Shear Difference Method and Application in Orthotropic Photoelasticity

1976 ◽  
Vol 98 (4) ◽  
pp. 369-374 ◽  
Author(s):  
C. E. Knight ◽  
H. Pih
Keyword(s):  
Plane Stress ◽  
Difference Method ◽  
Two Dimensional ◽  
The Third ◽  
Material Orientation ◽  
Stress Components ◽  
Tensile Strip ◽  
Principal Directions ◽  
Stress Optic Law ◽  
Good Agreement

The shear difference method is developed here for application to orthotropic photoelasticity problems. The two-dimensional stress-optic law which was presented in another paper is used. The stress-optic law provides two equations for the three plane stress components and the shear difference method may be used to obtain the third relation. This paper presents the development of the general orthotropic shear difference method for any material orientation. For orientations aligned with the material principal directions, the relations are identical to the isotropic shear difference method. The solution of an orthotropic tensile strip with a central hole demonstrates application of the orthotropic shear difference method and further confirms the orthotropic stress-optic law. Good agreement was found between the photoelastic and theoretical solutions.

A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

Analysis of creep-induced strains and stresses in notches subjected to a cyclic load

2007 ◽  
Vol 42 (5) ◽  
pp. 361-375 ◽  
Author(s):  
J E Nuñez ◽  
G Glinka
Keyword(s):  
Finite Element ◽  
Plane Stress ◽  
External Load ◽  
Cyclic Load ◽  
Time Dependent ◽  
Cyclic Loads ◽  
Creep Response ◽  
Stress Components ◽  
Estimation Of Time ◽  
Good Agreement

A method for the estimation of time-dependent strains and stresses in notches subjected to a cyclic load is discussed in the paper. The proposed solution is an extension of the methodology proposed previously for notches under a steady external load. A new algorithm is proposed to predict the creep response near notches in plane stress components subjected to cyclic loads. Predictions were compared with finite element data, and good agreement was obtained for various geometrical and material configurations.

Two-Dimensional Stress and Inertia Combinations

1957 ◽  
Vol 61 (557) ◽  
pp. 353-354
Author(s):  
D. E. R. Godfrey
Keyword(s):  
Plane Stress ◽  
Two Dimensional ◽  
Stress Theory ◽  
Stress Components ◽  
Established Fact ◽  
Photoelastic Analysis ◽  
Image Position

A Similarity in properties will be demonstrated between the moments and product of inertia of a lamina and the components of plane stress. It is now a well established fact that in two-dimensional stress theory it is advantageous to use certain combinationsof the stress components.1First, it will be shown that the use of similar combinations of the moments and product of inertia leads to a useful graphical means of obtaining these quantities for awkwardly placed axes and also to some results not normally to be found in the text-books. Secondly, an application to photoelastic analysis is also made.

Stress Distribution in Rotating Discs with Non-Central Holes

1964 ◽  
Vol 15 (2) ◽  
pp. 107-121 ◽  
Author(s):  
W. A. Green ◽  
G. T. J. Hooper ◽  
R. Hetherington
Keyword(s):  
Stress Distribution ◽  
Numerical Solution ◽  
Plane Stress ◽  
Two Dimensional ◽  
Stress Distributions ◽  
Uniform Thickness ◽  
Dimensional Model ◽  
One Dimensional ◽  
Rotating Discs ◽  
Good Agreement

SummaryThe stress distribution in rotating circular discs containing a central hole and a symmetrical array of non-central holes is determined by numerical solution of the equations of generalised plane stress. Particular attention is given to an annulus containing the holes and of width approximately eight hole diameters, in which the full two-dimensional equations are solved. The region outside this annulus is treated as radially symmetric and the stresses there are determined from a simpler one-dimensional model. Stress distributions are reported for uniform discs of fixed geometry containing 10, 20 and 45 holes. Results are also obtained for 20-hole discs of non-uniform thickness comprising a uniformly tapered disc, a disc with a thickened annulus containing the holes, and a uniform disc with each hole surrounded by thickened bosses. As a check on the numerical method, calculations have been carried out on a disc of identical geometry to one examined photoelastically bv Leist and Weber with good agreement. The effect of changing Poisson's ratio for this particular disc is also examined.

Analysis of Creep Induced Strains and Stresses in Notches Subjected to Cyclic Load

2005 ◽  
Author(s):  
Enrique Nunez ◽  
Gregorz Glinka
Keyword(s):  
Finite Element ◽  
Plane Stress ◽  
External Load ◽  
Cyclic Load ◽  
Time Dependent ◽  
Cyclic Loads ◽  
Creep Response ◽  
Stress Components ◽  
Estimation Of Time ◽  
Good Agreement

A method for the estimation of time-dependent strains and stresses in notches subjected to cyclic load is discussed in the paper. The proposed solution is an extension of the methodology proposed previously for notches under steady external load. A new algorithm is proposed to predict creep response near notches in plane stress components subjected to cyclic loads. Predictions were compared against finite element data and good agreement was obtained for various geometrical and material configurations.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

A Difference Method for Plane Problems in Magnetoelastodynamics

1972 ◽  
Vol 39 (3) ◽  
pp. 689-695 ◽  
Author(s):  
W. W. Recker
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Method ◽  
Difference Method ◽  
Necessary Condition ◽  
Two Dimensional ◽  
Symmetric Hyperbolic System ◽  
Von Neumann ◽  
First Order ◽  
Independent Variables

The two-dimensional equations of magnetoelastodynamics are considered as a symmetric hyperbolic system of linear first-order partial-differential equations in three independent variables. The characteristic properties of the system are determined and a numerical method for obtaining the solution to mixed initial and boundary-value problems in plane magnetoelastodynamics is presented. Results on the von Neumann necessary condition are presented. Application of the method to a problem which has a known solution provides further numerical evidence of the convergence and stability of the method.

Sign in / Sign up

Export Citation Format

Share Document