Two-dimensional model for composite beams and its state-space based mixed finite element solution by DQM

Most one-dimensional composite beam theories are based on simplified shear deformation assumptions, or even ignore shear deformation, which have limitations in analyzing multilayer beams with significant material differences. Therefore, this paper firstly proposed a two-dimensional analytical model for composite beams through the equivalent transformation of cross section. Based on the mixed variational principle, the state equations are then derived by finite element meshing and interpolation along the length of the beam, with nodal displacements and their energy-conjugated stresses as state variables. Subsequently, the differential quadrature method (DQM) is introduced to solve the equations and a two-dimensional analysis method for composite beams is established. Due to the use of displacements and stresses as fundamental variables in the state equations, various transfer characteristics of displacements and stresses at the interlayer interfaces of composite beams can be conveniently handled. This method is finally verified by numerical examples of steel–concrete composite beams and concrete beams with corrugated steel webs. Since no assumptions of displacement and stress distributions along the thickness of beams are required, the present method can provide benchmarks for various one-dimensional beam theories.