程用于获得运动的控制方程。通过忽略材料长度比例参数可以恢复经典模型的本梁模型用于预测微复合梁的尺寸相关响应。结果表明，本研究对于微复合梁的弯曲，振动和屈曲问题是有效的。给出了一些新结果，可以作为将来研究的基准。

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