Analysis of a Semi-Infinite Strip With Constant Stress Flanges Under Concentrated Loads

1966 ◽  
Vol 33 (3) ◽  
pp. 571-574 ◽  
Author(s):  
H. R. Meck
Keyword(s):  
Stress Distribution ◽  
Exact Solutions ◽  
Closed Form ◽  
Complex Variable ◽  
Constant Stress ◽  
Infinite Strip ◽  
Concentrated Loads ◽  
Simple Complex ◽  
Variable Analysis

An analysis is presented for a semi-infinite strip reinforced by flanges and subjected to concentrated in-plane loads at the ends of the flanges. The taper which results in constant flange stress is determined, and the stress distribution in the sheet is also found. A simple complex variable analysis is used which leads to exact solutions in closed form.

A Concentrated Force Problem of Plane Strain or Plane Stress

1947 ◽  
Vol 14 (3) ◽  
pp. A246
Author(s):  
A. E. Green
Keyword(s):  
Closed Form ◽  
Plane Strain ◽  
Plane Stress ◽  
Complex Variable ◽  
Elliptical Hole ◽  
Minor Axis ◽  
Concentrated Force ◽  
Large Plate ◽  
Force Problem ◽  
Variable Analysis

Abstract The problem in plane strain or plane stress of a large plate containing an elliptical hole, which is loaded by line forces at the ends of the minor axis of the ellipse, is solved in closed form by using complex variable analysis.

An inhomogeneous problem for an elastic half-strip: An exact solution

2021 ◽  
pp. 108128652199641
Author(s):  
Mikhail D Kovalenko ◽  
Irina V Menshova ◽  
Alexander P Kerzhaev ◽  
Guangming Yu
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Theory Of Elasticity ◽  
Orthogonality Relation ◽  
Infinite Strip ◽  
Inhomogeneous Problem ◽  
Half Strip

We construct exact solutions of two inhomogeneous boundary value problems in the theory of elasticity for a half-strip with free long sides in the form of series in Papkovich–Fadle eigenfunctions: (a) the half-strip end is free and (b) the half-strip end is firmly clamped. Initially, we construct a solution of the inhomogeneous problem for an infinite strip. Subsequently, the corresponding solutions for a half-strip are added to this solution, whereby the boundary conditions at the end are satisfied. The Papkovich orthogonality relation is used to solve the inhomogeneous problem in a strip.

Ward’s Solitons II: Exact Solutions

1998 ◽  
Vol 50 (6) ◽  
pp. 1119-1137 ◽  
Author(s):  
Christopher Kumar Anand
Keyword(s):  
Algebraic Geometry ◽  
Exact Solutions ◽  
Closed Form ◽  
Solution Space ◽  
Compact Surface ◽  
Closed Form Expression ◽  
Chiral Model ◽  
Form Expression ◽  
Holomorphic Bundles

AbstractIn a previous paper, we gave a correspondence between certain exact solutions to a (2 + 1)-dimensional integrable Chiral Model and holomorphic bundles on a compact surface. In this paper, we use algebraic geometry to derive a closed-form expression for those solutions and show by way of examples how the algebraic data which parametrise the solution space dictates the behaviour of the solutions.

scholarly journals New Conditions for Obtaining the Exact Solutions of the General Riccati Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Lazhar Bougoffa
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Riccati Equation ◽  
Direct Method ◽  
Equivalent Equation ◽  
A Direct Method

We propose a direct method for solving the general Riccati equationy′=f(x)+g(x)y+h(x)y2. We first reduce it into an equivalent equation, and then we formulate the relations between the coefficients functionsf(x),g(x), andh(x)of the equation to obtain an equivalent separable equation from which the previous equation can be solved in closed form. Several examples are presented to demonstrate the efficiency of this method.

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