Extended isogeometric analysis based on Bézier extraction for an FGM plate by using the two-variable refined plate theory

Tan, Pengfei; Nguyen‐Thanh, Nhon; Zhou, Kun

doi:10.1016/j.tafmec.2017.02.002

Cited by 38 publications

(9 citation statements)

References 49 publications

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“…After adopting the derivation of the Hamilton's principal and weak formulation, the weak form of the nonlinear problem of FG plates under transverse load can be briefly expressed as (10) in which includes in-plane and bending strains and represents shear strains.…”

Section: Functionally Graded Materials With Porositiesmentioning

confidence: 99%

“…Thanks to these striking features, FGMs have been extensively applied to various engineering applications including aerospace, defence, automotive, nuclear power, bio-engineering and other areas [2,3]. There have been extensive efforts working on the analysis of FG structures in the literature [4][5][6][7][8][9][10]. Due to technical issues during the manufacturing process, porosities may appear within the FGMs and cause reduction in the strength of the materials.…”

Section: Introductionmentioning

confidence: 99%

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Geometrically nonlinear polygonal finite element analysis of functionally graded porous plates

Nguyen

Lee

et al. 2018

Advances in Engineering Software

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In this study, an efficient polygonal finite element method (PFEM) in combination with quadratic serendipity shape functions is proposed to study nonlinear static and dynamic responses of functionally graded (FG) plates with porosities. Two different porosity types including even and uneven distributions through the plate thickness are considered. The quadratic serendipity shape functions over arbitrary polygonal elements including triangular and quadrilateral ones, which are constructed based on a pairwise product of linear shape functions, are employed to interpolate the bending strains. Meanwhile, the shear strains are defined according to the Wachspress coordinates. By using the Timoshenko's beam to interpolate the assumption of the strain field along the edges of polygonal element, the shear locking phenomenon can be naturally eliminated. Furthermore, the C 0-type higher-order shear deformation theory (C 0-HSDT), in which two additional variables are included in the displacement field, significantly improves the accuracy of numerical results. The nonlinear equations of static and dynamic problems are solved by Newton-Raphson iterative procedure and by Newmark's integration scheme in association with the Picard methods, respectively. Through various numerical examples in which complex geometries and different boundary conditions are involved, the proposed approach yields more stable and accurate results than those generated using other existing approaches.

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Section: Functionally Graded Materials With Porositiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Geometrically nonlinear polygonal finite element analysis of functionally graded porous plates

Nguyen

Lee

et al. 2018

Advances in Engineering Software

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“…The main superiority of this presented technique of fully homogeneous equation containing the nonlinear coefficient term c 1 of TSDT models is directly derived from the dynamic equilibrium differential equations to obtain the natural frequencies of thick FGM cylindrical shells under free vibrations. Tan et al (2017) presented the extended IGA (XIGA) method and two-variable refined plate theory to investigate the static and dynamic results for the FGM plates; the effects of side-to-thickness ratio and crack length on the static and dynamic are also investigated. Huang et al (2017) presented the XIGA method to investigate the buckling results for the Mindlin-Reissner plates; the effects of various plate shapes, side-tothickness ratio, and crack length on the buckling are also investigated.…”

Section: Introductionmentioning

confidence: 99%

Vibration frequency of thick functionally graded material cylindrical shells with fully homogeneous equation and third-order shear deformation theory under thermal environment

Hong

2020

Journal of Vibration and Control

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The effects of third-order shear deformation theory and varied shear correction coefficient on the vibration frequency of thick functionally graded material cylindrical shells with fully homogeneous equation under thermal environment are investigated. The nonlinear coefficient term of displacement field of third-order shear deformation theory is included to derive the fully homogeneous equation under free vibration of functionally graded material cylindrical shells. The determinant of the coefficient matrix in dynamic equilibrium differential equations under free vibration can be represented into the fully fifth-order polynomial equation, thus the natural frequency can be found. Two parametric effects of environment temperature and functionally graded material power law index on the natural frequency of functionally graded material thick cylindrical shells with and without the nonlinear coefficient term of displacement fields are computed and investigated.

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“…, 35, 36, 37, 38]. Taking advantages of extended FEM (XFEM) and IGA, extended IGA (XIGA) has been developed for fracture analysis [39,40,41,42,43,44]. However, IGA based on NURBS imposes rigidity on volume meshing, which requires special technique to accommodate trimmed surfaces, local refinement or in-congruent surface descriptions at the opposing faces.…”

Section: Introductionmentioning

confidence: 99%

Static and free-vibration analyses of cracks in thin-shell structures based on an isogeometric-meshfree coupling approach

Nguyen‐Thanh

Zhou

2018

Comput Mech

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Extended isogeometric analysis based on Bézier extraction for an FGM plate by using the two-variable refined plate theory

Cited by 38 publications

References 49 publications

Geometrically nonlinear polygonal finite element analysis of functionally graded porous plates

Geometrically nonlinear polygonal finite element analysis of functionally graded porous plates

Vibration frequency of thick functionally graded material cylindrical shells with fully homogeneous equation and third-order shear deformation theory under thermal environment

Static and free-vibration analyses of cracks in thin-shell structures based on an isogeometric-meshfree coupling approach

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