A new eight‐node quadrilateral shear‐bending plate finite element

Polit, O.; Touratier, M.; Lory, Pierre

doi:10.1002/nme.1620370303

Cited by 64 publications

(59 citation statements)

References 28 publications

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“…The ÿnite element approximations of the assumed displacement ÿeld components are hereafter symbolically written as u h i (x 1 ; x 2 ; x 3 ) where the superscript h refers to the mesh L h e . From the kinematics (see equations (6), (12) and (15) …”

Section: Interpolation For the Bending-torsion-traction Beam Elementmentioning

confidence: 99%

“…We then obtain for a sandwich composite beam the following coe cients appearing in equations (12) due to symmetries of the problem:…”

Section: 22mentioning

confidence: 99%

“…12 The element has good features for all the standard requirements. Numerical analyses have been performed upon various sandwich beams, and a parametric study is given to show the e ects of diver parameters such as length-to-thickness ratio, shear modular ratio, boundary conditions, free and constrained torsion.…”

Section: Introductionmentioning

confidence: 99%

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AC1 finite element including transverse shear and torsion warping for rectangular sandwich beams

Ganapathi

Patel

Polit

et al. 1999

Int. J. Numer. Meth. Engng.

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SUMMARYA new three-noded C 1 beam ÿnite element is derived for the analysis of sandwich beams. The formulation includes transverse shear and warping due to torsion. It also accounts for the interlaminar continuity conditions at the interfaces between the layers, and the boundary conditions at the upper and lower surfaces of the beam. The transverse shear deformation is represented by a cosine function of a higher order. This allows us to avoid using shear correction factors. A warping function obtained from a three-dimensional elasticity solution is used in the present model. Since the ÿeld consistency approach is accounted for interpolating the transverse strain and torsional strain, an exact integration scheme is employed in evaluating the strain energy terms.Performance of the element is tested by comparing the present results with exact three-dimensional solutions available for laminates under bending, and the elasticity three-dimensional solution deduced from the de Saint-Venant solution including both torsion with warping and bending. In addition, three-dimensional solid ÿnite elements using 27 noded-brick elements have been used to bring out a reference solution not available for sandwich structures having high shear modular ratio between skins and core. A detailed parametric study is carried out to show the e ects of various parameters such as length-to-thickness ratio, shear modular ratio, boundary conditions, free (de Saint-Venant) and constrained torsion.

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Section: Interpolation For the Bending-torsion-traction Beam Elementmentioning

confidence: 99%

“…We then obtain for a sandwich composite beam the following coe cients appearing in equations (12) due to symmetries of the problem:…”

Section: 22mentioning

confidence: 99%

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AC1 finite element including transverse shear and torsion warping for rectangular sandwich beams

Ganapathi

Patel

Polit

et al. 1999

Int. J. Numer. Meth. Engng.

Self Cite

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show abstract

“…The kinematic equation (4) According to the transverse shear locking condition, the other shear bending generalized displacements and the rotation angle ω 3 h are interpolated by Lagrange quadratic functions, denoted by N q j (ξ ). This choice allows the same order of interpolation for both w h 0 ,1 and ω 3 h in the corresponding transverse shear strain components due to bending, thus avoiding transverse shear locking according to the field compatibility approach [Polit et al 1994].…”

Section: Resolution Of the Thermomechanical Problemmentioning

confidence: 99%

A refined sine-based finite element with transverse normal deformation for the analysis of laminated beams under thermomechanical loads

Vidal¹,

Polit²

2009

JOMMS

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In the framework of a sine model family, two new three-node beam finite elements including the transverse normal effect are designed for the analysis of laminated beams. They are based on a sine distribution with layer refinement and a second-order expansion for the deflection. The transverse shear strain is obtained using a cosine function, avoiding the use of shear correction factors. This kinematics accounts for the interlaminar continuity conditions on the interfaces between layers, and the boundary conditions on the upper and lower surfaces of the beam. A conforming FE approach is carried out using Lagrange and Hermite interpolations. It is important to notice that the number of unknowns is independent of the number of layers.Both mechanical and thermomechanical tests for thin and thick beams are presented in order to evaluate the capability of these new finite elements to give accurate results with respect to elasticity or finite element reference solutions. Both convergence velocity and accuracy are discussed and this new finite element yields very satisfactory results at a low computational cost. In particular, the transverse stress computed from the constitutive relation is well estimated with regards to classical equivalent single layer models. This work focuses on the necessity to take into account the transverse normal stress, especially for thick beam and coupled analysis.

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“…The second method [65] uses similar sampling points, but it evaluates the transverse shear strains directly in the middle of the element instead of using the mean value of two points as shown in Fig. 28b.…”

Section: Assumed Natural Strainmentioning

confidence: 99%

Rectangular shell elements based on the absolute nodal coordinate formulation

Hyldahl¹

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This thesis concerns the development of tools that are useful for designing machine systems and components in an virtual environment using flexible multibody dynamics. Initially, flexible multibody dynamics is briefly reviewed to explain available formalisms and possible applications of this method. Subsequently, attention is turned towards the analysis of structures that undergo large deformations and rotations using shell finite elements based on the absolute nodal coordinate formulation, ANCF. This topic is the focus for the remainder of the thesis.The thesis is divided into three main parts. The first part acts as a general introduction to ANCF based shell finite elements and sums up available elements found in the research literature. In the end, a new ANCF element developed during this PhD project is presented which gives enhanced modeling capabilities of problems including e.g. moving boundary conditions. The second part concerns the performance and behavior of a certain class of ANCF shell elements that are developed for analysis of thin shell structures. This includes discussions on differences concerning their kinematic descriptions and disclosure of certain issues regarding their performance. Those being sensitivity to irregular mesh, pour representation of curved structures and load dependent convergence when analyzing curved structures.The final part concerns the development of a new versatile ANCF shell element. This element is distinguished by being able to describe both thin and thick curved structures. This part contains a thorough derivation of its kinematics and stiffness description, as well as numerical examples to demonstrate its performance. However, this part of the study is not yet complete.Finally, the findings of this PhD project are summed up in a conclusion and possibilities for further studies and perspectives are outlined.v ResuméDenne afhandling omhandler udviklingen af vaerktøjer, som er nyttige til at designe maskiner og maskindele i et virtuelt miljø vha. fleksibel flerlegemedynamik. Indledningsvist gives der en kort gennemgang af den fleksible flerlegeme-dynamik, for at give et overblik over metoden og dens mulige anvendelser. Dernaest flyttes opmaerksomheden over på analyse af strukturer som udsaettes for store deformationer og rotationer vha. endelige skalelementer (eng: shell finite elements) baseret på absolutte knude koordinater (eng: absolute nodal coordinate formulation, ANCF). Dette emne vil vaere fokus i resten af afhandlingen.Afhandlingen er inddelt i 3 dele. Den første del giver en general introduktion til ANCF skal-elementer, og opsummerer de forskellige elementklasser som kan findes i litteraturen. Mod slutningen introduceres der et nyt ANCF skal-element, som er udviklet under dette ph.d.-projekt. Dette element muliggør forbedret modellering af problemer med mobile randbetingelser.Anden del omhandler effektiviteten og egenskaberne hos en saerlig klasse af ANCF skal-elementer, som er udviklet specielt til analyse af tynde skalstrukturer. Heri diskuteres der...

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A new eight‐node quadrilateral shear‐bending plate finite element

Cited by 64 publications

References 28 publications

AC1 finite element including transverse shear and torsion warping for rectangular sandwich beams

AC1 finite element including transverse shear and torsion warping for rectangular sandwich beams

A refined sine-based finite element with transverse normal deformation for the analysis of laminated beams under thermomechanical loads

Rectangular shell elements based on the absolute nodal coordinate formulation

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