scholarly journals Discussion: “A Method of Solution for the Elastic Quarter-Plane” (Hete´nyi, M., 1960, ASME J. Appl. Mech., 27, pp. 289–296)

1961 ◽  
Vol 28 (1) ◽  
pp. 150-150
Author(s):  
H. Poritsky
Keyword(s):  
Quarter Plane ◽  
Method Of Solution

A Method of Solution for the Elastic Quarter-Plane

1960 ◽  
Vol 27 (2) ◽  
pp. 289-296 ◽  
Author(s):  
M. Hete´nyi
Keyword(s):  
Boundary Conditions ◽  
Half Plane ◽  
Normal Force ◽  
Tangential Force ◽  
Uniform Loading ◽  
Quarter Plane ◽  
Method Of Solution ◽  
Simple Recursion

It is shown in this paper that for given loads on the elastic quarter-plane the prescribed boundary conditions can be fulfilled by repeated superposition of known solutions for the elastic half-plane. This leads to a sequence of infinite integrals of a simple recursion pattern. The solution is exact, since the sequence may be continued to obtain any required accuracy. Solutions are derived in this manner for three types of boundary loads: (a) concentrated normal force, (b) concentrated tangential force, and (c) partially distributed uniform loading.

Numerical Methods for Solving Physically Nonlinear Problems for Inhomogeneous Thick-Walled Shells

2017 ◽  
Vol 865 ◽  
pp. 325-330 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Lyudmila S. Polyakova
Keyword(s):  
Numerical Method ◽  
Nonlinear Problems ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Deformation Diagram ◽  
Method Of Solution ◽  
Properties Of Materials ◽  
Physical Fields ◽  
Cylinders And Spheres ◽  
Numerical Method Of Solution

The paper proposes the numerical method of solution the problems of calculation the stress state in thick-walled cylinders and spheres from physically nonlinear inhomogeneous material. The urgency of solved problem due to the change of mechanical properties of materials under the influence of different physical fields (temperature, humidity, radiation, etc.). The deformation diagram describes the three-parameter formula. The numerical method used the method of successive approximations. The results of numerical calculation are compared with the test analytical solutions obtaining the authors with some restrictions on diagram parameters. The obtained results can be considered quite satisfactory.

Bounds on the Maximum Contact Stress of an Indented Elastic Layer

1971 ◽  
Vol 38 (3) ◽  
pp. 608-614 ◽  
Author(s):  
Y. C. Pao ◽  
Ting-Shu Wu ◽  
Y. P. Chiu
Keyword(s):  
Half Space ◽  
Contact Stress ◽  
Elastic Layer ◽  
Theory Of Elasticity ◽  
Contact Conditions ◽  
Practical Applications ◽  
Method Of Solution ◽  
Elastic Layers ◽  
Maximum Contact ◽  
Contact Stress Distribution

This paper is concerned with the plane-strain problem of an elastic layer supported on a half-space foundation and indented by a cylinder. A study is presented of the effect of the contact condition at the layer-foundation interface on the contact stresses of the indented layer. For the general problem of elastic indenter or elastic foundation, the integral equations governing the contact stress distribution of the indented layer derived on the basis of two-dimensional theory of elasticity are given and a numerical method of solution is formulated. The limiting contact conditions at the layer-foundation interface are then investigated by considering two extreme cases, one with the indented layer in frictionless contact with the half space and the other with the indented layer rigidly adhered to the half space. Graphs of the bounds on the maximum normal stress occurring in indented elastic layers for the cases of rigid cylindrical indenter and rigid half-space foundation are obtained for possible practical applications. Some results of the elastic indenter problem are also presented and discussed.

The laminar boundary-layer equation: a method of solution by means of an automatic computer

1955 ◽  
Vol 51 (2) ◽  
pp. 320-332 ◽  
Author(s):  
D. C. F. Leigh
Keyword(s):  
Boundary Layer ◽  
Asymptotic Solution ◽  
Laminar Boundary Layer ◽  
Iterative Process ◽  
Boundary Layer Equation ◽  
Algebraic Equations ◽  
Automatic Computer ◽  
Linear Algebraic Equations ◽  
Method Of Solution ◽  
Incompressible Boundary

ABSTRACTA method, very suitable for use with an automatic computer, of solving the Hartree-Womersley approximation to the incompressible boundary-layer equation is developed. It is based on an iterative process and the Choleski method of solving a simultaneous set of linear algebraic equations. The programming of this method for an automatic computer is discussed. Tables of a solution of the boundary-layer equation in a region upstream of the separation point are given. In the upstream neighbourhood of separation this solution is compared with Goldstein's asymptotic solution and the agreement is good.

The Preparation and Property Research on Laponite-Poly (L-Lactide) Composite Film

2013 ◽  
Vol 750-752 ◽  
pp. 1919-1923 ◽  
Author(s):  
Guo Xian Zhou ◽  
Ming Wei Yuan ◽  
Lin Jiang ◽  
Ming Long Yuan ◽  
Hong Li Li
Keyword(s):  
Electron Microscopy ◽  
Thermal Stability ◽  
Tensile Strength ◽  
Composite Film ◽  
Composite Films ◽  
Complexing Agent ◽  
Solution Blending ◽  
Method Of Solution ◽  
Thermal Stability Of ◽  
Scanning Electron

The laponite-poly (L-lactide) composite films are prepared by the method of solution blending with polylactide (PLA) and laponite. The result shows that the homogeneous and smooth composite film is prepared with 1, 4-dioxane. Thermogravimetry analysis (TG) and tensile strength studies demonstrate that the thermal stability and tensile strength are improved with the laponite added. The scanning electron microscopy (SEM) measurement indicates that the pores of composite films get uniform and network structure is more and more compact with compared to pure PLA film. The present study reveals that the laponite as a complexing agent can improve the mechanical properties and thermal stability of PLA.

An iterative method of solution for equilibrium and optimization problems

2008 ◽  
Vol 69 (8) ◽  
pp. 2709-2719 ◽  
Author(s):  
Yongfu Su ◽  
Meijuan Shang ◽  
Xiaolong Qin
Keyword(s):  
Iterative Method ◽  
Optimization Problems ◽  
Method Of Solution
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