Closed form solutions for an anisotropic composite beam on a two-parameter elastic foundation

Beams resting on elastic foundations are widely used in engineering design such as railroad tracks, pipelines, bridge decks, and automobile frames. Laminated composite beams can be tailored for specific requirements offer a desirable framework foundations. Therefore, the analysis of flexural behaviour laminated is important consequence. Exact solutions deflection with coupling terms between stretching, shearing, bending twisting, two-parameter various types loading boundary conditions, presented first time. The proposed new formulation based Euler–Bernoulli beam theory having four degrees freedom, namely two principal directions, axial elongation twist. Governing equations conditions derived from principle virtual work expressed compact matrix–vector form. By decoupling both directions twist elongation, fourth-order differential equation transformed into system first-order equations. An exact solution this obtained using fundamental matrix approach. Fundamental matrices different configurations foundation provided. ability mathematical model predicting verified numerically by comparison results available literature. In addition, anisotropic analysed stacking sequences, conditions. effect coefficients also investigated discussed.