scholarly journals Equilibrium of Two-Dimensional Cycloidal Pantographic Metamaterials in Three-Dimensional Deformations

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1523 ◽  
Author(s):  
Daria Scerrato ◽  
Ivan Giorgio
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Variational Formulation ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Element Analysis ◽  
Elastic Continuum ◽  
Bias Extension ◽  
Three Dimensional Space

A particular pantographic sheet, modeled as a two-dimensional elastic continuum consisting of an orthogonal lattice of continuously distributed fibers with a cycloidal texture, is introduced and investigated. These fibers conceived as embedded beams on the surface are allowed to be deformed in a three-dimensional space and are endowed with resistance to stretching, shearing, bending, and twisting. A finite element analysis directly derived from a variational formulation was performed for some explanatory tests to illustrate the behavior of the newly introduced material. Specifically, we considered tests on: (1) bias extension; (2) compressive; (3) shear; and (4) torsion. The numerical results are discussed to some extent. Finally, attention is drawn to a comparison with other kinds of orthogonal lattices, namely straight, parabolic, and oscillatory, to show the differences in the behavior of the samples due to the diverse arrangements of the fibers.

THREE DIMENSIONAL FINITE ELEMENT SIMULATION OF THE FRETTING WEAR PROBLEMS

2006 ◽  
Vol 20 (25n27) ◽  
pp. 3890-3895 ◽  
Author(s):  
CHOON YEOL LEE ◽  
JOON WOO BAE ◽  
BYUNG SUN CHOI ◽  
YOUNG SUCK CHAI
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Three Dimensional ◽  
Fretting Wear ◽  
Symmetric Model ◽  
Two Dimensional ◽  
Element Analysis ◽  
Inconel 690 ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

The structural integrity of steam generators in nuclear power plants is very much dependent upon the fretting wear characteristics of Inconel 690 U-tubes. In this study, a finite element analysis was used to investigate fretting wear on the secondary side of the steam generator, which arises from flow-induced vibrations (FIV) between the U-tubes and supports or foreign objects. Two-dimensional and three-dimensional finite element analyses were adopted to investigate the fretting wear problems. The purpose of the two-dimensional analysis, which simulated the contact between a punch and a plate, was to demonstrate the validity of using finite element analysis to analyze fretting wear problems. This was achieved by controlling the value of the wear constant and the number of cycles. The two-dimensional solutions obtained from this study were in good agreement with previous results reported by Strömberg. In the three-dimensional finite element analysis, a quarterly symmetric model was used to simulate tubes contacting at right angles. The results of the analyses showed donut-shaped wear along the contacting boundary, which is a typical feature of fretting wear.

Finite element analysis of peak stress and stress gradient at an elliptical through-hole

2017 ◽  
Vol 52 (5) ◽  
pp. 277-287
Author(s):  
Kristine Klungerbo ◽  
Gunnar Härkegård
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Plane Strain ◽  
Stress Gradient ◽  
Three Dimensional ◽  
Peak Stress ◽  
Two Dimensional ◽  
Element Analysis ◽  
Dimensional Finite Element ◽  
Through Hole

The peak stress and stress gradient (parameters required for fatigue strength assessment) at an elliptical through-hole in a wide plate under uniaxial tension have been studied by means of three-dimensional finite element analysis with high mesh density. Dimensionless variables have been used throughout the investigation. The accuracy of two-dimensional finite element analysis has been assessed by extrapolating peak stress at an elliptical hole to infinite plate width and mesh density and comparing the extrapolated value with the closed-form Kolosov–Inglis solution (deviation < 0.2%). First- and second-order elements with full and reduced integration have been employed. Methods for determining stress gradients, using a varying number of nodal stresses, have been investigated. The accuracy of three-dimensional finite element analysis has been assessed by comparing the plane-strain peak stress for an elliptical through-hole with the corresponding plane-strain value from two-dimensional analysis (deviation < 0.1%). Peak stresses at the apex of the elliptical through-hole have also been determined for this three-dimensional mesh assuming a free plate surface. In particular, beside the maximum peak stress and its location, peak stresses have been determined at the surface and at the mid-plane of the plate for thicknesses ranging from 0.2 to 10 times the axis of the elliptical hole. The stress gradients at these locations have been determined, too. The minimum stress gradient is observed at the location of maximum stress. For sufficiently thin and thick plates, the mid-plane stresses approach two-dimensional plane-stress and generalised plane-strain solutions, respectively.

scholarly journals Approximate solution of the Signorini problem by the finite element method in three-dimensional space

2021 ◽  
Vol 21 (2) ◽  
pp. 203-214
Author(s):  
A.Y. Zolotukhin ◽  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Signorini Problem ◽  
The Finite Element Method ◽  
Three Dimensional Space ◽  
Element Method

The finite element method is usually used for two-dimensional space. The paper investigates the finite element method for solving the Signorini problem in three-dimensional space.

scholarly journals Two - Dimensional Finite Element Analysis of Composite Patch Repairs Using Shell Laminate Elements

2003 ◽  
Vol 12 (2) ◽  
pp. 096369350301200
Author(s):  
George J Tsamasphyros ◽  
George N Kanderakis ◽  
Nikos K Furnarakis ◽  
Zaira P Marioli-Riga
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Element Analysis ◽  
Composite Patch ◽  
Out Of Plane ◽  
Dimensional Finite Element ◽  
Patch Repairs ◽  
Three Dimensional Finite Element

A host of one and two-sided composite patch reinforcements of metallic structures with different patch thickness were considered, in order to compare two-dimensional finite element analysis using shell laminate elements with three-dimensional finite element analysis. In order to verify the accuracy of this approach a parametric study has been performed and the 2D results were compared to the outcome of the corresponding three-dimensional finite element analysis, which accuracy has been experimentally verified in previous works. It was found that for the case of two-sided reinforcement the results obtained by the two methods were in very good agreement. For the case of one-sided reinforcement some deviation of the results of two-dimensional analysis has been observed, which was due to the tendency of the structure for out-of-plane bending, resulting from the bonding of a reinforcing patch to only one face of the structure. According to the results of this parametric study and since most aircraft structures are constrained against local out-of-plane bending (e.g. aircraft skins through stringers) two-dimensional finite elements analysis using shell laminate elements is proposed as an accurate and easy to use analysis tool for the design of both one and two-sided composite patch repairs of relatively simple structures.

Role of Material Properties in the Finite Element Solution for Three-Dimensional Composites—A Sensitivity Study

1995 ◽  
Vol 209 (2) ◽  
pp. 157-160
Author(s):  
H-B Hellweg ◽  
M A Crisfield
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Material Properties ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Sensitivity Study ◽  
Two Dimensional ◽  
Element Analysis ◽  
The Impact

Three-dimensional material test data for orthotropic laminae are difficult to obtain. Consequently, various simplifications are made for the material properties of individual layers in a finite element analysis, ranging from the assumption of transversely isotropic layers to applying two-dimensional material data in a three-dimensional analysis. In order to investigate the impact and validity of such simplifications, the sensitivity of the stresses and deformations in a finite element analysis on the material properties was investigated.

Study on Stability of High Embankment with Strong Weathering Filling under Complicated Stress Conditions

2011 ◽  
Vol 97-98 ◽  
pp. 78-84
Author(s):  
Sheng Chuan Liu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Three Dimensional ◽  
Strength Reduction ◽  
Slope Instability ◽  
Instability Criterion ◽  
Two Dimensional ◽  
Element Analysis ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

Strength reduction elasto-plastic finite element analysis defines the reduction factor when slope has been destroyed as the slope stability factor of safety, which combines with strength reduction technique, the limit equilibrium theory and the principle of elastic-plastic finite element. Three-dimensional finite element analysis should be used in stability analysis of slope because it can overcome the short advantages of two-dimensional finite element and can simulate the complex topographic and geological conditions. Based on the large-scale triaxial shear test, the modified Duncan-Chang model is established. Based on strength reduction elasto-plastic finite element, stability of high fill embankment was studied with three-dimensional finite element method considering the complex terrain conditions. Study results suggest that plastic strain and displacement mutant of slip surface node can be a sign of slope instability as a whole. At the same time calculation of three-dimensional finite element also does not converge. Therefore, it can be slope instability criterion calculate whether the finite element static analysis converges or not. On the other hand, stability safety factor of high fill embankment under three-dimensional conditions is larger than that of two-dimensional conditions, which shows that boundary conditions of high fill embankment enhance its stability.

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