Legendre spectral finite elements for Reissner–Mindlin composite plates

Abstract

a b s t r a c tLegendre spectral finite elements (LSFEs) are examined in their application to Reissner-Mindlin composite plates for static and dynamic deformation on unstructured grids. LSFEs are high-order Lagrangian-interpolant finite elements whose nodes are located at the Gauss-Lobatto-Legendre quadrature points. Nodal quadrature is employed for mass-matrix calculations, which yields diagonal mass matrices. Full quadrature or mixed-reduced quadrature is used for stiffness-matrix calculations. Solution accuracy is examined in terms of model size, computation time, and memory storage for LSFEs and for quadratic serendipity elements calculated in a commercial finite-element code. Linear systems for both model types were solved with the same sparse-system direct solver. At their best, LSFEs provide many orders of magnitude more accuracy than the quadratic elements for a fixed measure (e.g., computation time). At their worst, LSFEs provide the same accuracy as the quadratic elements for a given measure. The LSFEs were insensitive to shear locking and were shown to be more robust in the thinplate limit than their low-order counterparts.

Spectral Methods for Modelling of Wave Propagation in Structures in Terms of Damage Detection—A Review

“…Legendre spectral finite elements with mixed quadrature have been, however, locking free and are significantly more accurate than low-order finite-elements for a given model size or total computation time. An example of similar elements but regarding composite plates for static and dynamic deformation on unstructured grids has been analysed by [141]. The authors have analysed Legendre spectral finite elements application to Reissner-Mindlin composite plates.…”

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“…The spectral finite elements have been successfully used in the simulation of fluid dynamics, two‐dimensional elastic wave propagation in solid media in geophysics, elastodynamics and acoustic wave propagation. However, there has been limited application of these elements to dynamic analysis of beam and plate elements. Sprague and Purkayastha showed that, for static and dynamic analyses of composite‐material plates, LSFEs can provide orders of magnitude of greater accuracy, for either a given model size or computation time, when compared with common low‐order elements.…”

“…However, there has been limited application of these elements to dynamic analysis of beam and plate elements. Sprague and Purkayastha showed that, for static and dynamic analyses of composite‐material plates, LSFEs can provide orders of magnitude of greater accuracy, for either a given model size or computation time, when compared with common low‐order elements.…”

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“…24 However, there has been limited application of these elements to dynamic analysis of beam 25, 26 and plate elements. [27][28][29] Sprague and Purkayastha 29 showed that, for static and dynamic analyses of composite-material plates, LSFEs can provide orders of magnitude of greater accuracy, for either a given model size or computation time, when compared with common low-order elements.FAST is an open-source computer-aided engineering and analysis tool developed by the National Renewable Energy Laboratory (NREL) for analysing both land-based and offshore wind turbines under realistic operating conditions. The beam model provided in the ElastoDyn FAST module is not capable of predictive analysis of highly flexible, composite wind turbine blades.…”

“…24 However, there has been limited application of these elements to dynamic analysis of beam 25, 26 and plate elements. [27][28][29] Sprague and Purkayastha 29 showed that, for static and dynamic analyses of composite-material plates, LSFEs can provide orders of magnitude of greater accuracy, for either a given model size or computation time, when compared with common low-order elements.…”