A Laplace Transform Approach for the Size-Dependent Static Analysis of Laminated Composite Micro-Beams Using Modified Couple Stress Theory

In this study, static bending behavior of fiber-reinforced multilayered symmetric composite micro-beams is analytically investigated using modified couple Stress Theory. The Laplace transform method is applied to solve the governing differential equations. The micro-scale stiffness coefficient is extended in terms to fully reflect layer-based anisotropy. Through comprehensive parametric analyses, the effects of size, stacking sequence, fiber orientation angle, and material anisotropy on static displacement are evaluated. The results show that as the size effect parameter increases, the "size-dependent stiffening" mechanism stabilizes the structure and reduces displacements. It is revealed that classical theory underestimates stiffness in microstructures, and that the outer layer fiber angles and the degree of material anisotropy play a decisive role in the severity of this size effect.