Bending analysis of agglomerated carbon nanotube-reinforced beam resting on two parameters modified Vlasov model foundation

The present work deals with bending behavior of nanocomposite beam resting on two parameters modified Vlasov model foundation (MVMF), with consideration of agglomeration and distribution of carbon nanotubes (CNTs) in beam matrix. Equivalent fiber based on Eshelby–Mori–Tanaka approach is employed to determine influence of CNTs aggregation on elastic properties of CNT-reinforced beam. The governing equations are deduced using the principle of minimum potential energy under assumption of the Euler–Bernoulli beam theory. The MVMF required the estimation of γ parameter; to this purpose, unique iterative technique based on variational principles is utilized to compute value of the γ and subsequently fourth-order differential equation is solved analytically. Eventually, the transverse displacements and bending stresses are obtained and compared for different agglomeration parameters, various boundary conditions simultaneously and variant elastic foundation without requirement to instate values for foundation parameters.