25.08.2021 - 11:15
On August 25 at 11:15 Hina Arif will defend her doctoral thesis “Stability analysis of stepped nanobeams with defects” for obtaining the degree of Doctor of Philosophy (in Mathematics).
Professor Jaan Lellep, University of Tartu
Professor Károly Jármai, University of Miskolc (Hungary)
Professor Juha Paavola, Aalto University (Finland)
In the current dissertation, the stability analysis of nonlocal elastic nanobeams is carried out. The nanobeams under consideration are of rectangular cross-section with piecewise constant thicknesses subjected to the axial compressions. It is assumed that the nanobeams are weakened by the defects like steps, cracks, and internal supports. The cracks are considered to be stable surface cracks that are located at the re-entrant corners of the steps penetrated throughout the thickness of the nanobeam.
To analyze the buckling of nanobeams, an analytical approach has been developed within the framework of Eringen's nonlocal theory of elasticity to embrace the small size effect. The nonlocal theory of elasticity for Euler-Bernoulli nanobeams is combined with the linear fracture mechanics to develop an approximate method for the stability analysis of nanobeams and nanocolumns. The crack effect is considered by coupling the local compliance of the structure with the stress intensity factor which can be calculated by the methods of linear fracture mechanics. The critical buckling loads for axially loaded stepped nanobeams and nanocolumns with cracks and with the internal supports are calculated. The influence of nonlocal parameters, crack parameters, steps, intermediate support location, and the other physical parameters on the stability of nanobeams is investigated.
The method developed for stepped nanobeams with cracks is applied to the simply supported, clamped, and cantilever nanobeams. The case of stepped nanobeam with intermediate rigid support is studied separately. Since conducting experiments at nanolevel is difficult to handle, the accuracy of the presented methods is verified by the comparison of results with the available work in the literature. MATLAB tools are used to provide significant numerical results.
The defence will be held in Zoom: https://ut-ee.zoom.us/j/94134414642?pwd=NlZTR0xjSFZoMFpTaENiQ083OXNkUT09
Meeting ID: 941 3441 4642, Passcode: arif.
Narva mnt 18–1007 and via video bridge