Application of strain gradient elasticity theory for buckling analysis of protein microtubules

In this paper, size effect of microtubules (MTs) is studied via modified strain gradient elasticity theory for buckling. MTs are modeled by Bernoulli–Euler beam theory. By using the variational principle, the governing equations for buckling and related boundary conditions are obtained in conjunctions with the strain gradient elasticity. The size effect for buckling analysis of MTs is investigated and results are presented in graph form. The results obtained by strain gradient elasticity theory are discussed through the numerical simulations. The results based on the modified couple stress theory, nonlocal elasticity theory and classical elasticity theories have been also presented for comparison purposes.