Separated representations of 3D elastic solutions in shell geometries

Abstract

Background: The solution of 3D models in degenerated geometries in which some characteristic dimensions are much lower than the other ones -e.g. beams, plates, shells,..- is a tricky issue when using standard mesh-based discretization techniques. Methods: Separated representations allow decoupling the meshes used for approximating the solution along each coordinate. Thus, in plate or shell geometries 3D solutions can be obtained from a sequence of 2D and 1D problems allowing fine and accurate representation of the solution evolution along the thickness coordinate while keeping the computational complexity characteristic of 2D simulations. In a former work this technique was considered for addressing the 3D solution of thermoelastic problems defined in plate geometries. In this work, the technique is extended for addressing the solution of 3D elastic problems defined in shell geometries. Results: The capabilities of the proposed approach are illustrated by considering some numerical examples involving different degrees of complexity, from simple shells to composite laminates involving stiffeners. Conclusions: The analyzed examples prove the potentiality and efficiency of the proposed strategy, where the computational complexity was found evolving as reported in our former works, proving that 3D solutions can be computed at a 2D cost.