Exact solutions for laminated composite beams using a unified state space formulation

The variationally consistent methodology for generating state space models of 1D composite beams is evolved systematically and used to establish such models corresponding to different composite higher order beam theories. The state space form always yields the state vector in terms of generalized displacements and its associated generalized forces. It can handle arbitrary material coupling in a general manner and satisfy all the boundary conditions simultaneously. Numerical results of generally laminated beams under transverse loading using four warping functions of the normal and shear deformation theories for different boundary conditions are provided and compared with previous studies from the literature.