Assessment of multi-cracked non-uniform FGM beams using an equilibrium-based finite element formulation

Abstract

A novel, simple and effective finite element formulation is introduced for the quasi-static analysis of functionally graded nonuniform Timoshenko beams with multiple and open concentrated cracks. This formulation relies on a complementary variational approach based on a set of approximations that satisfy all equilibrium conditions of the boundary-value problem in a strong form. As a result, this formulation is naturally free from the well-known shear-locking phenomenon. The effectiveness of the formulation is numerically demonstrated through its application to various problems, with the obtained results analysed and discussed.