Study On Refined Theory Of Bi-layer Beams

The bi-layer beams are made of two different material beams. Compared with conventional single-beam, the bi-layer beam has simple structure, good mechanical performance and economic and practical advantages. This paper mainly studies the refined theory of bi-later beams and provides credible theory for engineering application.First, from the 3D theory of elasticity, using the P-N general solution and trigonometric operator method, the stress and displacement expressions of bi-later beams for an isotropic body are derived without ad hoc assumptions. And in the case of non-homogeneous boundary conditions, the governing equations of bi-later beams for an isotropic body can be obtained. Then, using Biot thermoelastic solution, Lur’e method and the boundary conditions of Winkler foundation, the refined theory of thermoelastic beam posting inside Winkler foundation is given without ad hoc assumptions. In the end, on the basis of layer wise theory, the refined theory of thermoelastic bi-layer beams is obtained from the thermoelastic solution and Lur’e method. In the case of the bi-layer beam under non-homogeneous boundary conditions, the approximate deflection equation of the thermoelastic bi-layer beam is also obtained.For transversely isotropic beams, according to the E-L general solution and trigonometric operator method, the refined theory of bi-layer beams for a transversely isotropic body is given without ad hoc assumptions. Under transverse surface loading,the governing equations about transverse displacement of interface can be obtained directly from the refined theory. In addition, one example is examined to illustrate the application of the transversely theory of bi-layer beams proposed. Based on transversely isotropic thermoelastic general solution and Lur’e method, refined theory of transversely isotropic thermoelastic beam and refined theory of transversely isotropic thermoelastic beam posting inside Winkler foundation are both obtained. At last, on the basis of thermoelastic beam theory for a transversely isotropic body and layer wise theory, the refined theory of thermoelastic bi-layer beams for a transversely isotropic body is obtained. If the bi-layer beam is under non-homogeneous boundary conditions, the approximate deflection equation is derived.