Abstract
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.
Highlights
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
The computed results obtained by using the in-plane-out-of-plane separated representations are again compared to the ones obtained by using standard 3D linear finite elements
We proposed in our former works a procedure based on the separated representation of the displacement field involved in elastic problems defined in plate domains that allowed calculating fully 3D elastic solutions by solving a sequence of 2D and 1D problems, the former ones define in the plane and the last ones in the thickness
Summary
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. Plates and shells are very common in nature and they inspired engineers that used both from the very beginning of structural mechanics. Shells offer a diversity of possible shapes and geometries, some of them with simple curvature and most of them with double curvature. Many times they are assembled in complex structural systems, in many applications they contain many stiffeners as in the case of aircraft fuselages. In general the design of such structural elements requires the calculation of stresses, strains and displacements for the design loads. Other designs require considering more complex behaviors Other designs require considering more complex behaviors (e.g. non-linear elasticity due to material or geometrical non linearities, elastoplastic behaviors usually encountered in material forming – forging, bending, ... –, or complex multiphysics behaviors as the ones encountered in composites manufacturing processes implying change of phases, crystallization, polymerization, ... coupled with rich thermomechanical mechanisms)
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