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.

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.

Analytical Solution of Sidewise Buckling of Two-Hinged Circular Arch under Concentrated Force

2013 ◽  
Vol 676 ◽  
pp. 170-174
Author(s):  
Ju Tao Kuang ◽  
Ai Rong Liu ◽  
Qi Ca Yu ◽  
Jiang Dong Deng
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Lateral Displacement ◽  
Displacement Function ◽  
Buckling Load ◽  
The Finite Element Method ◽  
Concentrated Force ◽  
Critical Buckling Load ◽  
Circular Arch ◽  
Good Agreement

By the setting torsional and lateral displacement function of sidewise buckling of two-hinged circular arch under concentrated force, the single-arch structure's bending, torsional deformation and external force potential can be constructed. An analytical solution for the lateral critical buckling load of two-hinged arch is first deduced by using the energy method; the results are also compared and analyzed by the finite element method. The results show that the analytical solution of single arch’s lateral critical buckling load is in good agreement with the finite element numerical solution, and the validity of the formula is proven.

scholarly journals A Semi-Analytical Solution for Elastic Analysis of Rotating Thick Cylindrical Shells with Variable Thickness Using Disk Form Multilayers

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammad Zamani Nejad ◽  
Mehdi Jabbari ◽  
Mehdi Ghannad
Keyword(s):  
Cylindrical Shell ◽  
Analytical Solution ◽  
Differential Equations ◽  
Variable Thickness ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
First Order ◽  
Thick Cylinder ◽  
Good Agreement

Using disk form multilayers, a semi-analytical solution has been derived for determination of displacements and stresses in a rotating cylindrical shell with variable thickness under uniform pressure. The thick cylinder is divided into disk form layers form with their thickness corresponding to the thickness of the cylinder. Due to the existence of shear stress in the thick cylindrical shell with variable thickness, the equations governing disk layers are obtained based on first-order shear deformation theory (FSDT). These equations are in the form of a set of general differential equations. Given that the cylinder is divided intondisks,nsets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. A numerical solution using finite element method (FEM) is also presented and good agreement was found.

An Integral Equation Method for Predicting Acoustic Emission within Enclosures

1985 ◽  
Vol 199 (2) ◽  
pp. 133-137 ◽  
Author(s):  
D T I Francis ◽  
M M Sadek
Keyword(s):  
Integral Equation ◽  
Finite Element ◽  
Acoustic Emission ◽  
Analytical Solution ◽  
Numerical Solution ◽  
Finite Element Methods ◽  
Exact Analytical Solution ◽  
Integral Equation Method ◽  
Absorption Characteristics ◽  
Good Agreement

A method is presented for calculating the acoustic emission of a vibrating body within an enclosure whose surface has known absorption characteristics. It is based on a numerical solution of the Helmholtz integral equation. Solutions are given for the case of a pulsating sphere within a sphere, and good agreement with the exact analytical solution is reported. The method is of value for small and medium scale problems at lower frequencies, where traditional techniques are less reliable. It is also potentially less demanding computationally than finite element methods.

Shape Factors for Irregular Glass Reinforced Plastic Pipes – An Analytical and Numerical Approach

2011 ◽  
Vol 471-472 ◽  
pp. 279-284 ◽  
Author(s):  
Ikram K. Ismail ◽  
Abdennour Seibi
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Tangential Stress ◽  
Shape Factor ◽  
Beam Theory ◽  
Design Guidelines ◽  
Maximum Tangential Stress ◽  
Circular Pipe ◽  
Shape Factors ◽  
Irregular Shapes

This paper presents the development of a mathematical model based on curved beam theory of composite pipes with irregular shapes under diametral loading. The analytical solution was validated through finite element models of the same pipe shapes under similar loading conditions. Four shapes (circular, elliptical, rectangular, and egg shaped pipes) were considered in this study. The analytical and finite element results were used to estimate the shape factor defined by the ratio of the maximum tangential stress of an irregular shape over the maximum tangential stress for a circular pipe. Comparison of the load-deflection curves for the four different shapes revealed that the egg pipe is the stiffest among the rest of the pipes while the square shape is the most flexible one. The analytical solution and finite element results were used to determine the shape factor for the four pipe shapes taking into account the circular pipe as the base shape. Both results were in good agreement and can be used as design guidelines for the irregular shapes without resorting to the conduct of any further testing.

Stresses Around an Elliptic Hole in a Cylindrical Shell

1969 ◽  
Vol 36 (1) ◽  
pp. 39-46 ◽  
Author(s):  
M. V. V. Murthy
Keyword(s):  
Cylindrical Shell ◽  
Stress Distribution ◽  
Theoretical Analysis ◽  
Circular Cylindrical Shell ◽  
Elliptic Hole ◽  
Major Axis ◽  
Axial Tension ◽  
Method Of Solution ◽  
Bending Stresses ◽  
Curvature Parameter

A theoretical analysis is presented for the membrane and bending stresses around an elliptic hole in a long, thin, circular cylindrical shell with the major axis of the hole parallel to the axis of the shell. The analysis has been carried out for the case of axial tension. The method of solution involves a perturbation in a curvature parameter and the results obtained are valid, if the hole is small in size compared to the shell. Formulas, from which the complete stress distribution at the hole can be calculated, are presented.

Forced Plane Strain Motion of Cylindrical Shells—A Comparison of Shell Theory With Elasticity Theory

1973 ◽  
Vol 40 (3) ◽  
pp. 725-730 ◽  
Author(s):  
P. S. Pawlik ◽  
H. Reismann
Keyword(s):  
Cylindrical Shell ◽  
Analytical Solution ◽  
Elasticity Theory ◽  
Plane Strain ◽  
Outer Surface ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Initial Response ◽  
Linear Elasticity Theory ◽  
Specific Loading

A radially directed load is suddenly applied to a portion of the outer surface of a circular cylindrical shell which responds in a state of plane strain. An analytical solution for the resulting dynamic response is obtained within the context of linear elasticity theory, Flu¨gge shell theory, and an “improved” shell theory. A comparison of results for specific loading conditions indicates that the improved theory is far superior to the Flu¨gge theory in terms of predicting both the magnitude and characteristics of the response. However, as expected, neither shell theory satisfactorily predicts the wave character of the initial response.

Finite-element modelling of two-disc shrink fit assembly and an evaluation of material pairs of discs

2010 ◽  
Vol 225 (2) ◽  
pp. 263-273 ◽  
Author(s):  
F Ozturk
Keyword(s):  
Finite Element ◽  
Stress Distribution ◽  
Finite Element Modelling ◽  
The Finite Element Method ◽  
Uniform Stress ◽  
Element Modelling ◽  
Hollow Shaft ◽  
Complex Shapes ◽  
Shrink Fit ◽  
Good Agreement

In this study, a two-disc shrink fit assembly was modelled in two dimension using ABAQUS/Standard to determine the interfacial pressures with respect to the interferences. Steel—steel and steel—aluminium material pairs were considered. Inner disc of the assembly was considered as hollow and solid shafts, respectively. The results indicate that the finite-element results were in good agreement with the analytical results. In the hollow shaft assembly, both the hollow shaft and the outer disc had non-uniform stress distribution. In the solid shaft assembly, uniform stress distribution for the solid shaft and non-uniform stress distribution for the outer disc were determined. It was pointed out that same pressure can be obtained by different interference with different material pairs. If the assembly has complex shapes, the finite-element method gives more comprehensive and accurate results than the analytical method.

An Analytical Solution for Stress and Displacement in Casing-Cement Combined Cylinder under Non-Uniform Loading

2011 ◽  
Vol 291-294 ◽  
pp. 2133-2138 ◽  
Author(s):  
Mu Hui Fan ◽  
Yong Shu Jiao ◽  
Zong Xi Cai
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Analytical Solution ◽  
Computer Program ◽  
Theory Of Elasticity ◽  
Composite Cylinder ◽  
The Finite Element Method ◽  
Uniform Loading ◽  
Cement Sheath ◽  
Good Agreement

Based on the theory of elasticity and taken the casing-cement sheath as a totally contacted composite cylinder subjected to arbitrarily distributed loading on inner and outer surfaces, an analytical solution in Fourier serial form was obtained for stresses and displacements. A computer program was developed to evaluate the stress and displacement in the combined cylinder. The results are in good agreement with those from the finite element method (FEM). With these solutions we can investigate the interaction between casing and the cement sheath. This is of importance in improving the design of casing.

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