Bending analysis of a perforated microbeam with laplace transform

Abstract

In recent years, the analysis of materials and elements with dimensions at nano/micro levels has gained momentum. While analyzing these small-scale materials and elements, higher-order elasticity theories have started to be used instead of classical elasticity theories (CETs). One of these theories, which includes a small-scale parameter in its constitutive equations, is the modified couple stress theory (MCST). In this study, the bending analysis of a cantilever perforated microbeam is investigated by MCST and Euler-Bernoulli (EB) beam theory. First, the perforation characteristics of the microbeam are described and incorporated into the equation governing the bending problem based on the modified couple stress theory found in the literature. Then, the Laplace transform is applied to the governing equation. The known boundary conditions of the cantilever microbeam are substituted into the equation and the inverse Laplace transform is applied to obtain the deflection equation.