Layerwise mixed least-squares finite element models for static and free vibration analysis of multilayered composite plates

Moleiro, F.; Soares, Carlos A. Mota; Reddy, J. N.

doi:10.1016/j.compstruct.2009.07.005

Cited by 49 publications

(10 citation statements)

References 20 publications

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“…While spectral FEs, first developed for fluid dynamics, 9 have seen successful use in, e.g., geophysics, elastodynamics, and acoustics, LSFEs have seen only limited applications for small-deformation structural plate and beam elements (see, e.g., Refs. [10][11][12][13], and only recently have been applied to large static deformation. 14 Absent in much of the LSFE published work are rigorous efficiency comparisons of the proposed elements with existing low-order elements.…”

Section: Introductionmentioning

confidence: 99%

A Legendre Spectral Finite Element Implementation of Geometrically Exact Beam Theory

Wang

Sprague

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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This paper considers Legendre spectral finite elements (LSFEs) for linear and nonlinear elastic deformation of composite beams. LSFEs are high-order Lagrangian-interpolant finite elements with nodes located at the Gauss-Lobatto-Legendre quadrature points. Geometrically exact beam theory (GEBT) is adopted as the theoretical framework, where coupling effects (which usually exist in composite structures) and geometric nonlinearity are taken into consideration. Preliminary results are shown for two example problems. In the first example, the planar linear deflection and natural frequencies of a tapered beam are calculated with LSFEs and with first-order finite elements found in a commercial code. In the second example, the planar nonlinear deflection of a beam subjected to a tip moment is examined with LSFEs and first-order finite elements. For both cases, the LSFEs exhibit exponential convergence rates and are dramatically more accurate than low-order finite elements for a given model size.

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Section: Introductionmentioning

confidence: 99%

A Legendre Spectral Finite Element Implementation of Geometrically Exact Beam Theory

Wang

Sprague

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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“…Therefore, the resulting strain field is also continuous and, because the constitutive relation is discontinuous (constant in each lamina), the achieved stress field becomes discontinuous. Several important recent studies [11][12][13][14][15][16] have focused on improving the stress analysis and other issues by following the displacement À rotation formulations of laminated plates and shells. Readers are invited to read these studies for important information and a good review on the subject of displacement À rotation-based formulations.…”

Section: Introductionmentioning

confidence: 99%

A FEM continuous transverse stress distribution for the analysis of geometrically nonlinear elastoplastic laminated plates and shells

Coda

Sampaio

Paccola

2015

Finite Elements in Analysis and Design

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“…Kudela et al [9] applied LSFEs in space and time to wave propagation in RM composite plates, where square elements were used along with nodal quadrature. Moleiro et al [10,11] applied LSFEs in a least-squares formulation for RM plates where static deformation and natural frequencies were calculated on a structured grid for a rectangular plate. Unlike Zrahia and Bar-Yoseph [6], who employed nodal quadrature, Moleiro et al [10,11] employed full Gauss-Legendre quadrature for mass and stiffness inner products.…”

Section: Introductionmentioning

confidence: 99%

Legendre spectral finite elements for Reissner–Mindlin composite plates

Sprague

Purkayastha

2015

Finite Elements in Analysis and Design

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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.

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Layerwise mixed least-squares finite element models for static and free vibration analysis of multilayered composite plates

Cited by 49 publications

References 20 publications

A Legendre Spectral Finite Element Implementation of Geometrically Exact Beam Theory

A Legendre Spectral Finite Element Implementation of Geometrically Exact Beam Theory

A FEM continuous transverse stress distribution for the analysis of geometrically nonlinear elastoplastic laminated plates and shells

Legendre spectral finite elements for Reissner–Mindlin composite plates

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