Exact Solutions for Time-Varying Bending Behavior of Multilayer Orthotropic Beams Bonded by Viscoelastic Interlayers

Abstract

This study proposed exact solutions for the purpose of investigating and understanding the time-varying bending behavior of a multilayer orthotropic beam bonded by viscoelastic interlayers. In the analytical model, each orthotropic layer involved four independent elastic constants and was modeled on the basis of the two-dimensional (2D) elasticity theory. The interlayer exhibited viscoelastic properties and was described by the standard linear solid model. By means of Fourier series expansion, the general solutions of stresses and displacements were derived with unknown coefficients, which were analytically determined by interfacial and loading conditions, in which the convolution was converted by the Laplace transform. The results of numerical examples showed that the present solutions converged rapidly and were consistent with the finite element solutions. Comparison of the present 2D solutions with the one-dimensional (1D) solutions based on the Euler–Bernoulli beam theory indicated that the 1D solutions were inaccurate for thick beams. The effects of viscoelastic material and orthotropic constants on the long-term stresses and displacements in the beam were thoroughly examined. These results provided a reference for the optimization of a multilayer orthotropic beam design.