Polygonal shell elements with assumed transverse shear and membrane strains

Ho-Nguyen-Tan, Thuan; Kim, Hyun‐Gyu

doi:10.1016/j.cma.2019.02.044

Cited by 20 publications

(9 citation statements)

References 57 publications

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“…As shown in Figure 17A, a good convergence is obtained as the mesh is refined. Numerical results show that VEM on polygonal meshes and polygonal shell elements on polygonal meshes (PSE_Poly) 29 have the same convergence results.…”

Section: Numerical Experimentsmentioning

confidence: 88%

“…Moreover, several alternative approaches deal with polygonal element formulations, such as those based on the Washpress function and the scaled boundary finite element method. [29][30][31][32] VEM is different from classical numerical methods. It doesn't need to define explicit expressions of shape functions and only uses degrees of freedom to calculate the stiffness matrix, which is very convenient and effective.…”

Section: Introductionmentioning

confidence: 99%

“…This method can be considered either a generalization of the finite element method under a polygonal or polyhedral element or the final evolution of the mimetic finite difference method. Moreover, several alternative approaches deal with polygonal element formulations, such as those based on the Washpress function and the scaled boundary finite element method 29–32 . VEM is different from classical numerical methods.…”

Section: Introductionmentioning

confidence: 99%

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An enriched virtual element method for 2D‐3C generalized membrane shell model on surface

Yang,

Shen,

Zhao

et al. 2024

Numerical Meth Engineering

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Dealing with complex shell surfaces using the finite element method, we are often limited to simple geometric meshes such as triangles and quadrangles and have to refine the meshes to meet the calculation accuracy requirements, significantly increasing the calculation cost. The virtual element method (VEM), a new numerical method with high mesh flexibility, has been widely applied to many physical and mechanical problems. To the best of our knowledge, this method has yet to be studied for membrane shell models so far. In this paper, for the first time, we provide an enriched conforming VEM discrete scheme for the two‐dimensional three‐component (2D‐3C) generalized membrane shell (GMS) model proposed by Ciarlet et al. Furthermore, we prove the VEM discrete solution's existence and uniqueness for the GMS. Numerical experiments demonstrate that this discrete scheme is convergent and stable and can accurately represent the membrane stress state of conical, cylindrical, hyperbolical, and spherical shells clamped along a portion of their lateral faces. At the same time, we show the diversity of the grid subdivision. Thus, we develop the VEM for the GMS model successfully. In the future, we will continue to study the VEM for other shell models.

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Section: Numerical Experimentsmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An enriched virtual element method for 2D‐3C generalized membrane shell model on surface

Yang,

Shen,

Zhao

et al. 2024

Numerical Meth Engineering

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show abstract

“…The relative errors of v A obtained by meshes H1, H2, H3, and H4 are plotted in Figure 15(B). Furthermore, the results obtained by shell element PSE‐Poly 22 with similar meshes are also plotted for comparison. It can be seen that element HSDF‐PSH can obtain very stable and precise results with various element sides.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Katili et al 21 also constructed a polygonal thin/thick plate element by smoothed finite element method. Ho‐Nguyen‐Tan and Kim 22 developed a polygonal degenerated shell elements by assuming covariant shear strain field and employing the mixed interpolation technique. Aurojyoti et al 23 proposed an n ‐sided polygonal finite element for nonlocal nonlinear analysis of plates and laminates based on Reddy's third‐order shear deformation theory.…”

Section: Introductionmentioning

confidence: 99%

Shape‐free arbitrary polygonal hybrid stress/displacement‐function flat shell element for linear and geometrically nonlinear analyses

Cen

et al. 2021

Numerical Meth Engineering

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A high-performance shape-free arbitrary polygonal hybrid stress/displacement -function flat shell finite element method is proposed for linear and geometrically nonlinear analyses of shells. First, an arbitrary polygonal Mindlin-Reissner plate element and an arbitrary polygonal membrane element with drilling degrees of freedom are constructed based on hybrid displacement-function and hybrid stress-function methods, respectively. Both elements have only two corner nodes along each edge. Second, by assembling the plate and the membrane elements, an arbitrary polygonal flat shell element is constructed. Third, based on the corotational method, a proper best-fit corotated frame for geometrically nonlinear polygonal elements is designed. By updating the analytical trial functions of shell element in each increment step, the original linear flat shell element is generalized to a geometrically nonlinear model. Numerical examples show that the new element possesses excellent performance for both linear and geometrically nonlinear analyses, and possesses outstanding flexibility in dealing with complex loading distributions and mesh shapes.

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An efficient method for shape and topology optimization of shell structures

Ho-Nguyen-Tan

Kim

2022

Struct Multidisc Optim

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Polygonal shell elements with assumed transverse shear and membrane strains

Cited by 20 publications

References 57 publications

An enriched virtual element method for 2D‐3C generalized membrane shell model on surface

An enriched virtual element method for 2D‐3C generalized membrane shell model on surface

Shape‐free arbitrary polygonal hybrid stress/displacement‐function flat shell element for linear and geometrically nonlinear analyses

An efficient method for shape and topology optimization of shell structures

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