A three-node shell element based on the discrete shear gap and assumed natural deviatoric strain approaches

Rama, Gil; Marinković, Dragan; Zehn, Manfred

doi:10.1007/s40430-018-1276-4

Cited by 5 publications

(6 citation statements)

References 44 publications

(46 reference statements)

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“…The developed element combines features of already developed and in literature available shell elements. It implements the mechanical field of the element proposed by Rama et al [20] that was also extended to composite laminates by Rama et al [21], and the electric field, including the both way coupling between the two, as described in the work by Marinkovic and Rama [22]. As the mentioned references provide detailed derivations, the element description given in this section will not go into all the details, but for the sake of completeness, some major aspects of the development will be presented together with the most important matrices.…”

Section: Piezoelectric 3-node Shell Element With Drilling Degree Of Freedommentioning

confidence: 99%

“…The plate stiffness is obtained by deriving the bending strains directly from the displacement field. The resulting bending strain-displacement matrix reads [20]:…”

Section: Fig 2 3-node Shell Element As a Superposition Of Plate And Membrane Elementsmentioning

confidence: 99%

“…The developed element implements the discrete shear gap technique originally proposed by Bletzinger et al [23] and improved by the cell strain smoothing technique suggested by Ngyen-Thoi et al [24]. The resulting transverse shear strain-displacement matrix for a triangular element is given by [20]…”

Section: Fig 2 3-node Shell Element As a Superposition Of Plate And Membrane Elementsmentioning

confidence: 99%

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Abaqus Implementation of a Corotational Piezoelectric 3-Node Shell Element With Drilling Degree of Freedom

Marinković

Rama²,

Zehn³

2019

FU Mech Eng

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Integration of classical, passive structures and active elements based on multi-functional materials resulted in a novel structural concept denoted as active structures. The new structural systems are characterized by self-sensing and actuation. Coupling the two distinctive features by means of a controller enables a number of exquisite functionalities such as vibration suppression, noise attenuation, shape control, structural health monitoring, etc. Reliable, accurate and highly efficient modeling tools are an important ingredient of the active structure design. This paper addresses the Abaqus implementation of a recently developed piezoelectric 3-node shell element. The element uses co-rotational formulation to cover geometric nonlinearities. Special techniques are used to address the issues originating from low-order interpolation functions. The discrete shear gap is used to resolve the shear locking, while the assumed natural deviatoric strain technique improves the membrane behavior. Examples are computed in Abaqus upon implementation of the developed element.

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Section: Piezoelectric 3-node Shell Element With Drilling Degree Of Freedommentioning

confidence: 99%

“…The plate stiffness is obtained by deriving the bending strains directly from the displacement field. The resulting bending strain-displacement matrix reads [20]:…”

Section: Fig 2 3-node Shell Element As a Superposition Of Plate And Membrane Elementsmentioning

confidence: 99%

Section: Fig 2 3-node Shell Element As a Superposition Of Plate And Membrane Elementsmentioning

confidence: 99%

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Abaqus Implementation of a Corotational Piezoelectric 3-Node Shell Element With Drilling Degree of Freedom

Marinković

Rama²,

Zehn³

2019

FU Mech Eng

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“…Finite element method is an efficient approach for numerical analysis of shell structures. Over last decades, a number of studies have been done to develop an efficient shell element with simple formulation [1][2][3]. There are three types of shell element that can be employed in shell analysis: (1) flat shell element which is formed by superposition of membrane and plate bending elements; (2) degenerated shell element which is formulated based on solid-shell theory; and (3) curved shell element which is defined based on classical shell theory.…”

Section: Introductionmentioning

confidence: 99%

An efficient three-node triangular Mindlin–Reissner flat shell element

Sangtarash

Arab

Sohrabi

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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Shell elements are extensively used by engineers for modeling the behavior of shell structures. Among common shell elements, triangular shell elements are not influenced by element warping. This paper proposes a new three-node triangular flat shell element with six degrees of freedom per each node, named TMRFS. The element is formed by assemblage of new bending and membrane elements. The bending element is formulated based on the hybrid displacement function element method and Mindlin-Reissner plate theory. In this element, an assumed displacement function is employed as the trial function. The membrane component is an unsymmetric triangular membrane element with drilling vertex rotations. The membrane element employs two different types of displacement fields as the test and trial functions. The test function is a displacement field which is the same as one used in well-known Allman triangular element. Meanwhile, instead of displacement field, the analytical stress field is considered as the trial function. Numerical tests show that the accuracy of the proposed flat shell element is reasonable in comparison with some popular triangular elements and its performance is insensitive to geometry, load and boundary conditions. Moreover, the proposed element preserves the advantages of its formulation including free of membrane locking, shear locking and stiffness matrix singularity problems.

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“…In other words, the shell buckling is a major part of thin-walled structures designing. Many researches were also implemented on the buckling analysis of shells theoretically and numerically [14][15][16][17][18][19][20]. A review article, in which all researches about the buckling of composite cylinders until 1975 had been explained briefly, was prepared by Simitses [21].…”

Section: Introductionmentioning

confidence: 99%

Shell instability analysis by using mixed interpolation

Rezaiee‐Pajand

Masoodi

2019

J Braz. Soc. Mech. Sci. Eng.

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In this paper, buckling and post-buckling behavior of plates and shells are investigated. An efficient triangular shell element having six nodes is employed in this study. To consider large deflection and rotation, total Lagrangian formulation is utilized. The authors employ mixed interpolation for strain fields to deviate shear and membrane locking phenomena. The effects of different types of boundary conditions and geometry properties of plates and shells are studied. An almost complete literature review is also provided to show the progress of researches about the current topics. Various states of buckling including bifurcation and snap-through are assessed in different problems. In this study, the popular benchmarks of shell structures are analyzed to show the accuracy and capability of element. In addition, some new benchmarks which can be used by other researchers are also introduced and solved. Further, a comparison study between the proposed element and NLDKGQ element in OpenSees software is implemented for some complex curved shell structures.

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A three-node shell element based on the discrete shear gap and assumed natural deviatoric strain approaches

Cited by 5 publications

References 44 publications

Abaqus Implementation of a Corotational Piezoelectric 3-Node Shell Element With Drilling Degree of Freedom

Abaqus Implementation of a Corotational Piezoelectric 3-Node Shell Element With Drilling Degree of Freedom

An efficient three-node triangular Mindlin–Reissner flat shell element

Shell instability analysis by using mixed interpolation

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