scholarly journals The J-area integral applied in peridynamics

2021 ◽  
Author(s):  
Christer Stenström ◽  
Kjell Eriksson
Keyword(s):  
Exact Analytical Solution ◽  
Infinite Plate ◽  
Contour Integral ◽  
Mode I ◽  
Integration Contour ◽  
Original Formulation ◽  
Element Analysis ◽  
Central Crack ◽  
Area Integral ◽  
The Finite Element Analysis

AbstractThe J-integral is in its original formulation expressed as a contour integral. The contour formulation was, however, found cumbersome early on to apply in the finite element analysis, for which method the more directly applicable J-area integral formulation was later developed. In a previous study, we expressed the J-contour integral as a function of displacements only, to make the integral directly applicable in peridynamics (Stenström and Eriksson in Int J Fract 216:173–183, 2019). In this article we extend the work to include the J-area integral by deriving it as a function of displacements only, to obtain the alternative method of calculating the J-integral in peridynamics as well. The properties of the area formulation are then compared with those of the contour formulation, using an exact analytical solution for an infinite plate with a central crack in Mode I loading. The results show that the J-area integral is less sensitive to local disturbances compared to the contour counterpart. However, peridynamic implementation is straightforward and of similar scope for both formulations. In addition, discretization, effects of boundaries, both crack surfaces and other boundaries, and integration contour corners in peridynamics are considered.

scholarly journals Experimental determination and finite element analysis of coefficients of the multi-parameter Williams series expansion in the vicinity of the crack tip in linear elastic materials. Part II

2021 ◽  
pp. 72-85
Author(s):  
L. V Stepanova
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Rectangular Plate ◽  
Series Expansion ◽  
Numerical Solutions ◽  
Element Analysis ◽  
Central Crack ◽  
The Finite Element Analysis ◽  
Abaqus Software

In this study coefficients of the multi-parameter Williams power series expansion for the stress field in the vicinity of the central crack in the rectangular plate and in the semi-circular notched disk under bending are obtained by the use of the finite element analysis. In SIMULIA Abaqus, the finite element analysis software, the numerical solutions for these two cracked geometries are found. The rectangular plate with the central crack has the geometry similar to the geometry used in the digital photoelasticity. Numerical simulations of the same cracked specimen as in the experimental photoelasticity method are performed. The numerical solutions obtained are utilized for the determination of the coefficients of the Williams series expansion. The higher-order coefficients are extracted from the finite element method calculations implemented in Simulia Abaqus software package and the outcomes are compared to experimental values. Determination of the coefficients of the terms of this series is performed using the least squares-based regression technique known as the over-deterministic method, for which stresses data obtained numerically in SIMULIA Abaqus software are taken as inputs. The plate with a small central crack has been considered either. This kind of the cracked specimen has been utilized for comparison of coefficients of the Williams series expansion obtained from the finite element analysis with the coefficients known from the theoretical solution based on the complex variable theory in plane elasticity. It is shown that the coefficients of the Williams series expansion match with good accuracy. The higher-order terms in the Williams series expansion for the semi-circular notch disk are found.

scholarly journals A M-theta Method on Mode I and II Failure of Two Cameroonian Hardwoods in Bending

2019 ◽  
Vol 4 (3) ◽  
pp. 176-182
Author(s):  
Hervice Kouefouet ◽  
Jeanne Sandrine Takam Mabekou ◽  
Joseph Albert Fosting Mukam ◽  
Pierre Kisito Talla ◽  
Rostand Pitti Moutou
Keyword(s):  
Finite Element ◽  
Bending Test ◽  
Mode I ◽  
Pure Mode ◽  
Element Analysis ◽  
Finite Element Software ◽  
Path Independence ◽  
The Finite Element Analysis ◽  
Edge Notch ◽  
Theta Method

This work deals with the numerical simulation on bending test to characterize two Cameroonian hardwoods under mode I and II loading for different crack lengths. The finite element analysis for fracture in orthotropic medium is developed. The algorithm of fracture is introduced in a finite element software Cast3M. According to the Mtheta method, the calculation of the stress intensity factors and the energy release rate for pure mode I and II fracture are deduced using a SENB (Single Edge Notch Bending) specimen. The path independence of Mθ-method on the specimen is confirmed.

Analysis of Mode-I crack growth arresting mechanism in curved laminated joint

2019 ◽  
Vol 08 (01) ◽  
pp. 1950001
Author(s):  
N. Jeevan Kumar
Keyword(s):  
Research Work ◽  
Crack Arrest ◽  
Primary Objective ◽  
Mode I ◽  
Closure Technique ◽  
Element Analysis ◽  
Fea Model ◽  
The Finite Element Analysis ◽  
Bonded Joint ◽  
Crack Retardation

The critical damage for carbon fiber structures, which are being employed in aircraft structures, is known as delamination/crack. Fasteners are commonly installed to arrest the delamination by clamping the laminate together. Fasteners are installed in each corner of the delaminated zone to provide significant arrest capability, shifting the failure mode away from delamination under most conditions. The Finite Element Analysis (FEA) model is constructed to study the effectiveness of the fastener as crack arrest mechanism. The FEA results show that the fastener provides significant crack retardation capability in Mode-I condition. An analytical model is developed for the delamination embedded between the skin and stiffener interface of the joint. The fasteners are modeled with spring elements. The analysis is solved with Virtual Crack Closure Technique (VCCT) approach. The primary objective of the current research work is to enhance the safety of bonded joint by providing arrest mechanisms.

Pseudo-Interference Stiffness Estimation in Gear Teeth Contact

1996 ◽  
Author(s):  
Geunho Lee ◽  
Kazem Kazarounian ◽  
Herbert A. Koenig
Keyword(s):  
Exact Analytical Solution ◽  
Contact Region ◽  
Accurate Estimation ◽  
Analysis Method ◽  
Mesh Stiffness ◽  
Element Analysis ◽  
Gear Teeth ◽  
Finite Element Analysis Method ◽  
The Finite Element Analysis ◽  
Stiffness Characteristics

Abstract One of the important factors in gear dynamic analysis is accurate estimation of the mesh stiffness. To accurately model the mesh stiffness characteristics, the Pseudo-Interference Stiffness Estimation (PISE) method is proposed. PISE draws upon the finite element analysis method. It also analyzes the non-linear, geometric based characteristics of the local contact region. Consequently, PISE is used to model the elastic deformation at the mesh regions and estimate the corresponding stiffnesses in the elastic region. In this paper, as an example, PISE is applied to the two cylinders’ contact problem. Thus the PISE solution is compared with exact analytical solution which is readily available in literature. Subsequently, PISE is used to model the contact region and estimate the mesh stiffness of a gear system.

Experimental and numerical analysis of piezoelectric active repair of edge-cracked plate

2018 ◽  
Vol 29 (18) ◽  
pp. 3656-3666 ◽  
Author(s):  
Ahmed Abuzaid ◽  
Meftah Hrairi ◽  
MSI Shaik Dawood
Keyword(s):  
Finite Element ◽  
Analytical Model ◽  
Piezoelectric Actuator ◽  
Experimental Results ◽  
Weight Functions ◽  
Mode I ◽  
Element Analysis ◽  
Cracked Plate ◽  
The Finite Element Analysis ◽  
Relative Errors

This article proposes an alternative model for active repair for an edge-cracked plate with adhesively bonded piezoelectric actuator. It computes the Mode-I stress intensity factor (SIF) produced by the piezoelectric actuators using appropriate derived geometrical weight functions. Furthermore, this article presents an experimental study to verify the proposed analytical model and the finite element analysis using ANSYS software. Therefore, the analytical, finite element and experimental results for Mode-I opening of the crack conditions are demonstrated. Parametric analysis to understand the influence and to study the efficiency of the piezoelectric actuator on mitigation of the Mode-I SIF was conducted. The obtained analytical solution is applicable in the calculation of Mode-I SIF with reasonable accuracy. The result indicated that the maximum reduction of SIF is achieved with the application of high external voltage and thin thickness actuator. The relative errors of the analytical model and the experimental results are less than 10% in all the cases studied in this article.

A two degrees of freedom comb capacitive-type accelerometer with low cross-axis sensitivity

2019 ◽  
Vol 13 (3) ◽  
pp. 5334-5346
Author(s):  
M. N. Nguyen ◽  
L. Q. Nguyen ◽  
H. M. Chu ◽  
H. N. Vu
Keyword(s):  
Degrees Of Freedom ◽  
Proof Mass ◽  
Vibration Modes ◽  
Electrode Structure ◽  
Element Analysis ◽  
Mechanical Coupling ◽  
Fully Differential ◽  
Mode Effects ◽  
The Finite Element Analysis ◽  
Cross Axis

In this paper, we report on a SOI-based comb capacitive-type accelerometer that senses acceleration in two lateral directions. The structure of the accelerometer was designed using a proof mass connected by four folded-beam springs, which are compliant to inertial displacement causing by attached acceleration in the two lateral directions. At the same time, the folded-beam springs enabled to suppress cross-talk causing by mechanical coupling from parasitic vibration modes. The differential capacitor sense structure was employed to eliminate common mode effects. The design of gap between comb fingers was also analyzed to find an optimally sensing comb electrode structure. The design of the accelerometer was carried out using the finite element analysis. The fabrication of the device was based on SOI-micromachining. The characteristics of the accelerometer have been investigated by a fully differential capacitive bridge interface using a sub-fF switched-capacitor integrator circuit. The sensitivities of the accelerometer in the two lateral directions were determined to be 6 and 5.5 fF/g, respectively. The cross-axis sensitivities of the accelerometer were less than 5%, which shows that the accelerometer can be used for measuring precisely acceleration in the two lateral directions. The accelerometer operates linearly in the range of investigated acceleration from 0 to 4g. The proposed accelerometer is expected for low-g applications.

Tread Depth Effects on Tire Rolling Resistance

2001 ◽  
Vol 29 (3) ◽  
pp. 134-154 ◽  
Author(s):  
J. R. Luchini ◽  
M. M. Motil ◽  
W. V. Mars
Keyword(s):  
Finite Element Analysis ◽  
Common Knowledge ◽  
Rolling Resistance ◽  
Test Method ◽  
Tire Model ◽  
Element Analysis ◽  
Truck Tires ◽  
The Finite Element Analysis ◽  
Equilibrium Test ◽  
Depth Effects

Abstract This paper discusses the measurement and modeling of tire rolling resistance for a group of radial medium truck tires. The tires were subjected to tread depth modifications by “buffing” the tread surface. The experimental work used the equilibrium test method of SAE J-1269. The finite element analysis (FEA) tire model for tire rolling resistance has been previously presented. The results of the testing showed changes in rolling resistance as a function of tread depth that were inconsistent between tires. Several observations were also inconsistent with published information and common knowledge. Several mechanisms were proposed to explain the results. Additional experiments and models were used to evaluate the mechanisms. Mechanisms that were examined included tire age, surface texture, and tire shape. An explanation based on buffed tread radius, and the resulting changes in footprint stresses, is proposed that explains the observed experimental changes in rolling resistance with tread depth.

Interactive Graphics for the Analysis of Tires

1985 ◽  
Vol 13 (3) ◽  
pp. 127-146 ◽  
Author(s):  
R. Prabhakaran
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Approximate Solutions ◽  
Interactive Graphics ◽  
Element Analysis ◽  
Analysis Process ◽  
Physical Problems ◽  
The Finite Element Analysis ◽  
Analysis Computer ◽  
Discretization Technique

Abstract The finite element method, which is a numerical discretization technique for obtaining approximate solutions to complex physical problems, is accepted in many industries as the primary tool for structural analysis. Computer graphics is an essential ingredient of the finite element analysis process. The use of interactive graphics techniques for analysis of tires is discussed in this presentation. The features and capabilities of the program used for pre- and post-processing for finite element analysis at GenCorp are included.

Finite Element Analysis of Nonuniformity of Tires with Imperfections5

2007 ◽  
Vol 35 (3) ◽  
pp. 226-238 ◽  
Author(s):  
K. M. Jeong ◽  
K. W. Kim ◽  
H. G. Beom ◽  
J. U. Park
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Three Dimensional ◽  
Element Model ◽  
Radial Force ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Dimensional Finite Element ◽  
Force Variation ◽  
Three Dimensional Finite Element

Abstract The effects of variations in stiffness and geometry on the nonuniformity of tires are investigated by using the finite element analysis. In order to evaluate tire uniformity, a three-dimensional finite element model of the tire with imperfections is developed. This paper considers how imperfections, such as variations in stiffness or geometry and run-out, contribute to detrimental effects on tire nonuniformity. It is found that the radial force variation of a tire with imperfections depends strongly on the geometrical variations of the tire.

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