Accurate Calculation of Stress Distributions in Multiholed Plates

1965 ◽  
Vol 87 (3) ◽  
pp. 331-335 ◽  
Author(s):  
L. E. Hulbert ◽  
F. W. Niedenfuhr
Keyword(s):  
Computer Program ◽  
Plane Stress ◽  
Symmetric Groups ◽  
Thin Plates ◽  
Stress Distributions ◽  
Accurate Calculation ◽  
Point Matching ◽  
Shallow Shells ◽  
Matching Technique ◽  
Stress Functions

This paper discusses the application of the point-matching technique in obtaining the solution of many problems involving multiholed thin plates undergoing generalized plane stress. The stress functions appropriate to plates with symmetric groups of holes are described. A large number of problems solved by a computer program are described and compared with published results. Problems are solved also for which there are no known published results. Two interesting new problems are discussed in detail. The results show the power and flexibility of the technique. The extension of the methods to permit the solution of problems in the deflection of thin, multiholed plates and shallow shells is discussed.

Exact Elasticity Solutions for Stresses and Deflections in Curved Beams and Rings of Exponential and T-Sections

1991 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Plane Stress ◽  
Numerical Results ◽  
Neutral Axis ◽  
Curved Beams ◽  
Equilibrium Stress ◽  
Different Boundary Conditions ◽  
Stress Functions ◽  
Elasticity Solutions

Abstract Exact elasticity solutions for stresses and deflections (displacements) in curved beams and rings of varying thicknesses are developed using polar elasticity and state of plane stress. Basic forms of differential equations of equilibrium, stress functions, and differential equations of compatibility are given. They are solved to develop expressions for radial, tangential, and shearing stresses for moment, force, and combined loadings. Neutral axis location for each type of loading is determined. Expressions for displacements are developed utilizing strain-displacement relationships of polar elasticity satisfying boundary conditions on displacements. In case of full rings stresses are as in curved beams with properly defined moment loading, but displacements differ satisfying different boundary conditions. The developments for constant thicknesses are used to develop solutions for curved beams and rings with T-sections. Comparative numerical results are given.

Point-matching technique for rectangular-cross-section dielectric rod

1971 ◽  
Vol 7 (17) ◽  
pp. 497 ◽  
Author(s):  
A.L. Cullen ◽  
O. Özkan ◽  
L.A. Jackson
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Point Matching ◽  
Matching Technique

scholarly journals Deformation and Mechanical Behaviors of SCSF and CCCF Rectangular Thin Plates Loaded by Hydrostatic Pressure

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Jun Gao ◽  
Faning Dang ◽  
Zongyuan Ma ◽  
Jie Ren
Keyword(s):  
Hydrostatic Pressure ◽  
Internal Force ◽  
Theoretical Research ◽  
Thin Plates ◽  
Mechanical Behaviors ◽  
Water Gate ◽  
Small Deflection ◽  
Dimensionless Stress ◽  
Stress Functions ◽  
Minimum Potential

Elastic rectangular thin plate problems are very important both in theoretical research and engineering applications. Based on this, the flexural deformation functions of the rectangular thin plates with two opposite edges simply supported, one edge clamped and one edge free (SCSF) and three edges clamped and one edge free (CCCF), loaded by hydrostatic pressure are determined by single trigonometric series. And the flexural deformation functions are solved via the principle of minimum potential energy. Next, the internal force and stress functions of rectangular thin plates with two boundary conditions are obtained based on the small deflection bending theory of thin plates. The dimensionless deflection, dimensionless internal force, and dimensionless stress functions of the rectangular thin plates are established as well. The analytic solution in this paper is validated by the finite element method. Finally, the influence of aspect ratio λ and Poisson’s ratio μ on the deformation and mechanical behaviors of the rectangle thin plates is analyzed in this paper. This research can provide references for the plane water gate problem in seaports and channels.

Solution of axisymmetric torsion problems by point matching

1971 ◽  
Vol 6 (2) ◽  
pp. 124-133 ◽  
Author(s):  
G J Matthews ◽  
C J Hooke
Keyword(s):  
Boundary Conditions ◽  
Numerical Technique ◽  
Point Matching ◽  
Analytical Results ◽  
Elasticity Equations ◽  
Matching Technique ◽  
Basic Solutions ◽  
Axisymmetric Bodies

A general numerical technique is presented for the solution of the problem of torsion of axisymmetric bodies. The method superimposes a number of basic solutions of the elasticity equations using the point-matching technique so as to satisfy approximately the prescribed boundary conditions of a body. Results obtained by this technique are compared with those obtained by alternative experimental and theoretical techniques for various body geometries to assess the accuracy of the method. The technique is then applied to the problem of the torsion of shouldered shafts since large discrepancies exist between the experimental and analytical results available for this type of structure.

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