A refined four-noded membrane element with rotational degrees of freedom

MacNeal, Richard H.; Harder, R. L.

doi:10.1016/0045-7949(88)90094-6

Cited by 159 publications

(75 citation statements)

References 10 publications

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“…where the generalized variables fd e g (and the second time derivatives) are restricted to the domain of integration A e and an approximation is considered at a local level in each finite element as stated in (28). As usually, the relation between the elemental degrees of freedom and the global ones is established through the connectivity matrices ½R e , expressed as:…”

Section: Weak Form Finite Element Discretizationmentioning

confidence: 99%

“…To stabilize the assembly it can be used a membrane formulation with drilling degrees of freedom [28][29][30] or a fictitious drilling stiffness [24,31,32].…”

Section: Drilling Degrees Of Freedommentioning

confidence: 99%

“…The drilling associated spurious zero energy mode is avoided applying the stabilization procedure proposed by MacNeal and Harder [28].…”

Section: Rank Deficiencymentioning

confidence: 99%

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A generalized layerwise finite element for multi-layer damping treatments

2005

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This paper presents a 4-node facet type quadrangular shell finite element, based on a layerwise theory, developed for dynamic modelling of laminated structures with viscoelastic damping layers. The bending stiffness of the facet shell element is based on the Reissner-Mindlin assumptions and the plate theory is enriched with a shear locking protection adopting the MITC approach. The membrane component is corrected by using incompatible quadratic modes and the drilling degrees of freedom are introduced through a fictitious stiffness stabilization matrix. Linear static tests, using several pathological tests, showed good and convergent results. Dynamic analysis evaluation is provided by using two eigenproblems with exact analytical solution, as well as a conical sandwich shell with a closed-form analytical solution and a semianalytical ring finite element solution. The applicability of the proposed finite element to viscoelastic core sandwich plates is assessed through experimental validation.

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Section: Weak Form Finite Element Discretizationmentioning

confidence: 99%

“…To stabilize the assembly it can be used a membrane formulation with drilling degrees of freedom [28][29][30] or a fictitious drilling stiffness [24,31,32].…”

Section: Drilling Degrees Of Freedommentioning

confidence: 99%

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A generalized layerwise finite element for multi-layer damping treatments

2005

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“…Compared with the bilinear compatible quadrilateral membrane element formulation, more accurate results are obtained when in-plane rotations are used as an extra DOF. However, in certain studies additional dependent nodes are needed for the formulation, such as an underlying eight-noded element in [3]. Similarly, Allman [4] formulated a quadrilateral element from four triangular elements with rotational DOF.…”

Section: Introductionmentioning

confidence: 98%

Static and dynamic convergence studies of a four‐noded membrane finite element with rotational degrees of freedom based on displacement superposition

Çalık-Karaköse

Askes

2010

Numer Methods Biomed Eng

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SUMMARYStatic and dynamic performance tests of a four-noded quadrilateral isoparametric membrane finite element enriched with rotational degrees of freedom (DOF) are presented. The formulation is based on displacement superposition whereby the in-plane displacements are decomposed additively into a regular, low-order contribution (governed by the nodal in-plane displacements) and a higher-order contribution (governed by the nodal in-plane rotations). The sensitivity of the element to element distortion and element aspect ratio is investigated. Comparisons with standard bilinear finite elements are made for static and dynamic loading case. It is demonstrated that the studied element exhibits an accuracy per DOF that is superior to the standard bilinear finite element.

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“…Q4R the quasi-conforming counterpart of AQ proposed by Lin et al [10] Q4S: Mac-Neal and Harder's refined membrane element with drilling degree of freedom [11] 07 the Sze element [12] Q8: the Mac -Neal [13] Allman element [8] …”

Section: Components Ie Nine Stress Modes Are Involved Since the Amentioning

confidence: 99%

A new strain-based finite element for plane elasticity problems

Hamadi

Ayoub

Maalem³

2016

Engineering Computations

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent A New Strain-Based Finite Element for Plane Elasticity Problems ABSTRACTIn this paper, a new quadrilateral strain-based element is developed. The element has five nodes, four at the corners as well as an internal node. Through the introduction of the internal node, the numerical performance of the element proved to be superior to existing elements, even though a static condensation is required. From several numerical examples, it is shown that convergence can be achieved with the use of only a small number of finite elements. The proposed element can be used to solve general plane elasticity problems resulting in excellent results. The results obtained are comparable with those given by the robust element Q8.

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A refined four-noded membrane element with rotational degrees of freedom

Cited by 159 publications

References 10 publications

A generalized layerwise finite element for multi-layer damping treatments

A generalized layerwise finite element for multi-layer damping treatments

Static and dynamic convergence studies of a four‐noded membrane finite element with rotational degrees of freedom based on displacement superposition

A new strain-based finite element for plane elasticity problems

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