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Comparison of weak and strong formulations for 3D stress predictions of composite beam structures

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Comparison of weak and strong formulations for 3D stress predictions of composite beam structures. / Ojo, S. O.; Patni, M.; Weaver, P. M.

In: International Journal of Solids and Structures, Vol. 178-179, 01.12.2019, p. 145-166.

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Ojo, S. O. ; Patni, M. ; Weaver, P. M. / Comparison of weak and strong formulations for 3D stress predictions of composite beam structures. In: International Journal of Solids and Structures. 2019 ; Vol. 178-179. pp. 145-166.

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@article{7ea99fe615264c94929c6a2a7464ba25,
title = "Comparison of weak and strong formulations for 3D stress predictions of composite beam structures",
abstract = "Accurate full field stress responses are often necessary to predict the structural performance of composite structures. The Unified Formulation (UF) is a promising approach to realise efficient and accurate 3D stress predictions of beam-like structures by using recently proposed hierarchical Serendipity Lagrange Elements (SLE) for capturing the 2D response of the beam cross-section while the 1D behaviour along the beam axis is captured using the Finite Element Method (FEM). Despite the computational merits of SLE elements, the performance of UF-SLE-FEM model is strongly influenced by FEM mesh discretisation along the beam's longitudinal axis. With respect to multi-layered beam structures, a high density FEM mesh may lead to loss of efficiency of the UF-SLE-FEM model due to a significant increase in the number of degrees of freedom required to obtain convergence. This study proposes high-order refined formulations of the 1D structure based on strong-form, Differential Quadrature Method (DQM) and weak form, FEM for 3D stress analysis of composite structures. The proposed high-order strong-form DQM and weak-form FEM models, which are benchmarked against exact solutions, lead to significant computational advantages over UF-SLE-FEM models of similar accuracies. However, the symmetry and positive definiteness of the stiffness matrices of FEM models offer a numerical advantage over the strong-form DQM model with non-symmetric, non-positive definite stiffness matrices.",
keywords = "3D stress, Differential quadrature method, Higher order finite element, Serendipity Lagrange element, Unified formulation",
author = "Ojo, {S. O.} and M. Patni and Weaver, {P. M.}",
year = "2019",
month = "12",
day = "1",
doi = "10.1016/j.ijsolstr.2019.06.016",
language = "English",
volume = "178-179",
pages = "145--166",
journal = "International Journal of Solids and Structures",
issn = "0020-7683",
publisher = "Pergamon Press",

}

RIS - suitable for import to EndNote

TY - JOUR

T1 - Comparison of weak and strong formulations for 3D stress predictions of composite beam structures

AU - Ojo, S. O.

AU - Patni, M.

AU - Weaver, P. M.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - Accurate full field stress responses are often necessary to predict the structural performance of composite structures. The Unified Formulation (UF) is a promising approach to realise efficient and accurate 3D stress predictions of beam-like structures by using recently proposed hierarchical Serendipity Lagrange Elements (SLE) for capturing the 2D response of the beam cross-section while the 1D behaviour along the beam axis is captured using the Finite Element Method (FEM). Despite the computational merits of SLE elements, the performance of UF-SLE-FEM model is strongly influenced by FEM mesh discretisation along the beam's longitudinal axis. With respect to multi-layered beam structures, a high density FEM mesh may lead to loss of efficiency of the UF-SLE-FEM model due to a significant increase in the number of degrees of freedom required to obtain convergence. This study proposes high-order refined formulations of the 1D structure based on strong-form, Differential Quadrature Method (DQM) and weak form, FEM for 3D stress analysis of composite structures. The proposed high-order strong-form DQM and weak-form FEM models, which are benchmarked against exact solutions, lead to significant computational advantages over UF-SLE-FEM models of similar accuracies. However, the symmetry and positive definiteness of the stiffness matrices of FEM models offer a numerical advantage over the strong-form DQM model with non-symmetric, non-positive definite stiffness matrices.

AB - Accurate full field stress responses are often necessary to predict the structural performance of composite structures. The Unified Formulation (UF) is a promising approach to realise efficient and accurate 3D stress predictions of beam-like structures by using recently proposed hierarchical Serendipity Lagrange Elements (SLE) for capturing the 2D response of the beam cross-section while the 1D behaviour along the beam axis is captured using the Finite Element Method (FEM). Despite the computational merits of SLE elements, the performance of UF-SLE-FEM model is strongly influenced by FEM mesh discretisation along the beam's longitudinal axis. With respect to multi-layered beam structures, a high density FEM mesh may lead to loss of efficiency of the UF-SLE-FEM model due to a significant increase in the number of degrees of freedom required to obtain convergence. This study proposes high-order refined formulations of the 1D structure based on strong-form, Differential Quadrature Method (DQM) and weak form, FEM for 3D stress analysis of composite structures. The proposed high-order strong-form DQM and weak-form FEM models, which are benchmarked against exact solutions, lead to significant computational advantages over UF-SLE-FEM models of similar accuracies. However, the symmetry and positive definiteness of the stiffness matrices of FEM models offer a numerical advantage over the strong-form DQM model with non-symmetric, non-positive definite stiffness matrices.

KW - 3D stress

KW - Differential quadrature method

KW - Higher order finite element

KW - Serendipity Lagrange element

KW - Unified formulation

UR - http://www.scopus.com/inward/record.url?scp=85068265592&partnerID=8YFLogxK

U2 - 10.1016/j.ijsolstr.2019.06.016

DO - 10.1016/j.ijsolstr.2019.06.016

M3 - Article

VL - 178-179

SP - 145

EP - 166

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

ER -