The undercurrent research survey explores the roles of nonlocality and strain gradient size dependencies in nonlinear asymmetric buckling of shallow nanoscale arches having dissimilar end conditions through a numerical analysis. The arches, made from a functionally graded graphene nanofiller reinforced composite(FG-GNRC), are subjected to discretional radial concentrated loads along with converting of temperature. To account for the size dependencies, the exploration is carried out stemming from the nonlocal strain gradient theory(NSGT) in the sense of a quasi-2D parabolic shear flexible concept of curved beam. The material properties of the contemplated FG-GNRC sandwich are determined using the modified Halpin-Tsai micromechanics model. Subsequently, an extended isogeometric analysis(XIGA) is manipulated comprising insertion plus multiplication of knots to achieve the demanded lower continuity allocated to the integration between flexural and tangential reflexes. It is perceived that the both softening and stiffening concomitants assigned to the salient concentrated radial loads obtained by the developed NSGT-based XIGA diminish from the first upper limit to the second one, and then likewise from the first lower limit to the second one. Although, by becoming the upsurge in temperature higher,these softening and stiffening concomitants get more remarkable.