An Explicit Hybrid Stabilized Eighteen‐node Solid Element for Thin Shell Analysis

Sze, Ka-Shing; TAY, M. H.

doi:10.1002/(sici)1097-0207(19970530)40:10<1839::aid-nme141>3.3.co;2-f

Cited by 11 publications

(31 citation statements)

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“…Solid-Shell elements which possess no rotational d.o.f.s and are applicable to thin plate/shell analyses have attracted considerable attention [1][2][3][4][5][6][7][8][9]. Compared to the degenerated-shell elements, solid-shell elements are advantageous in the following aspects.…”

Section: Introductionmentioning

confidence: 99%

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An eighteen-node hybrid-stress solid-shell element for homogenous and laminated structures

Sze¹,

Yao²,

Pian³

2002

Finite Elements in Analysis and Design

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Solid-shell elements are often equipped with two layers of nodes. Thus, the thickness (normal) strain along the thickness direction is essentially constant. When these elements are subjected to pure bending, the shrinkage/expansion induced by the in-plane strain and the Poisson's ratio coupling in the upper and lower halves of the elements cancel each other. With a constant thickness strain, the plane strain state is resulted that leads to thickness locking. In this paper, a modified generalized laminate stiffness matrix is devised to resolve not only the thickness locking but also some abnormalities of solid-shell elements in laminate analyses. Associated with the modified matrix, a set of generalized stresses can be defined and a modified Hellinger-Reissner functional can be derived by treating the generalized stresses as the independent variables. Based on the functional, an eigenteen-node hybrid-stress solid-shell element suitable for laminate analyses is proposed via a stabilization approach. All the benchmark tests indicate that the present stabilized element is close to the reduced integration element in accuracy.

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Section: Introductionmentioning

confidence: 99%

“…To resolve thickness locking in homogeneous elements, enhanced assumed strain modes [5,6], hybrid-stress formulation [3,9,12] and the plane stress enforcement [1,2,4,7,8] have been resorted to.…”

Section: Introductionmentioning

confidence: 99%

An eighteen-node hybrid-stress solid-shell element for homogenous and laminated structures

Sze¹,

Yao²,

Pian³

2002

Finite Elements in Analysis and Design

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“…Unfortunately, the so-formed elements encounter the risk of shear and membrane lockings as their thickness becomes small. To alleviate lockings, a number of noteworthy techniques have been proposed including uniformly reduced integration, selectively reduced integration (Zienkiewicz, Taylor & Too 1971;Hughes, Cohen & Haroun 1978), heterosis elements , c-stabilization method (Belytschko, Ong, Liu & Kennedy 1984;Belytschko, Wong & Stolarski 1989), hybrid/mixed formulation (Lee & Pian 1978;Lee, Dai, & Yeom 1985;Rhiu & Lee 1987;Rhiu & Lee 1988;Rhiu, Russel & Lee 1990;Saleeb, Chang, Graf & Yingyeunyong 1990;Kim & Lee 1992;Basar, Ding & Kraetzig 1992;Sze 1994b;Guan & Tang 1995;Sze, Yi & Tay 1997), assumed strain methods (MacNeal 1978;Bathe & Dvorkin 1986;Huang & Hinton 1986;Park & Stanley 1986;Belytschko, Wong & Stolarski 1989, Flores, Onate & Zarate 1995, etc. Among them, the URI (uniformly reduced integrated) elements have an outstanding accuracy and computational ef®ciency.…”

Section: Introductionmentioning

confidence: 99%

“…Another stabilization technique was recently developed by the ®rst author using the stress version of the HellingerReissner Principle (Sze 1993;Sze 1994a;Sze 1994b;Sze, Yi & Tay 1997). In the technique, the higher order stress modes are strictly contravariant in nature and chosen by adhering to the covariant strain derived from the commutable zero energy modes of the geometrically regular URI elements.…”

Section: Introductionmentioning

confidence: 99%

A hybrid stress nine-node degenerated shell element for geometric nonlinear analysis

Sze

Zheng

1999

Computational Mechanics

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A stabilized nine-node degenerated shell element, previously derived for linear analysis by the admissible matrix formulation, is extended to geometrically nonlinear analysis. The assumed stress modes pertinent to stabilization matrix are contravariant in nature and their energy products with the displacement-derived covariant strain can be programmed without resorting to numerical integration and the Gram-Schmidt orthogonalization. Numerical tests show that its accuracy is virtually identical to the uniformly reduced integration element.

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“…An eight-node solid-shell element is derived for geometric non-linear analysis of homogeneous and laminated elastic shells to analyze piezoelectric structures. Following the common practice of resolving shear and trapezoidal lockings in this particular element configuration, ANS is employed to interpolate the natural thickness and transverse shear strains [12][13][14][15][16] . To overcome the thickness locking, an ad hoc modified generalized laminate stiffness matrix is adopted.…”

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confidence: 99%

A hybrid-stress solid-shell element for non-linear analysis of piezoelectric structures

Yao

Sze

2009

Sci. China Ser. E-Technol. Sci.

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This paper presents eight-node solid-shell elements for geometric non-linear analyze of piezoelectric structures. To subdue shear, trapezoidal and thickness locking, the assumed natural strain method and an ad hoc modified generalized laminate stiffness matrix are employed. With the generalized stresses arising from the modified generalized laminate stiffness matrix assumed to be independent from the ones obtained from the displacement, an extended Hellinger-Reissner functional can be derived. By choosing the assumed generalized stresses similar to the assumed stresses of a previous solid element, a hybrid-stress solid-shell element is formulated. The presented finite shell element is able to model arbitrary curved shell structures. Non-linear numerical examples demonstrate the ability of the proposed model to analyze nonlinear piezoelectric devices.piezoelectric structures, solid-shell element, hybrid-stress, geometric non-linearThe non-linear characteristics can significantly influence the performance of piezoelectric structures. The nonlinear problems of piezoelectric structures comprise of geometrically nonlinear and material nonlinearity. Generally, only the strong electric field subject to piezoelectric material, just the material nonlinearity of piezoelectric structures is considered [1][2][3][4] . When the electric field is not too large, geometrically nonlinear analysis is only considered for nonlinear problem. The researcher has already carried out many beneficial researches concerning geometrically non-lineariy [5][6][7][8][9][10][11] . The nonlinear electric potential distribution in piezoelectric layer was described by introducing internal electric potential node in ref. [5]. A solid shell element for large deformable composite structures with piezoelectric layers and active vibration control was presented in ref. [6]. But, an optimal number of enhancing assumed strain (EAS) parameters was used for composite structures in this reference. A modified generalized laminate stiffness matrix is adopted for composite structures in this paper.In this paper, geometric non-linear is considered only, but piezoelectric non-linearity is not taken ino account. An eight-node solid-shell element is derived for geometric non-linear analysis of homogeneous and laminated elastic shells to analyze piezoelectric structures. Following the common practice of resolving shear and trapezoidal lockings in this particular element configuration, ANS is employed to interpolate the natural thickness and transverse shear strains [12][13][14][15][16] . To overcome the thickness locking, an ad hoc modified generalized laminate stiffness matrix is adopted. Unlike EAS which can only reproduce accurate thickness stress and strain for homogeneous shells, the matrix also works properly for laminated shells. As a low-cost vehicle to enhance the element inplane response, selectively reduced integration (SRI) is applied to the in-plane shear strain. By taking the generalized stresses defined with respect to the

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An Explicit Hybrid Stabilized Eighteen‐node Solid Element for Thin Shell Analysis

Cited by 11 publications

References 0 publications

An eighteen-node hybrid-stress solid-shell element for homogenous and laminated structures

An eighteen-node hybrid-stress solid-shell element for homogenous and laminated structures

A hybrid stress nine-node degenerated shell element for geometric nonlinear analysis

A hybrid-stress solid-shell element for non-linear analysis of piezoelectric structures

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