scholarly journals Three-Dimensional Stress Concentration Around a Cylindrical Hole in a Semi-Infinite Elastic Body

1966 ◽  
Vol 33 (4) ◽  
pp. 855-865 ◽  
Author(s):  
C. K. Youngdahl ◽  
E. Sternberg
Keyword(s):  
Integral Transform ◽  
Finite Thickness ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Integral Form ◽  
The Body ◽  
Cylindrical Hole ◽  
Normal Displacement ◽  
Plane Boundary ◽  
Dimensional Solution

This paper contains a three-dimensional solution, exact within classical elastostatics, for the stresses and deformations arising in a half-space with a semi-infinite transverse cylindrical hole, if the body—at infinite distances from its cylindrical boundary—is subjected to an arbitrary uniform plane field of stress that is parallel to the bounding plane. The solution presented is in integral form and is deduced with the aid of the Papkovich stress functions by means of an especially adapted, unconventional, integral-transform technique. Numerical results for the nonvanishing stresses along the boundary of the hole and for the normal displacement at the plane boundary, corresponding to several values of Poisson’s ratio, are also included. These results exhibit in detail the three-dimensional stress boundary layer that emerges near the edges of the hole in the analogous problem for a plate of finite thickness, as the ratio of the plate thickness to the diameter of the hole grows beyond bounds. The results obtained thus illustrate the limitations inherent in the two-dimensional plane-strain treatment of the spatial plane problem; in addition, they are relevant to failure considerations and of interest in connection with experimental stress analysis.

Three-Dimensional Elastic Stress Fields of Finite Thickness Plates with Elliptical Hole

2007 ◽  
Vol 353-358 ◽  
pp. 74-77
Author(s):  
Zheng Yang ◽  
Chong Du Cho ◽  
Ting Ya Su ◽  
Chang Boo Kim ◽  
Hyeon Gyu Beom
Keyword(s):  
Stress Concentration ◽  
Plane Strain ◽  
Plane Stress ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Maximum Stress ◽  
Elastic Stress ◽  
Finite Thickness ◽  
Plate Thickness ◽  
Three Dimensional

Based on detailed three-dimensional finite element analyses, elastic stress and strain field of ellipse major axis end in plates with different thickness and ellipse configurations subjected to uniaxial tension have been investigated. The plate thickness and ellipse configuration have obvious effects on the stress concentration factor, which is higher in finite thickness plates than in plane stress and plane strain cases. The out-of-plane stress constraint factor tends the maximum on the mid-plane and approaches to zero on the free plane. Stress concentration factors distribute ununiformly through the plate thickness, the value and location of maximum stress concentration factor depend on the plate thickness and the ellipse configurations. Both stress concentration factor in the middle plane and the maximum stress concentration factor are greater than that under plane stress or plane strain states, so it is unsafe to suppose a tensioned plate with finite thickness as one undergone plane stress or plane strain. For the sharper notch, the influence of three-dimensional stress state on the SCF must be considered.

scholarly journals Three-Dimensional Lattice Boltzmann Simulation of Two-Phase Flow Containing a Deformable Body with a Viscoelastic Membrane

2011 ◽  
Vol 9 (5) ◽  
pp. 1397-1413 ◽  
Author(s):  
Toshiro Murayama ◽  
Masato Yoshino ◽  
Tetsuo Hirata
Keyword(s):  
Lattice Boltzmann ◽  
Present Method ◽  
Deformable Body ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Spherical Body ◽  
The Body ◽  
Elastic Model ◽  
Two Phase ◽  
Lattice Boltzmann Simulation

AbstractThe lattice Boltzmann method (LBM) with an elastic model is applied to the simulation of two-phase flows containing a deformable body with a viscoelastic membrane. The numerical method is based on the LBM for incompressible two-phase fluid flows with the same density. The body has an internal fluid covered by a viscoelastic membrane of a finite thickness. An elastic model is introduced to the LBM in order to determine the elastic forces acting on the viscoelastic membrane of the body. In the present method, we take account of changes in surface area of the membrane and in total volume of the body as well as shear deformation of the membrane. By using this method, we calculate two problems, the behavior of an initially spherical body under shear flow and the motion of a body with initially spherical or biconcave discoidal shape in square pipe flow. Calculated deformations of the body (the Taylor shape parameter) for various shear rates are in good agreement with other numerical results. Moreover, tank-treading motion, which is a characteristic motion of viscoelastic bodies in shear flows, is simulated by the present method.

scholarly journals Three-dimensional stress systems in isotropic plates. II

1948 ◽  
Vol 193 (1033) ◽  
pp. 229-248 ◽  
Keyword(s):  
Applied Stress ◽  
Plane Stress ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Integral Form ◽  
Approximate Theory ◽  
Numerical Work ◽  
Isotropic Plates

The problem of an isolated force uniformly distributed through a plate of finite thickness and acting parallel to the faces of the plate, which are free from applied stress, is solved in integral form. Numerical work is carried out for the average values of the stresses in order to compare the results with those found from the approximate theory of generalized plane stress. In addition, numerical values of the stresses are found on the faces of the plate and on the plane midway between the faces.

Effect of Radial Clearance on the Flow Between Corotating Disks in Fixed Cylindrical Enclosures

2002 ◽  
Vol 124 (3) ◽  
pp. 719-727 ◽  
Author(s):  
Mohammad Al-Shannag ◽  
Joan Herrero ◽  
Joseph A. C. Humphrey ◽  
Francesc Giralt
Keyword(s):  
Finite Thickness ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Disk Surface ◽  
Plane Boundary ◽  
Radial Clearance ◽  
Surface Shear ◽  
Entire Flow ◽  
Flow Domain ◽  
Computationally Intensive

Numerical results are obtained for the isothermal laminar flow of air between a pair of disks attached to and rotating with a hub in a fixed cylindrical enclosure. The presence of radial clearances or “gaps” between the rims of the disks and the curved enclosure wall, and the finite thickness of the disks, are considered in the calculations. The gaps allow time- and circumferentially-dependent axially-directed air flow exchanges between the contiguous inter-disk spaces. As a consequence, axisymmetric calculations of the flow, whether using boundary conditions in the gaps or extended to include the entire flow domain, fail to faithfully reproduce the experimentally measured radial variations of the mean and rms circumferential velocity components in the inter-disk space. Likewise, three-dimensional calculations using the symmetry-plane boundary condition in the gaps also fail to reproduce these variations. In contrast, computationally intensive three-dimensional calculations of the entire flow domain, including the gaps, yield results in very good agreement with the measured mean and rms velocities. These three-dimensional calculations reveal large velocity fluctuations in the gap regions accompanied by corresponding large fluctuations of the inter-disk flow, reflecting a destabilization of the structure and dynamics of the latter by the former. The axisymmetric calculations as well as those using the symmetry-plane condition in the gap are included in this study principally to elucidate their shortcomings in simulating the three-dimensional flows considered; they are not the main goal of the study. Notwithstanding, the physically approximate, full domain axisymmetric calculations yield useful qualitative results. They show that increasing gap size decreases disk surface shear and the associated disk torque coefficient, but at the cost of destabilizing the inter-disk flow. This observation is in agreement with earlier findings and is better understood as the result of the present study.

An Exact Three-Dimensional Solution for Simply Supported Rectangular Piezoelectric Plates

1996 ◽  
Vol 63 (3) ◽  
pp. 628-638 ◽  
Author(s):  
P. Bisegna ◽  
F. Maceri
Keyword(s):  
Isotropic Material ◽  
Piezoelectric Plate ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Transversely Isotropic Material ◽  
Reference Case ◽  
Dimensional Solution ◽  
Simply Supported ◽  
Side Ratio

An exact three-dimensional solution for the problem of a simply supported rectangular homogeneous piezoelectric plate is obtained, in the framework of the linear theory of piezoelectricity. The plate is made of a transversely isotropic material, is earthed on the lateral boundary, and is subjected to prescribed surface charge and tractions on the end faces. The limit of this solution as the plate thickness aspect ratio approaches zero is explicitly carried out. The analytical results obtained may constitute a reference case when developing or applying two-dimensional plate theories for the analysis of more complex piezoelectric problems. A numerical investigation in the case of a square uniformly loaded plate is also performed, in order to evaluate the influence of the thickness-to-side ratio on the three-dimensional solution of the plate problem.

scholarly journals Three-dimesnional stress systems in isotropic plates. I

1948 ◽  
Vol 240 (825) ◽  
pp. 561-597 ◽  
Keyword(s):  
Applied Stress ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Cylindrical Hole ◽  
Stress Distributions ◽  
Numerical Work ◽  
Direction Parallel ◽  
Isotropic Plates ◽  
Plane Plate ◽  
Infinite Extent

General analysis is developed for certain three-dimensional stress distributions in a plane plate of infinite extent but of finite thickness which contains a circular cylindrical hole, the faces of the plate being free from applied stress. The analysis is used to solve the problem of a plate under uniform tension in a direction parallel to its faces, the cylindrical hole being free from applied stress. Numerical work is carried out for the case when the diameter of the hole is equal to the thickness of the plate.

Investigation on Mixed Mode Stress Intensity Factors for Inclined Surface Crack in Finite-Thickness Plates and Parameters Influence

2011 ◽  
Vol 217-218 ◽  
pp. 330-335
Author(s):  
Wei Xie ◽  
Shao Wei Tu ◽  
Qi Qing Huang ◽  
Zhi Ping Yin
Keyword(s):  
Stress Intensity ◽  
Mixed Mode ◽  
Finite Thickness ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Adaptive Method ◽  
Mixed Mode Fracture ◽  
Mesh Model ◽  
Mode Stress ◽  
Inclined Surface

In this paper, mixed mode stress intensity factor (SIF) solutions are computed for inclined surface cracks in finite-thickness plates. The S-version finite element method (S-FEM), which is an adaptive method and multi-scale computing method, are employed in the analyses. When S-FEM is applied to solve the fracture problem, local mesh model including cracks can be built independently from the global mesh model for modeling overall structure. The local model is superposed on the g- lobal one. Therefore, it is easy to introduce cracks in an existing mesh model. The influences of inc- lination angles, crack shape and plate thickness on the mixed mode fracture solution were investiga- ted. The solutions presented can be used to assess fail/safe conditions and fatigue crack growth for the three-dimensional cracks studied.

scholarly journals On the refined stress analysis in the applied elasticity problems accounting of gradient effects

2019 ◽  
Vol 489 (6) ◽  
pp. 585-591
Author(s):  
E. V. Lomakin ◽  
S. A. Lurie ◽  
L. N. Rabinskiy ◽  
Y. O. Solyaev
Keyword(s):  
Scale Parameter ◽  
Three Dimensional ◽  
Fundamental Property ◽  
Gradient Elasticity ◽  
Theory Of Elasticity ◽  
The Body ◽  
Length Scale Parameter ◽  
Gradient Theory ◽  
Length Scale ◽  
Dimensional Solution

The paper proposes an extension of the approaches of gradient elasticity of deformable media, which consists in using the fundamental property of solutions of the gradient theory - ​the smoothing of singular solutions of the classical theory of elasticity, converting them into a regular class not only for the problems of micromechanics, where the length scale parameter is of the order of the materials characteristic size, but for macromechanical problems. In these problems, the length scale parameter, as a rule, can be found from the macro-experiments or numerical experiments and does note have an extremely small values. It is shown, by attracting numerical three-dimensional modeling, that even one-dimensional gradient solutions make it possible to clarify the stress distribution in the constrained zones of the body and in the area of the loads application. It is shown that additional length scale parameters of the gradient theory are related with specific boundary effects and can be associated with structural geometric parameters and loading conditions that determine the features of the classical three-dimensional solution.

scholarly journals Three-Dimensional Thermoelastic Contact Model of Coated Solids with Frictional Heat Partition Considered

Coatings ◽  
2018 ◽  
Vol 8 (12) ◽  
pp. 470 ◽  
Author(s):  
Tingjian Wang ◽  
Xinxin Ma ◽  
Liqin Wang ◽  
Le Gu ◽  
Longcheng Yin ◽  
...  
Keyword(s):  
Present Model ◽  
Integral Transform ◽  
Three Dimensional ◽  
Fourier Integral ◽  
Contact Model ◽  
Frictional Heat ◽  
Normal Displacement ◽  
Fast Fourier Transformation ◽  
Thermoelastic Contact ◽  
Heat Partition

In this paper, a three-dimensional thermoelastic contact model of coated solids with the frictional heat partition considered is developed by introducing a frictional heat partition model. The influence coefficients of the temperature rise, normal displacement and stress components in the three-dimensional thermoelastic contact model are converted from their corresponding frequency response functions (FRFs) with a conversion method based on the fast Fourier transform (FFT), and the FRFs of solids coated with a homogeneous coating subjected to a coupled action of the mechanical loading and the frictional heat flux on its surface are deduced in the frequency domain by introducing a two-dimensional Fourier integral transform. The contact pressure and the frictional heat partition between the two bodies are solved by employing a fast numerical algorithm based on the conjugate gradient method (CGM) and a discrete convolution fast Fourier transformation (DC-FFT). Comparison between the solutions of the present model and those of a thermoelastic contact model in literature is conducted in order to validate the present model. Several specific conclusions on the effect of the sliding speed, thermoelastic properties and thickness of the coating are drawn based on the result of numerical investigation by utilizing the present model.

Effect of Thickness on the Stresses in a Plate With an Elliptic Hole

1977 ◽  
Vol 99 (2) ◽  
pp. 401-403 ◽  
Author(s):  
M. N. Bapu Rao
Keyword(s):  
Circular Hole ◽  
Thick Plate ◽  
Maximum Stress ◽  
Semimajor Axis ◽  
Plate Thickness ◽  
Elliptic Hole ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Uniform Tension

A three-dimensional analysis is presented for the stresses around an elliptic hole in an infinitely long thick plate subjected to uniform tension and shear. The maximum stress is found to depend on the ratio of plate thickness to the length of the semimajor axis of the hole, as well as on Poisson’s ratio. In the limiting cases the solution reduces to that of the circular-hole problem and the two-dimensional solution of the elliptic-hole problem.

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