Exact Elasticity Solutions for Stresses and Deflections in Curved Beams and Rings of Exponential and T-Sections

1993 ◽  
Vol 115 (3) ◽  
pp. 346-358 ◽  
Author(s):  
C. Bagci
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Plane Stress ◽  
Numerical Results ◽  
Neutral Axis ◽  
Curved Beams ◽  
Equilibrium Stress ◽  
Different Boundary Conditions ◽  
Stress Functions ◽  
Elasticity Solutions

Exact elasticity solutions for stresses and deflections (displacements) in curved beams and rings of varying thicknesses are developed using polar elasticity and state of plane stress. Basic forms of differential equations of equilibrium, stress functions, and differential equations of compatibility are given. They are solved to develop expressions for radial, tangential, and shearing stresses for moment, force, and combined loadings. Neutral axis location for each type of loading is determined. Expressions for displacements are developed utilizing strain-displacement relationships of polar elasticity satisfying boundary conditions on displacements. In case of full rings stresses are as in curved beams with properly defined moment loading, but displacements differ satisfying different boundary conditions. The developments for constant thicknesses are used to develop solutions for curved beams and rings with T-sections. Comparative numerical results are given.

Exact Elasticity Solutions for Stresses and Deflections in Curved Beams and Rings of Exponential and T-Sections

1991 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Plane Stress ◽  
Numerical Results ◽  
Neutral Axis ◽  
Curved Beams ◽  
Equilibrium Stress ◽  
Different Boundary Conditions ◽  
Stress Functions ◽  
Elasticity Solutions

Abstract Exact elasticity solutions for stresses and deflections (displacements) in curved beams and rings of varying thicknesses are developed using polar elasticity and state of plane stress. Basic forms of differential equations of equilibrium, stress functions, and differential equations of compatibility are given. They are solved to develop expressions for radial, tangential, and shearing stresses for moment, force, and combined loadings. Neutral axis location for each type of loading is determined. Expressions for displacements are developed utilizing strain-displacement relationships of polar elasticity satisfying boundary conditions on displacements. In case of full rings stresses are as in curved beams with properly defined moment loading, but displacements differ satisfying different boundary conditions. The developments for constant thicknesses are used to develop solutions for curved beams and rings with T-sections. Comparative numerical results are given.

Plane Stress Analysis of End-Loaded Orthotropic Curved Beams of Constant Thickness With Applications to Full Rings

1998 ◽  
Vol 120 (2) ◽  
pp. 368-374 ◽  
Author(s):  
N. Tutuncu
Keyword(s):  
Plane Stress ◽  
Plane Elasticity ◽  
Isotropic Case ◽  
Constant Thickness ◽  
Curved Beams ◽  
Degree Of Anisotropy ◽  
Stress Functions ◽  
Elasticity Solutions ◽  
Two Parameters ◽  
Plane Stress Analysis

Plane elasticity solutions using stress functions for stresses and displacements in orthotropic curved beams subjected to end moment and force loadings are presented. Applications to curved beams with straight portions and full rings are considered. The results are compared with the isotropic case. Two parameters, which essentially measure the degree of anisotropy, each pertaining to a different loading state are defined and their effects on the stress and displacement distributions are discussed. It has been shown that increasing these parameters reduced the stresses in the members.

scholarly journals A Comparison between Adomian Decomposition and Tau Methods

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Necdet Bildik ◽  
Mustafa Inc
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Numerical Results ◽  
Tau Method ◽  
Adomian Decomposition

We present a comparison between Adomian decomposition method (ADM) and Tau method (TM) for the integro-differential equations with the initial or the boundary conditions. The problem is solved quickly, easily, and elegantly by ADM. The numerical results on the examples are shown to validate the proposed ADM as an effective numerical method to solve the integro-differential equations. The numerical results show that ADM method is very effective and convenient for solving differential equations than Tao method.

Lateral Buckling of Cantilevered Circular Arches Under Various End Moments

2020 ◽  
Vol 20 (07) ◽  
pp. 2071005
Author(s):  
Y. B. Yang ◽  
Y. Z. Liu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Analytical Solutions ◽  
Analytical Approach ◽  
Three Dimensional ◽  
Curved Beams ◽  
Lateral Buckling ◽  
Circular Arch ◽  
Out Of Plane ◽  
The Moment

Lateral buckling of cantilevered circular arches under various end moments is studied using an analytical approach. Three types of conservative moments are considered, i.e. the quasi-tangential moments of the 1st and 2nd kinds, and the semi-tangential moment. The induced moments associated with each of the moment mechanisms undergoing three-dimensional rotations are included in the Newman boundary conditions. Using the differential equations available for the out-of-plane buckling of curved beams, the analytical solutions are derived for a cantilevered circular arch, which can be used as the benchmarks for calibration of other methods of analysis.

Buckling Analysis of Shells with a Circumferential Crack

2006 ◽  
Vol 306-308 ◽  
pp. 55-60
Author(s):  
I.S. Putra ◽  
T. Dirgantara ◽  
Firmansyah ◽  
M. Mora
Keyword(s):  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Buckling Analysis ◽  
Numerical Results ◽  
Buckling Load ◽  
Numerical Analyses ◽  
Radius Of Curvature ◽  
Critical Buckling Load ◽  
Different Boundary Conditions ◽  
Circumferential Crack

In this paper, buckling analysis of cylindrical shells with a circumferential crack is presented. The analyses were performed both numerically using FEM and experimentally. The numerical analyses and experiments were conducted for several crack lengths and radius of curvature, and two different boundary conditions were applied, i.e. simply support and clamp in all sides. The results show the effect of the presence of crack to the critical buckling load of the shells. There are good agreements between experimental and numerical results.

scholarly journals Thermally Charged MHD Bi-Phase Flow Coatings with Non-Newtonian Nanofluid and Hafnium Particles along Slippery Walls

Coatings ◽  
2019 ◽  
Vol 9 (5) ◽  
pp. 300 ◽  
Author(s):  
Rahmat Ellahi ◽  
Ahmed Zeeshan ◽  
Farooq Hussain ◽  
Tehseen Abbas
Keyword(s):  
Magnetic Susceptibility ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Couple Stress ◽  
Numerical Results ◽  
Phase Flow ◽  
Metallic Particles ◽  
Coupled Partial Differential Equations ◽  
Physical Quantities ◽  
Graphical Illustration

The present study is about the pressure-driven heated bi-phase flow in two slippery walls. The non-Newtonian couple stress fluid is suspended with spherically homogenous metallic particles. The magnetic susceptibility of Hafnium allures is taken into account. The rough surface of the wall is tackled by lubrication effects. The nonlinear coupled partial differential equations along with the associated boundary conditions are first reduced into a set of ordinary differential equations by using appropriate transformations and then numerical results were obtained by engaging the blend of Runge–Kutta and shooting techniques. The sway of physical quantities are examined graphically. An excellent agreement within graphical illustration and numerical results is achieved.

scholarly journals Explicit difference schemes for a pseudoparabolic equation with an integral condition

2012 ◽  
Vol 53 ◽  
Author(s):  
Justina Jachimavičienė
Keyword(s):  
Boundary Conditions ◽  
Integral Condition ◽  
Numerical Results ◽  
Difference Schemes ◽  
Pseudoparabolic Equation ◽  
Different Boundary Conditions ◽  
Explicit Schemes ◽  
Explicit Difference Schemes

The aim of this paper is to analyze three layer explicit schemes for a pseudoparabolic equation with different boundary conditions, including nonlocal ones. The numerical results are presented.

The Effect of Graded Strength on Damage Propagation in Continuously Nonhomogeneous Materials

2003 ◽  
Vol 125 (4) ◽  
pp. 412-417 ◽  
Author(s):  
Priya Thamburaj ◽  
Michael H. Santare ◽  
George A. Gazonas
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Damage Model ◽  
Numerical Results ◽  
Finite Element Code ◽  
Different Boundary Conditions ◽  
One Dimensional ◽  
Damage Propagation ◽  
Dynamic Finite Element ◽  
Nonhomogeneous Materials

A damage model developed by Johnson and Holmquist is implemented into a dynamic finite element code. This is then used to study the effect of grading of the phenomenological damage parameters on the propagation of damage through the material. The numerical results for two one-dimensional example problems with different boundary conditions are presented, wherein the effect of a gradient in the intact strength of the material on damage propagation is studied. The results show that introducing different strength gradients can alter the location of the site of maximum damage. This may have important implications in the design of impact resistant materials and structures.

Stress and Displacement Analysis of a Shell Intersection

1970 ◽  
Vol 92 (2) ◽  
pp. 303-308 ◽  
Author(s):  
K. C. Pan ◽  
R. E. Beckett
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Internal Pressure ◽  
Numerical Solution ◽  
Numerical Computation ◽  
Cylindrical Shells ◽  
Numerical Results ◽  
Radius Ratio ◽  
Displacement Analysis

The problem of two normally intersecting cylindrical shells subjected to internal pressure is considered. The differential equations used for the shells are solved subject to the boundary conditions imposed along the intersection between the two cylinders. Details of a procedure for obtaining a numerical solution are given. Numerical results for a radius ratio of 1:2 are presented. Problems encountered in the numerical computation are discussed and the results of the analysis are compared with experiment.

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