Abstract

The size-dependent bending and free vibration of bi-directional functionally graded graphene nanoplatelets reinforced composite (BDFG-GPLRC) microbeams are investigated based on the Timoshenko beam theory and isogeometric analysis (IGA). The modified couple stress theory (MCST) is employed to describe the scale effect of microbeams. GPLs are distributed as power functions along the thickness and axis directions and four types of distribution patterns are taken into account. Employing the minimum potential energy principle and Hamilton’s principle, the government equations are established and solved by IGA. Correctness and accuracy of this method are verified by comparing with a published paper. By means of several numerical examples, the effects of GPL weight fraction, power-law indexes, boundary conditions and scale parameter on bending and free vibration behaviors of BDFG-GPLRC microbeams are studied in detail.

摘要

基于Timoshenko束理论和等几何分析（IGA），研究了双向功能梯度石墨烯纳米片增强复合材料（BDFG-GPLRC）微束的尺寸依赖性弯曲和自由振动。改进的耦合应力理论（MCST）用于描述微束的尺度效应。GPL沿着厚度和轴方向作为幂函数分布，并且考虑了四种类型的分布模式。运用最小势能原理和汉密尔顿原理，由IGA建立并求解政府方程。通过与已发表的论文进行比较，验证了该方法的正确性和准确性。通过几个数值示例，GPL重量分数，幂律指数，