A Contact Stress Problem for a Rigid Smooth Sphere in an Extended Elastic Solid

1965 ◽  
Vol 32 (3) ◽  
pp. 651-655 ◽  
Author(s):  
I-Chih Wang
Keyword(s):  
Legendre Polynomials ◽  
Mixed Boundary ◽  
Three Dimensional ◽  
Elastic Solid ◽  
Rigid Sphere ◽  
Stress Distributions ◽  
Dual Series Equations ◽  
Axisymmetric Elasticity ◽  
Rigid Smooth ◽  
Smooth Sphere

A three-dimensional axisymmetric elasticity problem pertaining to the contact stresses between a smooth rigid sphere and an infinite elastic solid with a smooth spherical cavity of the same diameter has been considered. Uniaxial loading is applied to the solid at infinity, resulting in a separation along a portion of the boundary between the sphere and the solid. The problem has been considered as a mixed boundary-value problem of elasticity. The angle of contact and the stress distributions along the contact surface are determined by solving a set of dual-series equations associated with Legendre polynomials. Numerical results are presented.

scholarly journals On Triple Series Equations Involving Series of Jacobi Polynomials

1967 ◽  
Vol 15 (3) ◽  
pp. 221-231 ◽  
Author(s):  
K. N. Srivastava
Keyword(s):  
Boundary Value Problems ◽  
Legendre Polynomials ◽  
Jacobi Polynomials ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mixed Boundary Value Problems ◽  
Dual Series Equations

Recently Collins (2) has studied triple series equations involving series of Legendre polynomials. These equations arise in the study of mixed boundary value problems and can be regarded as extensions of the dual series equations considered by Collins in (1).

Some coplanar punch and crack problems in three-dimensional elastostatics

1963 ◽  
Vol 274 (1359) ◽  
pp. 507-528 ◽  
Keyword(s):  
Half Space ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Elastic Solid ◽  
Normal Derivative ◽  
Elastic Half Space ◽  
Fredholm Integral Equations ◽  
Stress Distributions ◽  
Crack Problems ◽  
Three Dimensional Space

Certain three-dimensional punch and crack problems for an elastic half-space and an infinite elastic solid respectively reduce to Dirichlet or Neumann problems in potential theory in which the potential is to be determined at all points of an infinite three-dimensional space, given its values or the values of its normal derivative on two or more coplanar circular regions. These problems are shown to be governed by infinite sets of Fredholm integral equations of the second kind, which can be solved approximately by iteration when the spacing between the circular regions is sufficiently large compared with their radii. The stress distributions in a half-space indented by two flat-ended circular punches and in an infinite solid containing two or more coplanar penny-shaped cracks opened under pressure are thus investigated.

scholarly journals Comparison of Tooth- and Bone-Borne Appliances on the Stress Distributions and Displacement Patterns in the Facial Skeleton in Surgically Assisted Rapid Maxillary Expansion—A Finite Element Analysis (FEA) Study

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1152
Author(s):  
Rafał Nowak ◽  
Anna Olejnik ◽  
Hanna Gerber ◽  
Roman Frątczak ◽  
Ewa Zawiślak
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Three Dimensional ◽  
Element Model ◽  
Rapid Maxillary Expansion ◽  
Stress Distributions ◽  
Maxillary Expansion ◽  
Facial Skeleton ◽  
Element Analysis ◽  
Maxillary Constriction

The aim of this study was to compare the reduced stresses according to Huber’s hypothesis and the displacement pattern in the region of the facial skeleton using a tooth- or bone-borne appliance in surgically assisted rapid maxillary expansion (SARME). In the current literature, the lack of updated reports about biomechanical effects in bone-borne appliances used in SARME is noticeable. Finite element analysis (FEA) was used for this study. Six facial skeleton models were created, five with various variants of osteotomy and one without osteotomy. Two different appliances for maxillary expansion were used for each model. The three-dimensional (3D) model of the facial skeleton was created on the basis of spiral computed tomography (CT) scans of a 32-year-old patient with maxillary constriction. The finite element model was built using ANSYS 15.0 software, in which the computations were carried out. Stress distributions and displacement values along the 3D axes were found for each osteotomy variant with the expansion of the tooth- and the bone-borne devices at a level of 0.5 mm. The investigation showed that in the case of a full osteotomy of the maxilla, as described by Bell and Epker in 1976, the method of fixing the appliance for maxillary expansion had no impact on the distribution of the reduced stresses according to Huber’s hypothesis in the facial skeleton. In the case of the bone-borne appliance, the load on the teeth, which may lead to periodontal and orthodontic complications, was eliminated. In the case of a full osteotomy of the maxilla, displacements in the buccolingual direction for all the variables of the bone-borne appliance were slightly bigger than for the tooth-borne appliance.

Finite Element Analysis of Poor Distal Contact of the Femoral Component of a Cementless Hip Endoprosthesis

1993 ◽  
Vol 207 (4) ◽  
pp. 255-261 ◽  
Author(s):  
M Taylor ◽  
E W Abel
Keyword(s):  
Finite Element ◽  
Stress Distribution ◽  
Influencing Factor ◽  
Three Dimensional ◽  
Stress Distributions ◽  
Element Analysis ◽  
Hip Endoprosthesis ◽  
Applied Loading ◽  
Femoral Geometry ◽  
Contact Models

The difficulty of achieving good distal contact between a cementless hip endoprosthesis and the femur is well established. This finite element study investigates the effect on the stress distribution within the femur due to varying lengths of distal gap. Three-dimensional anatomical models of two different sized femurs were generated, based upon computer tomograph scans of two cadaveric specimens. A further six models were derived from each original model, with distal gaps varying from 10 to 60 mm in length. The resulting stress distributions within these were compared to the uniform contact models. The extent to which femoral geometry was an influencing factor on the stress distribution within the bone was also studied. Lack of distal contact with the prosthesis was found not to affect the proximal stress distribution within the femur, for distal gap lengths of up to 60 mm. In the region of no distal contact, the stress within the femur was at normal physiological levels associated with the applied loading and boundary conditions. The femoral geometry was found to have little influence on the stress distribution within the cortical bone. Although localized variations were noted, both femurs exhibited the same general stress distribution pattern.

Heat and Mass Diffusion Including Shrinkage and Hygrothermal Stress during Drying of Holed Ceramics Bricks

2011 ◽  
Vol 312-315 ◽  
pp. 971-976 ◽  
Author(s):  
J. Barbosa da Silva ◽  
G. Silva Almeida ◽  
W.C.P. Barbosa de Lima ◽  
Gelmires Araújo Neves ◽  
Antônio Gilson Barbosa de Lima
Keyword(s):  
Moisture Content ◽  
Three Dimensional ◽  
Average Moisture Content ◽  
Stress Distributions ◽  
Drying Process ◽  
Convective Boundary ◽  
Volume Method ◽  
Hygrothermal Stress ◽  
Thermo Physical Properties ◽  
Good Agreement

The Aim of this Work Is to Present a Three-Dimensional Mathematical Modelling to Predict Heat and Mass Transport inside the Industrial Brick with Rectangular Holes during the Drying Including Shrinkage and Hygrothermalelastic Stress Analysis. the Numerical Solution of the Diffusion Equation, Being Used the Finite-Volume Method, Considering Constant Thermo-Physical Properties and Convective Boundary Conditions at the Surface of the Solid, it Is Presented and Analyzed. Results of the Temperature, Moisture Content and Stress Distributions, and Drying and Heating Kinetics Are Shown and Analyzed. Results of the Average Moisture Content and Surface Temperature of the Brick along the Drying Process Are Compared with Experimental Data (T = 80.0oC and RH = 4.6 %) and Good Agreement Was Obtained. it Was Verified that the Largest Temperature, Moisture Content and Stress Gradients Are Located in the Intern and External Vertexes of the Brick.

FEM Simulation Analysis of Cross Wedge Rolling Process

2011 ◽  
Vol 381 ◽  
pp. 72-75
Author(s):  
Bin Li
Keyword(s):  
Simulation Analysis ◽  
Three Dimensional ◽  
Fem Simulation ◽  
Rolling Process ◽  
Stress Distributions ◽  
Cross Wedge Rolling ◽  
Forming Process ◽  
Pressure Distributions ◽  
Metal Forming Process ◽  
Rolling Load

This paper investigates the interfacial slip between the forming tool and workpiece in a relatively new metal forming process, cross-wedge rolling. Based on the finite elements method, three-dimensional mechanical model of cross wedge rolling process has been developed. Examples of numerical simulation for strain, stress distributions and rolling load components have been included. The main advantages of the finite element method are: the capability of obtaining detailed solutions of the mechanics in a deforming body, namely, stresses, shapes, strains or contact pressure distributions; and the computer codes, can be used for a large variety of problems by simply changing the input data.

CFD SIMULATION OF SHEAR STRESS AND SECONDARY FLOWS IN URETHRA

2007 ◽  
Vol 19 (02) ◽  
pp. 117-127 ◽  
Author(s):  
Yang-Yao Niu ◽  
Ding-Yu Chang
Keyword(s):  
Shear Stress ◽  
Cfd Simulation ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Normal Female ◽  
Urinary System ◽  
Stress Distributions ◽  
Computational Fluid Dynamics Cfd ◽  
Peak Value ◽  
Lower Urinary

In this work, a preliminary numerical simulation of the lower urinary system using Computational Fluid Dynamics (CFD) is performed. Very few studies have been done on the simulation of three-dimensional urine through the lower urinary system. In this study, a simplified lower urinary model with rigid body assumption is proposed. The distributions of urine flow velocity, wall pressure and shear stress along the urethra are simulated based on MRI scanned uroflowmetry of a normal female. Numerical results show that violent secondary flows appear on the cross surface near the end of the urethra when the inflow rate is increased. The oscillative variation of pressure and shear stress distributions are found around the beginning section of the urethra when flow rate is at the peak value.

scholarly journals Note on the Solution of Transport Equation by Tau Method and Walsh Functions

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Abdelouahab Kadem ◽  
Adem Kilicman
Keyword(s):  
Transport Equation ◽  
Legendre Polynomials ◽  
Neutron Transport ◽  
Three Dimensional ◽  
Walsh Function ◽  
Dimensional Case ◽  
Angular Variable ◽  
Tau Method ◽  
Algebraic Equations ◽  
Neutron Transport Equation

We consider the combined Walsh function for the three-dimensional case. A method for the solution of the neutron transport equation in three-dimensional case by using the Walsh function, Chebyshev polynomials, and the Legendre polynomials are considered. We also present Tau method, and it was proved that it is a good approximate to exact solutions. This method is based on expansion of the angular flux in a truncated series of Walsh function in the angular variable. The main characteristic of this technique is that it reduces the problems to those of solving a system of algebraic equations; thus, it is greatly simplifying the problem.

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