scholarly journals On the Numerical Determination of Shrinkage Stresses

1970 ◽  
Vol 37 (1) ◽  
pp. 123-127 ◽  
Author(s):  
F. Bauer ◽  
E. L. Reiss
Keyword(s):  
Iterative Method ◽  
Numerical Solutions ◽  
Mixed Boundary ◽  
Thin Strip ◽  
Heated Plate ◽  
Two Dimensional ◽  
Numerical Determination ◽  
Mixed Boundary Value Problem ◽  
Elastic Plates

An iterative method is employed to obtain numerical solutions of a two-dimensional mixed boundary-value problem for rectangular elastic plates. The theory of plane stress is used. This problem is encountered when the edge of a uniformly heated plate is bonded to a rigid body and then allowed to cool. The numerical results are compared with two formal asymptotic expansions of the solution. They correspond to the limiting cases of a thin strip and a long strip. The development of boundary layers near the edges of the plate is observed. The numerically determined stresses achieve their largest values at the corner of the bonded edge.

A non-linear theory for a full cavitating hydrofoil in a transverse gravity field

1967 ◽  
Vol 29 (2) ◽  
pp. 317-336 ◽  
Author(s):  
Bruce E. Larock ◽  
Robert L. Street
Keyword(s):  
Gravity Field ◽  
Linear Theory ◽  
Mixed Boundary ◽  
Linear Method ◽  
Two Dimensional ◽  
Mixed Boundary Value Problem ◽  
Cavity Model ◽  
Cavity Size ◽  
Non Linear ◽  
Cavitating Hydrofoil

An analysis is made of the effect of a transverse gravity field on a two-dimensional fully cavitating flow past a flat-plate hydrofoil. Under the assumption that the flow is both irrotational and incompressible, a non-linear method is developed by using conformal mapping and the solution to a mixed-boundary-value problem in an auxiliary half plane. A new cavity model, proposed by Tulin (1964a), is employed. The solution to the gravity-affected case was found by iteration; the non-gravity solution was used as the initial trial of a rapidly convergent process. The theory indicates that the lift and cavity size are reduced by the gravity field. Typical results are presented and compared to Parkin's (1957) linear theory.

A Mixed Boundary-Value Problem of Elasticity With Parabolic Boundary

1957 ◽  
Vol 24 (1) ◽  
pp. 122-124
Author(s):  
Gunadhar Paria
Keyword(s):  
Stress Distribution ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Complex Variable ◽  
Hilbert Problem ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Mixed Boundary Value Problem ◽  
Parabolic Boundary

Abstract The problem of finding the stress distribution in a two-dimensional elastic body with parabolic boundary, subject to mixed boundary conditions, has been reduced to the solution of the nonhomogeneous Hilbert problem following the method of complex variable. The result has been compared with that for a straight boundary.

NUMERICAL STUDY OF THE KINEMATIC PARAMETERS OF AN EARTH DAM IN A MODEL EXPERIMENT

2021 ◽  
pp. 68-74
Author(s):  
V. Y. ZHARNITSKY ◽  
◽  
E. V. ANDREEV ◽  
O. A. BAYUK
Keyword(s):  
Model Experiment ◽  
Numerical Solutions ◽  
Residual Life ◽  
Numerical Study ◽  
Mixed Boundary ◽  
Earth Dam ◽  
Mixed Boundary Value Problem ◽  
Dynamic Effects ◽  
Kinematic Parameters ◽  
Gas Dynamic

To assess the convergence and stability of the methods for predicting the residual life of pressure hydrotechnical structures of general impact and gas-dynamic effects, a comparison of the analytical and numerical solutions was carried out by applying it to a mixed boundary value problem, cumulative initial and boundary conditions.

Crack Propagation in a Brittle Elastic Material With Defects

1999 ◽  
Vol 66 (1) ◽  
pp. 79-86 ◽  
Author(s):  
M. Valentini ◽  
S. K. Serkov ◽  
D. Bigoni ◽  
A. B. Movchan
Keyword(s):  
Asymptotic Solution ◽  
Asymptotic Analysis ◽  
Isotropic Medium ◽  
Numerical Solutions ◽  
Porous Ceramics ◽  
Qualitative Description ◽  
Mode I ◽  
Pure Mode ◽  
Two Dimensional

A two-dimensional asymptotic solution is presented for determination of the trajectory of a crack propagating in a brittle-elastic, isotropic medium containing small defects. Brittleness of the material is characterized by the assumption of the pure Mode I propagation criterion. The defects are described by Po´lya-Szego¨ matrices, and examples for small elliptical cavities and circular inclusions are given. The results of the asymptotic analysis, which agree well with existing numerical solutions, give qualitative description of crack trajectories observed in brittle materials with defects, such as porous ceramics.

Numerical determination of two-dimensional temperature fields in transpiration cooling

1984 ◽  
Vol 47 (6) ◽  
pp. 1459-1465
Author(s):  
A. V. Kurpatenkov ◽  
V. M. Polyaev ◽  
A. L. Sintsov
Keyword(s):  
Temperature Fields ◽  
Transpiration Cooling ◽  
Two Dimensional ◽  
Numerical Determination

Two-dimensional viscous gravity currents flowing over a deep porous medium

2001 ◽  
Vol 440 ◽  
pp. 359-380 ◽  
Author(s):  
JAMES M. ACTON ◽  
HERBERT E. HUPPERT ◽  
M. GRAE WORSTER
Keyword(s):  
Porous Medium ◽  
Numerical Solutions ◽  
Gravity Current ◽  
Constant Volume ◽  
Two Dimensional ◽  
Theoretical Predictions ◽  
Self Similar ◽  
Coefficient Of Viscosity ◽  
Good Agreement

The spreading of a two-dimensional, viscous gravity current propagating over and draining into a deep porous substrate is considered both theoretically and experimentally. We first determine analytically the rate of drainage of a one-dimensional layer of fluid into a porous bed and find that the theoretical predictions for the downward rate of migration of the fluid front are in excellent agreement with our laboratory experiments. The experiments suggest a rapid and simple technique for the determination of the permeability of a porous medium. We then combine the relationships for the drainage of liquid from the current through the underlying medium with a formalism for its forward motion driven by the pressure gradient arising from the slope of its free surface. For the situation in which the volume of fluid V fed to the current increases at a rate proportional to t3, where t is the time since its initiation, the shape of the current takes a self-similar form for all time and its length is proportional to t2. When the volume increases less rapidly, in particular for a constant volume, the front of the gravity current comes to rest in finite time as the effects of fluid drainage into the underlying porous medium become dominant. In this case, the runout length is independent of the coefficient of viscosity of the current, which sets the time scale of the motion. We present numerical solutions of the governing partial differential equations for the constant-volume case and find good agreement with our experimental data obtained from the flow of glycerine over a deep layer of spherical beads in air.

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