Flexural rigidity

About: Flexural rigidity is a research topic. Over the lifetime, 3829 publications have been published within this topic receiving 56780 citations.

Closed-form trigonometric solutions for inhomogeneous beam-columns on elastic foundation

Abstract: In this study, a special class of closed-form solutions for inhomogeneous beam-columns on elastic foundations is investigated. Namely the following problem is considered: find the distribution of the material density and the flexural rigidity of an inhomogeneous beam resting on a variable elastic foundation so that the postulated trigonometric mode shape serves both as vibration and buckling modes. Specifically, for a simply-supported beam on elastic foundation, the harmonically varying vibration mode is postulated and the associated semi-inverse problem is solved that result in the distributions of flexural rigidity that together with a specific law of material density, an axial load distribution and a particular variability of elastic foundation characteristics satisfy the governing eigenvalue problem. The analytical expression for the natural frequencies of the corresponding homogeneous beam-column with a constant characteristic elastic foundation is obtained as a particular case. For comparison the obtained closed-form solution is contrasted with an approximate solution based on an appropriate polynomial shape, serving as trial function in an energy method.

Interplay between bending and stretching in carbon nanoribbons

Abstract: We investigate the bending properties of carbon nanoribbons by combining continuum elasticity theory and tight-binding atomistic simulations. First, we develop a complete analysis of a given bended configuration through continuum mechanics. Then, we provide by tight-binding calculations the value of the bending rigidity in good agreement with recent literature. We discuss the emergence of a stretching field induced by the full atomic-scale relaxation of the nanoribbon architecture. We further prove that such an in-plane strain field can be decomposed into a first contribution due to the actual bending of the sheet and a second one due to edge effects.

Molecular mechanics modeling for properties of carbon nanotubes

Abstract: Molecular mechanics calculations for in-plane stiffness, shear modulus, and the bending rigidity of single-walled carbon nanotubes are reported in this work through the calculations of the strain energy for carbon nanotubes and graphite sheets subjected to various types of loading. Elastic rod and plate theories are employed to link the material properties of carbon nanotubes directly to the molecular mechanics calculations. The in-plane stiffness of carbon nanotubes is about 372–376J∕m2. The bending rigidity is found to be around 1.78eV for relatively large tubes and graphite sheets.

Buckling of thermalized elastic sheets

Abstract: Steady progress in the miniaturization of structures and devices has reached a scale where thermal fluctuations become relevant and it is thus important to understand how such fluctuations affect their mechanical stability. Here, we investigate the buckling of thermalized square sheets under either compression or shear. We demonstrate that thermal fluctuations increase the critical buckling load compared to the classical Euler buckling load due to the enhanced scale-dependent bending rigidity for sheets that are much larger than a characteristic thermal length scale. The presented results are universal and apply to a wide range of microscopic sheets. These results are especially relevant for atomically thin 2D materials, where thermal fluctuations can significantly increase the critical buckling load because the thermal length scale is on the order of nanometers at room temperature.