A STUDY ON THE NONLINEAR STABILITY OF ORTHOTROPIC SINGLE-LAYERED GRAPHENE SHEET BASED ON NONLOCAL ELASTICITY THEORY
Keywords:POSTBUCKLING, ORTHOTROPIC NANOPLATES, SMALL SCALE EFFECT, NONLOCAL PLATE THEORY
RECENTLY, GRAPHENE SHEETS HAVE SHOWN SIGNIFICANT POTENTIAL FOR ENVIRONMENTAL ENGINEERING APPLICATIONS SUCH AS WASTEWATER TREATMENT. IN THE PRESENT WORK, THE POSBUCKLING RESPONSE OF ORTHOTROPIC SINGLE-LAYERED GRAPHENE SHEET (SLGS) IS INVESTIGATED IN A CLOSED-FORM ANALYTICAL MANNER USING THE NONLOCAL THEORY OF ERINGEN. TWO OPPOSITE EDGES OF THE PLATE ARE SUBJECTED TO NORMAL STRESSES. THE NONLOCALITY AND GEOMETRIC NONLINEARITY ARE TAKEN INTO CONSIDERATION, WHICH ARISES FROM THE NANOSIZED EFFECTS AND MID-PLANE STRETCHING, RESPECTIVELY. NONLINEAR GOVERNING DIFFERENTIAL EQUATIONS (NONLOCAL COMPATIBILITY AND EQUILIBRIUM EQUATIONS) ARE DERIVED AND PRESENTED FOR THE AFOREMENTIONED STUDY. GALERKIN METHOD IS USED TO SOLVE THE GOVERNING EQUATIONS FOR SIMPLY SUPPORTED BOUNDARY CONDITIONS. IT IS SHOWN THAT THE NONLOCAL EFFECT PLAYS A SIGNIFICANT ROLE IN THE NONLINEAR STABILITY BEHAVIOR OF ORTHOTROPIC NANOPLATES. UNLIKE FIRST AND SECOND POSTBUCKLING MODES, NONLOCAL EFFECTS DECREASE WITH THE INCREASE OF LATERAL DEFLECTION AT HIGHER POSTBUCKLING MODES. IT IS ALSO OBSERVED THAT THE NONLOCALITY AND NONLINEARITY IS MORE PRONOUNCED FOR HIGHER POSTBUCKLING MODES.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY] that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).