A higher-order quadrilateral shell finite element for geometrically nonlinear analysis

Trinh, Minh-Chien; Jun, Hyungmin

doi:10.1016/j.euromechsol.2021.104283

Cited by 8 publications

(3 citation statements)

References 28 publications

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“…Numerical methods are mostly used for analysis, including meshless methods [8], boundary element methods [9], and finite element methods [10]. Among them, the finite element method is widely used, and scholars have proposed various computational formats, such as the total Lagrangian method (TL) and the updated Lagrangian method (UL) [11][12][13][14][15][16][17]. With the development of computer technology, the finite element method has become the most commonly used numerical analysis method in the field of engineering structures, and its calculation accuracy and efficiency are widely recognized.…”

Section: Introductionmentioning

confidence: 99%

A Study on the Applicability and Accuracy of the Discrete Element Method for Plates Based on Parameter Sensitivity Analysis

2023

Buildings

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In order to verify the accuracy and applicability of the discrete element method (DEM) in dealing with geometrically large deformations of continuous plate structures, both a single-parameter analysis and an orthogonal design method were adopted to analyze the displacement responses of the plate structures and were compared with those calculated using the finite element method (FEM). The single-parameter change condition involved the thickness-to-width ratio, elastic modulus, or Poisson’s ratio, while the multi-parameter change included boundary conditions, dimensions, load forms, thickness-to-width ratio, elastic modulus, and Poisson’s ratio. The results showed that displacements of the target locations were basically identical to those obtained according to FEM, with a maximum error of less than 5% under the single-parameter change condition. The maximum displacement error of the plate structures calculated using the DEM and FEM, respectively, was 4.212%, and the mean error and extreme difference of error parameters were 2.633% and 2.184%, respectively. These results indicate that the displacements of the plate structures calculated using the DEM were highly consistent with those obtained according to the FEM. Additionally, single-parameter changes and multi-parameter changes barely influenced the accuracy and suitability of the DEM in solving displacement response problems of plate structures. Therefore, the DEM is applicable in terms of dealing with displacement response problems of plate structures.

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Section: Introductionmentioning

confidence: 99%

A Study on the Applicability and Accuracy of the Discrete Element Method for Plates Based on Parameter Sensitivity Analysis

2023

Buildings

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“…The typical locking treatment approaches, which may not be restricted to solid-shell elements, include assumed natural strains (ANS), 18,19 enhanced assumed strain (EAS), 20 discrete strain gap (DSG), 21 B-method, [22][23][24][25] mixed formulations, 22,[26][27][28] selective/reduced integration, 26,[29][30][31] and projection techniques based on the moving least square (MLS). 32 Extensive literatures have reported that shells are studied by kinds of numerical methods: the finite element method (FEM), [33][34][35] the meshfree method, [36][37][38][39] and analytical 40,41 or semianalytical 42,43 methods and so forth. Apart from these, the approach of isogeometric analysis (IGA) introduced by Hughes et al 44 has also been frequently adopted in the analysis of laminated shells.…”

Section: Introductionmentioning

confidence: 99%

“…Extensive literatures have reported that shells are studied by kinds of numerical methods: the finite element method (FEM), 33–35 the meshfree method, 36–39 and analytical 40,41 or semianalytical 42,43 methods and so forth. Apart from these, the approach of isogeometric analysis (IGA) introduced by Hughes et al 44 has also been frequently adopted in the analysis of laminated shells 9,15,45–47 .…”

Section: Introductionmentioning

confidence: 99%

High‐fidelity tensor‐decomposition based matrix formation for isogeometric buckling analysis of laminated shells with solid‐shell formulation

Fan

Huang

Zeng

et al. 2022

Numerical Meth Engineering

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The computation cost of matrix formation in isogeometric analysis can be drastically reduced by employing tensor decomposition, but the performance like accuracy and robustness still depends on the approach used to realize the low‐rank approximation for the nonpolynomial integral kernels. In the buckling analysis of laminated shells with solid‐shell model, the integral kernels are not smooth in the thickness direction due to their material and stress distribution and have a high complexity because the curvilinear coordinate systems are involved in the representation of anisotropic constitutive relations, which makes it more difficult to guarantee the decomposition accuracy. This paper proposes a robust high‐fidelity tensor‐decomposition based matrix formation method for stiffness matrix and geometric stiffness matrix of the isogeometric buckling analysis problem. The proposed method avoids using a spline approximation and employs the hierarchical block‐wise decomposition approach (HBD) to obtain a determinate decomposition result, which saves more time without loss of accuracy and produces less canonical ranks with a reliable procedure. Besides, the matrix calculation is partly independent of the number of layers, showing a higher efficiency when the number of layers is larger. Finally, several experiments with various Gaussian curvatures are implemented to validate the proposed method.

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Stochastic bending and buckling analysis of laminated composite plates using Latin hypercube sampling

Trinh

Jun

2021

Engineering with Computers

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A higher-order quadrilateral shell finite element for geometrically nonlinear analysis

Cited by 8 publications

References 28 publications

A Study on the Applicability and Accuracy of the Discrete Element Method for Plates Based on Parameter Sensitivity Analysis

A Study on the Applicability and Accuracy of the Discrete Element Method for Plates Based on Parameter Sensitivity Analysis

High‐fidelity tensor‐decomposition based matrix formation for isogeometric buckling analysis of laminated shells with solid‐shell formulation

Stochastic bending and buckling analysis of laminated composite plates using Latin hypercube sampling

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