On optimization approaches of hybrid stress elements

Wu, Chuanyong; Cheung, Y.K.

doi:10.1016/0168-874x(95)00023-0

Cited by 57 publications

(49 citation statements)

References 11 publications

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“…A "nal remark is that both the assumed natural transverse normal strain and the assumed natural transverse shear strains lead to failure in patch tests for solid elements whereas the scaling method [2,26,27] does not. In view of the fact that solid-shell elements are employed predominately for shell analyses, failure in patch tests for solid elements appears to be acceptable.…”

Section: Resolving Trapezoidal Lockingmentioning

confidence: 98%

“…There are at least two plausible ways to overcome the trapezoidal locking. The "rst method has been used in References [2,26,27] and is applicable only to hybrid elements. Essentially, it scales the leverage matrix rows associated with the non-constant transverse normal stress modes.…”

Section: Resolving Trapezoidal Lockingmentioning

confidence: 99%

“…The normalized de#ections under the loads for a number of four-node plane and arch elements are listed in Table I. The plane elements include the Taylor et al QM6 incompatible element [30], Pian}Sumihara hybrid-stress element [25] and its scaled version [26].…”

Section: Resolving Trapezoidal Lockingmentioning

confidence: 99%

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A hybrid stress ANS solid-shell element and its generalization for smart structure modelling. Part I?solid-shell element formulation

Sze

Yao

2000

Int. J. Numer. Meth. Engng.

144

114

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SUMMARYIn the recent years, solid-shell "nite element models which possess no rotational degrees of freedom and applicable to thin plate/shell analyses have attracted considerable attention. Development of these elements are not straightforward. Shear, membrane, trapezoidal, thickness and dilatational lockings must be envisioned. In this part of this paper, a novel eight-node solid-shell element is proposed. To resolve the shear and trapezoidal lockings, the assumed natural strain (ANS) method is resorted to. The hybrid-stress formulation is employed to rectify the thickness and dilatational locking. The element is computationally more e$cient than the conventional hybrid elements by adopting orthogonal-assumed stress modes and enforcing admissible sparsity in the #exibility matrix. Popular benchmark tests are exercised to illustrate the e$cacy of the elements. In Part II of the paper, the element will be generalized for smart structure modelling by including the piezoelectric e!ect.

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Section: Resolving Trapezoidal Lockingmentioning

confidence: 98%

Section: Resolving Trapezoidal Lockingmentioning

confidence: 99%

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A hybrid stress ANS solid-shell element and its generalization for smart structure modelling. Part I?solid-shell element formulation

Sze

Yao

2000

Int. J. Numer. Meth. Engng.

144

114

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“…The advantage common in IQFMM and OQFMM is that both the methods create simulation results with quadrilateral accuracy. Furthermore, highly accurate quadrilateral elements [11,12] such as incompatible models and hybrid strength models can be easily implemented, thereby improving accuracy drastically. Additionally, the introduction of the patch element in IQFMM increases the dimension of the global sti!ness matrix by only n K #n @ , and OQFMM does not increase the dimension at all.…”

Section: Discussion and Comparisonmentioning

confidence: 99%

Quadrilateral approaches for accurate free mesh method

Furukawa

Yang

Yagawa

et al. 2000

Int. J. Numer. Meth. Engng.

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SUMMARYThis paper presents the formulation of free mesh method and two approaches of the method by incorporating quadrilateral elements. The approaches do not have any di!erence with the original free mesh method in their fundamental algorithms, wherein local system equations with triangular elements are created nodewise to create the global system equations, and their implementation is therefore very easy. The "rst approach creates quadrilateral elements inside every triangular element, whilst quadrilateral elements are generated outside every triangular element in the second approach. The results of numerical examples indicate that the approaches improve the accuracy of free mesh method, further opening the possibility for more improvement using an accurate quadrilateral element.

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“…There exists a penalty-augmented modification of the Pian-Sumihara quadrilateral constructed by Wu and Cheung [63] that achieves distortion insensitivity at the cost of rank deficiency.…”

Section: Table 3 Tip Deflections (Exact=100) For Slender Isotropic Camentioning

confidence: 99%

Supernatural QUAD4: A template formulation

Felippa

2006

Computer Methods in Applied Mechanics and Engineering

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On optimization approaches of hybrid stress elements

Cited by 57 publications

References 11 publications

A hybrid stress ANS solid-shell element and its generalization for smart structure modelling. Part I?solid-shell element formulation

A hybrid stress ANS solid-shell element and its generalization for smart structure modelling. Part I?solid-shell element formulation

Quadrilateral approaches for accurate free mesh method

Supernatural QUAD4: A template formulation

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