scholarly journals Theorems of relations between elastic modulus and the stiffness matrix coefficients of isotropic homogeneous finite elements

2019 ◽  
Vol 221 ◽  
pp. 01030
Author(s):  
Aleksandr Matveev
Keyword(s):  
Finite Element ◽  
Elastic Modulus ◽  
Finite Elements ◽  
Stiffness Matrix ◽  
Elastic Moduli ◽  
Matrix Coefficients

This paper formulates theorems establishing a mutually unambiguous relation between the stiffness matrix coefficients and elastic moduli of an isotropic homogeneous finite element (FE), which allows explicitly expressing the elastic moduli of the FE via a group of its stiffness matrix coefficients.

scholarly journals FINITE ELEMENTS FOR MODELLING BEAMS AFFECTED BY A DISTRIBUTED LOAD

1999 ◽  
Vol 5 (2) ◽  
pp. 91-99
Author(s):  
Stanislovas Kalanta
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Strain Field ◽  
Stiffness Matrix ◽  
Stress And Strain ◽  
Middle Section ◽  
Approximation Function ◽  
Distributed Load ◽  
Middle Node ◽  
Fifth Order

Usually a finite element with cubic deflection approximation function is applied when evaluating the stress and strain field of bar structures. But such an element only approximately evaluates the actual strain field of the bar affected by a distributed load. The improved finite elements (Fig 1, 2) with fourth and fifth-order deflection approximation functions (1), (6) and (13) are presented in the actual manuscript. The fifth-order deflection approximation function is used for modelling the beams affected by a linearly distributed load (11). The plain bending of the finite element is modelled by 5 and 6 freedom degrees. The additional 5th and 6th freedom degrees are the deflection and deviation of the middle node of element (Fig 2). The element stiffness matrices (Table 1, 2) and node force vectors are presented. The created finite elements exactly modells the stress and strain field of bars, which are affected by distributed load, and also allow to compute directly the middle section displacements of bars. It creates conditions for diminishing the volume of problems and obtaining information, which is necessary to be analysed later. The reduced finite elements (Fig 4) are created by the elimination of the internal freedom degrees. Their number of freedom degrees is decreased up to the number of freedom degrees of a usually applied finite element. But the reduced finite elements have all afore-mentioned qualities. Formulas (20) and (21) are derived expressing the middle node displacements by the final node displacements. These formulas allow to compute the middle section displacements of the bar already after the solution of equation system. The proposed reduced elements can be introduced and applied in engineering practice very easily, because their stiffness matrix coincide with the stiffness matrix of a usual bar finite element. The created elements with internal freedom degrees are very important for the problems of structures optimization with displacement constraints, because the constraint of bar middle section displacement can form just in case, when this displacement is one of the problem's unknown. Also it is very important to decrease the number of unknowns of optimization problem.

scholarly journals Regularities of stress state of unsupported working occurring in a layered massif

2019 ◽  
Vol 109 ◽  
pp. 00100
Author(s):  
Oleksii Tiutkin ◽  
Nataliia Petrosian ◽  
Anatolii Radkevych ◽  
Ahmad Alkhdour
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Modulus ◽  
Stress State ◽  
Numerical Analysis ◽  
Elastic Moduli ◽  
Element Model ◽  
Stress Components ◽  
The Matrix ◽  
Numerical Finite Element

The paper defines the regularities of stress state of unsupported working occurring in a layered massif. The relevance of the performed research is substantiated by the importance of determining the stresses of the contour of unsupported working when the elastic modulus of the matrix and the layer is varied. Since the application of analytic methods for this case is complex, we used a numerical finite element method, implemented in the SCAD. We developed a finite-element model of the above working, where the elastic moduli of the matrix and the layer varied greatly, while its position was unchanged (the layer laying in the middle of the working). The results of the numerical analysis allowed us to build the regularities of three stress components. In order to normalize cases of elastic modulus variation, a dimensionless χ -parameter is introduced which characterizes the relation between the elastic modulus of the matrix and the layer. The obtained regularities of the stress state of the χ-parameter have a functional character and allow to determine the stresses on the contour of the unsupportedworking, depending on the relation between the elastic moduli of the matrix and the layer for all possible spectrum of these parameters.

EFFECT OF MECHANICAL PROPERTIES OF THE SUBSTRATE TISSUES ON THE DETERMINATION OF ELASTIC MODULUS OF THE SCLERA USING INDENTATION TEST

2016 ◽  
Vol 16 (07) ◽  
pp. 1650085
Author(s):  
XIUQING QIAN ◽  
KUNYA ZHANG ◽  
ZHICHENG LIU
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Elastic Modulus ◽  
Elastic Moduli ◽  
Indentation Depth ◽  
Vitreous Body ◽  
Indentation Test ◽  
Posterior Pole

The sclera is an important connective tissue that protects the sensitive layers within the eyeball. Identifying the mechanical properties of the sclera near the posterior pole is necessary to analyze the deformation of the sclera and stresses changing in the optic nerve head tissues. We propose a method to determine the mechanical properties of the sclera using dimensional analysis, finite element method and the indentation test. The elastic moduli of the sclera for different indentation depths and positions were identified. We found that the elastic moduli of the sclera varied with indentation depth. This was due to the effect of the mechanical properties of the substrate tissues inside the sclera. The elastic modulus of the choroid had the biggest effect on the determination of elastic modulus of the sclera, whereas that of the vitreous body could be ignored when the ratio of the indentation depth to the thickness of the sclera was less than 0.5. The effects of mechanical properties of the substrate tissues become more pronounced at greater indentation depths.

Three Dimentional Finite Element Modeling of Microstructural Development of Nacre in Seashells and Implication on Mineralization of CaCO3

1999 ◽  
Vol 599 ◽  
Author(s):  
D. R. Katti ◽  
K. S. Katti
Keyword(s):  
Finite Element ◽  
Elastic Modulus ◽  
Organic Phase ◽  
Elastic Moduli ◽  
Three Dimensional ◽  
Tensile Tests ◽  
Multilayered Structure ◽  
Elastic Behavior ◽  
Microstructural Development ◽  
Organic Layer

AbstractThree dimensional finite element models of nacre were constructed based on reported microstructural studies on the ‘brick and mortar’ micro-architecture of nacre. 3D eight noded isoparametric brick elements were used to design the microarchitecture of nacre. Tensile tests were simulated using this model at stresses of 2 MPa which occur well within the elastic regime of nacre and thus effects related to locus and extent of damage were ignored. The reported values of elastic moduli of organic (0.005 GPa) and aragonitic platelets (205 GPa) were used in our simulations and the resulting displacements were found to be extremely large and corresponding to a very low modulus of 0.011 GPa. The reported elastic modulus of nacre is of the order of 50 GPa. The large displacements can possibly result from two possibilities. Firstly. the organic layer due to its multilayered structure is possibly composed of distinct layers of different elastic moduli. A significantly higher modulus of the organic phase may be possible near the organic-inorganic interface. Simulations using variable elastic moduli for the organic phase suggest that an elastic modulus of 15 GPa is consistent with the observed elastic behavior of nacre. A second possibility for the observed higher elastic modulus may arise from localized platelet-platelet contact. Since the observed modulus of nacre lies within the above two extremes (i.e. 15 GPa and 205 GPa) it is suggested that a combination of the two, i.e. a higher modulus of the organic phase near the organic-inorganic interface and localized platelet-platelet contact can result in the observed elastic properties of nacre.

Transverse Natural Vibrations of a Cracked Beam Loaded with a Constant Axial Force

1993 ◽  
Vol 115 (4) ◽  
pp. 524-528 ◽  
Author(s):  
M. Krawczuk ◽  
W. M. Ostachowicz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Numerical Calculations ◽  
Open Crack ◽  
Natural Vibrations ◽  
Cracked Beam ◽  
Matrix Calculation

The influence of transverse, one-edge open cracks on the natural frequencies of the cantilever beam subjected to vertical loads is analyzed. A finite element method (FE) is used for modelling the beam. A part of the cracked beam is modelled by beam finite elements with an open crack. Parts of the beam without a crack are modelled by standard beam finite elements. An algorithm of a linear stiffness matrix and a geometrical stiffness matrix calculation for a cracked element is presented. The results of numerical calculations obtained for the presented model are compared with the results of analytical calculations given in the literature and also with the results of numerical calculations obtained for a model with geometrical stiffness matrix of uncracked elements.

scholarly journals A New Mixed Functional-probabilistic Approach for Finite Element Accuracy

2020 ◽  
Vol 20 (4) ◽  
pp. 799-813
Author(s):  
Joël Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Asymptotic Relation ◽  
Probabilistic Approach ◽  
Random Variable ◽  
High Order ◽  
Relative Accuracy ◽  
The Difference ◽  
New Perspective

AbstractThe aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble–Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements {P_{k}} and {P_{m}} ({k<m}). Then we analyze the asymptotic relation between these two probabilistic laws when the difference {m-k} goes to infinity. New insights which qualify the relative accuracy in the case of high order finite elements are also obtained.

scholarly journals 3D Finite Element Analysis of Rotary Instruments in Root Canal Dentine with Different Elastic Moduli

2021 ◽  
Vol 11 (6) ◽  
pp. 2547 ◽  
Author(s):  
Carlo Prati ◽  
João Paulo Mendes Tribst ◽  
Amanda Maria de Oliveira Dal Piva ◽  
Alexandre Luiz Souto Borges ◽  
Maurizio Ventre ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Root Canal ◽  
Elastic Moduli ◽  
Reaction Force ◽  
Von Mises Stress ◽  
Elastic Behavior ◽  
Element Analysis ◽  
Heat Treated ◽  
Von Mises

The aim of the present investigation was to calculate the stress distribution generated in the root dentine canal during mechanical rotation of five different NiTi endodontic instruments by means of a finite element analysis (FEA). Two conventional alloy NiTi instruments F360 25/04 and F6 Skytaper 25/06, in comparison to three heat treated alloys NiTI Hyflex CM 25/04, Protaper Next 25/06 and One Curve 25/06 were considered and analyzed. The instruments’ flexibility (reaction force) and geometrical features (cross section, conicity) were previously investigated. For each instrument, dentine root canals with two different elastic moduli(18 and 42 GPa) were simulated with defined apical ratios. Ten different CAD instrument models were created and their mechanical behaviors were analyzed by a 3D-FEA. Static structural analyses were performed with a non-failure condition, since a linear elastic behavior was assumed for all components. All the instruments generated a stress area concentration in correspondence to the root canal curvature at approx. 7 mm from the apex. The maximum values were found when instruments were analyzed in the highest elastic modulus dentine canal. Strain and von Mises stress patterns showed a higher concentration in the first part of curved radius of all the instruments. Conventional Ni-Ti endodontic instruments demonstrated higher stress magnitudes, regardless of the conicity of 4% and 6%, and they showed the highest von Mises stress values in sound, as well as in mineralized dentine canals. Heat-treated endodontic instruments with higher flexibility values showed a reduced stress concentration map. Hyflex CM 25/04 displayed the lowest von Mises stress values of, respectively, 35.73 and 44.30 GPa for sound and mineralized dentine. The mechanical behavior of all rotary endodontic instruments was influenced by the different elastic moduli and by the dentine canal rigidity.

Finite Element Analysis of Creep Damage Behavior Near the Cavity on Bimaterial Interface

2006 ◽  
Vol 324-325 ◽  
pp. 951-954 ◽  
Author(s):  
Qing Min Yu ◽  
Zhu Feng Yue ◽  
Yong Shou Liu
Keyword(s):  
Finite Element ◽  
Elastic Moduli ◽  
Elastic Stress ◽  
Creep Damage ◽  
Ductile Material ◽  
Bimaterial Interface ◽  
Modulus Ratio ◽  
Element Analysis ◽  
Damage Law ◽  
The Difference

Fracture along an interface between materials plays a major role in failure of material. In this investigation, finite element calculations with Kachanov–Rabotnov damage law were carried out to study the creep damage distribution near the interface cavity in bimaterial specimens. The specimens with central hole were divided into three types. The material parameters of K-R law used in this paper were chosen for a brittle material and ductile material. All calculations were performed under four load cases. Due to the difference between elastic moduli of the bounded materials, the elastic stress field as a function of the Young’s modulus ratio (R=E1/E2) was determined. At the same time, the influence of model type on elastic stress distribution near the cavity was considered. Under the same conditions, the material with larger modulus is subjected to larger stress. The creep damage calculations show that the location of the maximum damage is different for each model. The distributions of creep damage for all three models are dependent on the material properties and load cases.

scholarly journals The Effects of Creep on Elastic Modulus Measurement Using Nanoindentation

2000 ◽  
Vol 649 ◽  
Author(s):  
G. Feng ◽  
A.H.W. Ngan
Keyword(s):  
Elastic Modulus ◽  
Elastic Deformation ◽  
Elastic Moduli ◽  
Holding Time ◽  
Time Dependent ◽  
Nanoindentation Test ◽  
Modification Method ◽  
Unloading Rate ◽  
Modulus Measurement

ABSTRACTDuring the unloading segment of nanoindentation, time dependent displacement (TDD) accompanies elastic deformation. Consequently the modulus calculated by the Oliver-Pharr scheme can be overestimated. In this paper we present evidences for the influence of the measured modulus by TDD. A modification method is also presented to correct for the effects of TDD by extrapolating the TDD law in the holding process to the beginning of the unloading process. Using this method, the appropriate holding time and unloading rate can be estimated for nanoindentation test to minimise the effects of TDD. The elastic moduli of three materials computed by the modification method are compared with the results without considering the TDD effects.

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