A strain-displacement variational formulation for laminated composite beams based on the modified couple stress theory

1. Introduction Mixed energy methods, e.g. Hellinger-Reissner (HR) method, can include stresses and displacements as unknowns in the formulation and can be made to satisfy equilibrium conditions as well as minimise total energy. The HR method accurately captures the full 3D stress field of general beams and plates [1]. The differential quadrature method (DQM) can be viewed as a more accurate, computationally efficient version of the finite difference method. It solves differential equations directly and therefore solves pointwise equilibrium expressions and can be more accurate than conventional FE methods. The present study aims to: • develop strain-displacement (SD) mixed energy method for stress analysis of laminated beams. • include couple-stress in the SD formulation to accurately predict 3D stresses of highly heterogeneous laminates. • implement DQM method to solve the governing equations subject to different boundary conditions.