Free edge stress prediction for magneto-electro-elastic laminates using a stress function based equivalent single layer theory

A stress function based equivalent single layer theory upon the Lekhnitskii stress functions is proposed for predicting the localized free edge stresses of magneto-electro-elastic composite layered laminates under extensional strain load and magnetic load. The stress trial functions are separated into the in-plane stress functions and out-of-plane stress functions, in which the out-of-plane stress functions are assumed by the combination of harmonic and hyperbolic functions. The in-plane unknown functions can be calculated from the governing equations obtained by taking the principle of complementary virtual work. A standard eigenvalue problem is formed to solve the ordinary differential equations. The obtained free edge stress components satisfy the prescribed traction free boundary condition. To verify the proposed method, both cross-ply and angle-ply cases are considered as the substrate laminate for both the mechanical and piezomagnetic loads. The results are also compared with those obtained by the finite element method to validate the efficiency of the proposed approach.