scholarly journals The Approximate Solution of Some Plane Boundary Value Problems of the Moment Theory of Elasticity

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Roman Janjgava
Keyword(s):  
Approximate Solution ◽  
Stress Concentration ◽  
General Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Theory Of Elasticity ◽  
Plane Boundary ◽  
Moment Theory ◽  
The Moment

We consider a two-dimensional system of differential equations of the moment theory of elasticity. The general solution of this system is represented by two arbitrary harmonic functions and solution of the Helmholtz equation. Based on the general solution, an algorithm of constructing approximate solutions of boundary value problems is developed. Using the proposed method, the approximate solutions of some problems on stress concentration on the contours of holes are constructed. The values of stress concentration coefficients obtained in the case of moment elasticity and for the classical elastic medium are compared. In the final part of the paper, we construct the approximate solution of a nonlocal problem whose exact solution is already known and compare our approximate solution with the exact one. Supposedly, the proposed method makes it possible to construct approximate solutions of quite a wide class of boundary value problems.

scholarly journals Analytical approximate solution of higher order boundary value problems via variational iteration method

BIBECHANA ◽  
2017 ◽  
Vol 15 ◽  
pp. 37-42
Author(s):  
Jamshad Ahmad ◽  
Zobia Hamid
Keyword(s):  
Approximate Solution ◽  
Mathematical Models ◽  
Boundary Value Problems ◽  
Iteration Method ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Higher Order ◽  
Analytical Approximate Solution ◽  
Variational Iteration

In this paper, application of variational iteration method has been successfully extended to obtain approximate solutions of some higher order boundary value problems. We emphasize the power of the method by testing three different mathematical models of distinct orders. The results are obtained by using only little iteration.  BIBECHANA 15 (2018) 37-42

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.

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