scholarly journals A Non-Singular Analytical Technique for Reinforced Non-Circular Holes in Orthotropic Laminate

2020 ◽  
Vol 25 (1) ◽  
pp. 92-105
Author(s):  
Pradeep Mohan ◽  
R. Ramesh Kumar
Keyword(s):  
Stress Distribution ◽  
Analytical Solution ◽  
Power Series ◽  
Orthotropic Shell ◽  
Infinite Plate ◽  
Stress Singularity ◽  
Power Series Solution ◽  
Element Analysis ◽  
Full Field ◽  
Analytical Technique

AbstractThe intricacy in Lekhnitskii’s available single power series solution for stress distribution around hole edge for both circular and noncircular holes represented by a hole shape parameter ε is decoupled by introducing a new technique. Unknown coefficients in the power series in ε are solved by an iterative technique. Full field stress distribution is obtained by following an available method on Fourier solution. The present analytical solution for reinforced square hole in an orthotropic infinite plate is derived by completely eliminating stress singularity that depends on the concept of stress ratio. The region of validity of the present analytical solution on reinforcement area is arrived at based on a comparison with the finite element analysis. The present study will also be useful for deriving analytical solution for orthotropic shell with reinforced noncircular holes.

An analytical solution of the Gibbs–Dehem equation in multicomponent systems

1970 ◽  
Vol 48 (5) ◽  
pp. 752-763 ◽  
Author(s):  
A. D. Pelton
Keyword(s):  
Analytical Solution ◽  
Power Series ◽  
Series Solution ◽  
Power Series Solution ◽  
Multicomponent Systems ◽  
Duhem Equation ◽  
Number Of Components ◽  
Analytical Power

A general analytical power-series solution of the Gibbs–Duhem equation in multicomponent systems of any number of components has been developed. The simplicity and usefulness of the solution is made possible through the choice of a special set of composition variables.

The Effects of Materials Properties & Angle Junction on Stress Concentration at Interface of Dissimilar Materials

2011 ◽  
Vol 383-390 ◽  
pp. 887-892
Author(s):  
Alireza Fallahi Arezoodar ◽  
Ali Baladi
Keyword(s):  
Stress Concentration ◽  
Stress Distribution ◽  
Stress Reduction ◽  
Stiffness Matrix ◽  
Stress Singularity ◽  
Dissimilar Materials ◽  
Element Analysis ◽  
Materials Properties ◽  
Main Factors ◽  
Elastic Modules

In dissimilar material joints, failure often occurs along the interface between two materials due to stress singularity. Stress distribution and its concentration depend on materials and geometry of the junction as the stress concentration depends on grain orientation and its stiffness matrix of neighboring grains in micro-scale. Inhomogenity of stress distribution at the interface of junction of two materials with different elastic modules and stress concentration in this zone are the main factors resulting in rupture of the junction. Effect of materials properties, thickness, and joining angle at the interface of aluminum-polycarbonate will be discussed in this paper. Computer simulation and finite element analysis by ABAQUS showed that convex interfacial joint leads to stress reduction at junction corners in compare with straight joint. This finding is confirmed by photoelastic experimental results.

The Stresses Around Square Holes with Rounded Corners

1958 ◽  
Vol 2 (03) ◽  
pp. 37-41
Author(s):  
Joseph S. Brock
Keyword(s):  
Stress Distribution ◽  
Analytical Solution ◽  
Infinite Plate ◽  
Mapping Function ◽  
Mapping Technique ◽  
Radius Of Curvature ◽  
Stress Concentrations ◽  
Method Of Solution ◽  
Christoffel Transformation ◽  
Square Hole

This paper presents an analytical solution for the stress distribution around a square hole with rounded corners in an infinite plate subjected to pure tension. The method of solution is a combination of a conformal mapping technique and the complexvariable method of Muskhelishvili. The form of the mapping function is obtained from the Schwarz-Christoffel transformation. The mapping function is general and gives a good approximation to square holes with rounded corners of arbitrary radius of curvature. The ratios of the corner radius to the width of the opening considered cover the range from 0.03 to 0.5. This is considered 1o be the interesting range for ship structures. The results are given in terms of stress concentrations around the boundary of the opening.

Characterization of Laser Processed Sub-Millimeter Lap Joints Between Copper and Aluminum Under Tensile Load

2010 ◽  
Author(s):  
A. Mian ◽  
M. Hailat ◽  
G. Newaz ◽  
R. Patwa ◽  
H. Herfurth
Keyword(s):  
Stress Distribution ◽  
Tensile Load ◽  
Lap Joints ◽  
Filler Materials ◽  
Element Analysis ◽  
Full Field ◽  
Fea Model ◽  
Lap Shear ◽  
Copper Aluminum

This paper presents the results of laser joined copper-aluminum lap shear samples without filler materials using an IPG 500W SM fiber laser. The length of the processed laser joint was about 20 mm and the width was about 200 μm. Laser-joined samples were tested under tensile loading to determine joint strengths. In addition, finite element analysis (FEA) was conducted to understand the stress distribution within the bond area under such loading. The FEA model provides a full-field stress distribution in and around the joint that cause eventual failure. We are still working on the topic, and more data will be published soon.

An Application of the Differential Transform Method to the Biochemical Reaction Systems

2013 ◽  
Vol 319 ◽  
pp. 151-156
Author(s):  
Mustafa Bayram ◽  
Kenan Yildirim ◽  
Muhammet Kurulay
Keyword(s):  
Analytical Solution ◽  
Power Series ◽  
Its Region ◽  
Differential Transform Method ◽  
Biochemical Reaction ◽  
Power Series Solution ◽  
Transform Method ◽  
Reaction Systems ◽  
Differential Transform ◽  
Theoretical Considerations

An approximate analytical solution for the biochemical reaction systems is derived using the differential transform method. The analytical solution, which is given in the form of a power series, is found to be highly accurate in predicting the behavior of the reaction in the very early stages. To accelerate the convergence of the power series solution and extend its region of applicability throughout the entire transient phase, we used differential transform method theoretical considerations has been discussed and some examples were presented to show the ability of the method for Biochemical reaction systems. We use MAPLE computer algebra system to solve given problems[4].

Analytical Solution for W-N Criteria for the Prediction of Notched Strength of an Orthotropic Shell

2000 ◽  
Vol 68 (2) ◽  
pp. 344-346 ◽  
Author(s):  
R. Ramesh Kumar ◽  
S. Jose ◽  
G. Venkateswara Rao
Keyword(s):  
Finite Element ◽  
Cylindrical Shell ◽  
Stress Distribution ◽  
Analytical Solution ◽  
Tangential Stress ◽  
Circular Hole ◽  
Circular Cylindrical Shell ◽  
Orthotropic Shell ◽  
Notched Strength ◽  
Good Agreement

Analytical solution for the tangential stress distribution ahead of a hole is needed for the theoretical prediction of notched strength of brittle laminate using the well-known W-N criteria. In the present study, tangential stress distribution in an orthotropic circular cylindrical shell under uniaxial loading with a circular hole is obtained intuitively with the use of a stress function. A good agreement is obtained for the stresses around and ahead of the circular hole in 0deg4±30degs and 90 deg laminates with the finite element results.

BENDING OF A SUBTLE-FINISHED PLATE ON ELASTIC BASE WITH SPECIAL CONDITIONS OF ITS WORK

2019 ◽  
pp. 424-430
Author(s):  
A. T. Marufiy ◽  
A. S. Kalykov
Keyword(s):  
Analytical Solution ◽  
Working Conditions ◽  
Fourier Transforms ◽  
Infinite Plate ◽  
Elastic Base ◽  
Generalized Solutions ◽  
Middle Plane ◽  
Actual Working

In this article, an analytical solution is obtained for the problem of bending a semi-infinite plate on an elastic Winkler base, taking into account incomplete contact with the base and the influence of longitudinal forces applied in the middle plane of the plate. The analytical solution is obtained by the method of generalized solutions using integral Fourier transforms. Any analytical solution is the result, approaching the actual working conditions of the designed structures.

scholarly journals Comparison of one versus two maxillary molars distalization with iPanda: a finite element analysis

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Kamontip Sujaritwanid ◽  
Boonsiva Suzuki ◽  
Eduardo Yugo Suzuki
Keyword(s):  
Finite Element ◽  
Stress Distribution ◽  
Alveolar Bone ◽  
Vertical Direction ◽  
Minimal Amount ◽  
Element Analysis ◽  
Molar Distalization ◽  
Second Molar ◽  
Maxillary Molars ◽  
Displacement Patterns

Abstract Background The purpose of this study was to compare the stress distribution and displacement patterns of the one versus two maxillary molars distalization with iPanda and to evaluate the biomechanical effect of distalization on the iPanda using the finite element method. Methods The finite element models of a maxillary arch with complete dentition, periodontal ligament, palatal and alveolar bone, and an iPanda connected to a pair of midpalatal miniscrews were created. Two models were created to simulate maxillary molar distalization. In the first model, the iPanda was connected to the second molar to simulate a single molar distalization. In the second model, the iPanda was connected to the first molar to simulate “en-masse” first and second molar distalization. A varying force from 50 to 200 g was applied. The stress distribution and displacement patterns were analyzed. Results For one molar, the stress was concentrated at the furcation and along the distal surface in all roots with a large amount of distalization and distobuccal crown tipping. For two molars, the stress in the first molar was 10 times higher than in the second molar with a great tendency for buccal tipping and a minimal amount of distalization. Moreover, the stress concentration on the distal miniscrew was six times higher than in the mesial miniscrew with an extrusive and intrusive vector, respectively. Conclusions Individual molar distalization provides the most effective stress distribution and displacement patterns with reduced force levels. In contrast, the en-masse distalization of two molars results in increased force levels with undesirable effects in the transverse and vertical direction.

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