A new Galerkin method for buckling of sandwich nanobeams

This paper studies static buckling of nanobeam sandwich beams, these beams consist of two layers of material that are attached to each other by a curved surface, this is also the novelty that this work does. The formulations are developed using the new third-order shear deformation theory in conjunction with nonlocal theory to demonstrate the size effect’s influence. This work employs both solutions simultaneously to solve the problem, one based on the finite element method (FEM) and the other using the new style Galerkin (GL) method, in which the parameters of this GL method are chosen more flexibly with different boundary conditions, demonstrating the impact of boundary conditions on the accuracy of the calculation results, this approach is the highlight of the present research. Numerous intriguing instances exist in the calculation results where it is possible to choose the appropriate parameter so that the beam’s critical burden is either maximal or minimal. This is the scientific premise for designing sandwich beams and selecting the appropriate parameters for their use in practice.