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Layerwise mixed elements with node-dependent kinematics for global-local stress analysis of multilayered plates using high-order Legendre expansions. (English) Zbl 1441.74265

Summary: Carrera Unified Formulation (CUF) is taken a step further to render node-dependent kinematics (NDK) capabilities to new layerwise finite elements based on Reissner’s Mixed Variational Theorem (RMVT), especially suited for global-local stress analysis of multilayered plates, ensuring high numerical accuracy and computational efficiency, all together. In the framework of CUF, as introduced originally for multilayered structures, any degree of kinematic refinement can be considered in agreement with Equivalent Single-Layer (ESL) or Layer-Wise (LW) theories to develop advanced finite element models, whether based on the Principle of Virtual Displacements (PVD) or RMVT. The degree of kinematic refinement, which usually holds equally for the entire element, can be taken a step further, by being assigned locally to each of its nodes, making full use of CUF to render NDK capabilities to the elements. Besides, even though the elements can adopt any type of nodal shape functions, high \(p\)-order hierarchical Legendre expansions (HLE) can also be combined with NDK, achieving excellent convergence rates. These capabilities combined, explored first under the PVD, are for once integrated in the proposed elements under RMVT to further benefit accurate stress analysis. These elements can be applied throughout the entire mesh, adapting to local, transitional and global regions straightforwardly, providing high numerical accuracy, locally, with minimal computational efforts, globally. The numerical results focus on stress analysis of multilayered composite plates, including local effects, to demonstrate the predictive capabilities of the proposed RMVT-based LW elements with NDK and HLE combined, considering well-known benchmark three-dimensional exact solutions for assessment.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74K20 Plates
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