Stability Analysis of Carbon Nanotube Reinforced Varying Cross-Section Bars Partially in Contact with Foundation via Energy-Based Finite Element Functional

In this study, stability analysis of varying cross-section carbon nanotube (CNT) reinforced bars partially resting on a foundation is presented. Using the proposed finite element formulation, critical buckling loads and mode shapes of bars are effectively determined. The effect of CNT reinforcement on the mechanical behavior of the structure is considered in the formulation using the Halpin–Tsai micromechanical model. In this way, geometric parameters at the nanoscale such as the thickness, length, and diameter of the CNT reinforcement particles are included in the model. By examining the structural behavior of the bars placed on the elastic foundation under different boundary conditions, the effect of the support condition is investigated for CNT reinforced variable cross-section bars. Cross-section changes are included in the model using different inertia functions. Thus, the effect of variable stiffness and the effectiveness of the foundation parameters on the stability analysis of CNT reinforced bars are examined. The analysis results presented in this study contribute to the understanding of the stability behavior of CNT reinforced structures, especially in contact with partial foundation.