Improved Timoshenko beam theory for mechanical and thermal flexural behavior of porous cross-ply laminated beams

This article studies the flexural response of porous cross-ply laminated beams under sinusoidal mechanical and thermal loads. The sinusoidal thermal load is linearly varying in the transverse direction. For the first time, this work takes into consideration three porosity distribution models. Moreover, the analysis is performed via an improved Timoshenko beam theory that eliminates the need for a shear correction factor and introduces a parabolic distribution for the transverse shear strain. The beams are simply supported. The virtual work principle is utilized to derive the governing equations. The governing equations are then solved analytically via Navier's rule for the simple support condition. The present work's validity is checked by comparison with the results of Bernoulli Euler's classical, Timoshenko's first-order, Sayyad-Ghugal's trigonometric, Reddy's higher-order, and exact elasticity beam theories. The proposed theory is found to provide the closest results to those of the elasticity theory in comparison with the other theories. Parametric studies are conducted to measure the influence of porosity parameters on the response. Porosity distribution model 1 seems to have the greatest effect on the displacement results for both the thermal and mechanical load cases, followed by porosity model 2. In the mechanical load case, the lateral and axial displacements increase as the porosity volume fraction increases. However, the displacements for the thermal load case decrease as the porosity volume fraction increases.