Asymmetric nonlinear instability of thermally induced microsize arches having dissimilar boundary conditions incorporating strain gradient tensors

Abstract

In the featured research investigation, the roles of different microstructural-dependent strain gradient tensors in the asymmetric nonlinear instability characteristics attributed to microsize arches having dissimilar boundary conditions subjected to thermal ambience amalgamated with a mechanical concentrated load applied in various positions. It is supposed that the microsize arches are constructed by functionally graded porous material reinforced by graphene platelets at nanoscale. The individual nonlinear dominate equations are extracted based upon the exponential shear deformation formulations of curved beam comprising modified strain gradient theory (MSGT) of continuum mechanics. Thereupon, the isogeometric analysis (IGA) employing non-uniform rational B-Splines is carried out to discretize and interpret the nonlinear problem on the basis of the displacement conformation in terms of the nodal values. Knot insertion along with the multiplication are considered to describe the discontinuities of internal forces caused by the applied mechanical concentrated load. It is demonstrated that by moving the locus of the applied concentrated load nearer to the simply supported end in comparison with the clamped one, the detected limit points reduce from four number to two number. In other words, the multitude of limit points allocated to the MSGT-based nonlinear asymmetric instability of FGP microsize arches relies upon the position of the imposed concentrated load. Moreover, it is discovered that by shifting the imposed concentrated load to a locus more neighboring to the clamped end, the prominence associated with the effect of microscale gradient tensors on the limit values increases, while by shifting it to a locus more neighboring to the simply supported end, this prominence tends to be reduced.