Deflection analysis of composite micro-beam on elastic foundation by strain gradient theory

In this article bending analysis of composite Euler-Bernoulli micro-beam made of functionally graded materials resting on elastic foundation by strain gradient theory has been studied. The material properties of structure have been assumed by Reddy ’ s power law model such as the bottom layer and top layer being ceramic and metal material respectively. At first, by using the assumptions of elasticity strain gradient theory and calculating the total potential energy of system after determining the work of external distributed load by using the Hamilton's principal the equations of motion have been derived. Note that the work down by the Winkler elastic foundation is considered. Because the solutions of mentioned equations are not possible by analytical method, the equations have been solved by generalized differential quadrature method in simply supported boundary conditions. By comparing the answers of problem with other published references, we confident form the obtained results. At the end, effect of material length scale and power law index coefficient of functionally graded materials and stiffness of elastic foundation on deflection of micro-beam has been studied. 5-Obtained deflection based on the classical theory is more than obtained deflection from the couple stress theory. Also, Obtained deflection based on the couple stress theory is more than the obtained deflection based on the strain gradient theory. This difference of the results increases by increasing the non-dimensional parameter h/l.