Second-Order Multiscale Analysis and Algorithms for Composite Mindlin Plate and Timoshenko Beam

This work presents a comprehensive framework for the multiscale characterization of advanced composite structures, focusing on Mindlin plates and Timoshenko beams with periodic microstructures. Using a second-order two-scale (SOTS) method, we uniformly derive asymptotic expansions for deflection and rotation to formulate effective homogenized models. The developed finite element procedures combine techniques to overcome shear locking, enabling efficient and accurate structural application. Numerical simulations verified the convergence of the model and demonstrated its superiority in capturing the rapid oscillation of local stress distribution, an important aspect for the design of reliable composites. By varying the thickness parameter, our model is shown to connect thin and thick theories for composite beam and plate problems. It thus provides a practical tool for the design and analysis of tailored composite structures, contributing to the development of innovative materials.