A universal asymptotic algorithm for elastic thin shells

2000 ◽  
Vol 11 (6) ◽  
pp. 573-594 ◽  
Author(s):  
A. G. ASLANYAN ◽  
A. B. MOVCHAN ◽  
Ö. SELSIL
Keyword(s):  
Boundary Value Problem ◽  
Eigenvalue Problems ◽  
Boundary Value ◽  
Thin Shells ◽  
Membrane Theory ◽  
Moment Theory ◽  
Elastic Shells ◽  
Thin Region ◽  
The Moment

This work presents an asymptotic algorithm for the derivation of equations of thin elastic shells. The algorithm is based on the analysis of a boundary value problem for the Navier system in a thin region. The analysis covers both the membrane theory and the moment theory of elastic shells, including the eigenvalue problems.

ПРИНЦИП ВОЗМОЖНЫХ ПЕРЕМЕЩЕНИЙ В МОМЕНТНОМЕМБРАННОЙ ДИНАМИЧЕСКОЙ ТЕОРИИ УПРУГИХ ТОНКИХ ОБОЛОЧЕК / The Principle of Possible Displacments in the Moment-Membrane Dynamic Theory of Elastic Thin Shells

2021 ◽  
pp. 10-19
Author(s):  
S. Sargsyan
Keyword(s):  
Boundary Value Problem ◽  
Dynamic Theory ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Thin Shells ◽  
Moment Theory ◽  
Thin Region ◽  
Membrane Dynamic ◽  
Dimensional Boundary ◽  
The Moment

В работе излагается моментно-мембранная динамическая теория упругих тонких оболочек на основе метода гипотез, который соответствует качественной стороне результата интегрирования трехмерной граничной задачи моментной теории упругости в тонкой области оболочки. На основе принципа возможных перемещений трехмерной моментной динамической теории упругости с независимыми полями перемещений и вращений и основных соотношений моментномембранной динамической теории упругих тонких оболочек, устанавливается принцип возможных перемещений для моментномембранной динамической теории упругих тонких оболочек./ In the present paper the moment-membrane dynamic theory of elastic thin shells is presented based on the hypotheses method, which corresponds to the qualitative side of the result of integration of the three-dimensional boundary-value problem of the moment theory of elasticity in a thin region of the shell. On the basis of the principle of possible displacements of the threedimensional moment dynamic theory of elasticity with independent fields of displacements and rotations and the basic relations of the moment-membrane dynamic theory of elastic thin shells, the principle of possible displacements for the moment-membrane dynamic theory of elastic thin shells is established.

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 Existence Theorems for Some Classes of Boundary Value Problems Involving the P(X)-Laplacian

2008 ◽  
Vol 13 (2) ◽  
pp. 145-158
Author(s):  
Ionica Andrei
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Theoretical Approach ◽  
Eigenvalue Problems ◽  
Nonlinear Eigenvalue Problem ◽  
Existence Theorems ◽  
Boundary Value ◽  
Mountain Pass ◽  
Mountain Pass Lemma

We prove an alternative for a nonlinear eigenvalue problem involving the p(x)-Laplacian and study a subcritical boundary value problem for the same operator. The theoretical approach is the Mountain Pass Lemma and one of its variants, which is very useful in the study of eigenvalue problems.

scholarly journals Simulation of microwave circuits and laser structures including PML by means of FIT

2005 ◽  
Vol 2 ◽  
pp. 107-112
Author(s):  
G. Hebermehl ◽  
J. Schefter ◽  
R. Schlundt ◽  
Th. Tischler ◽  
H. Zscheile ◽  
...  
Keyword(s):  
Electric Field ◽  
Boundary Value Problem ◽  
Large Scale ◽  
Eigenvalue Problems ◽  
Boundary Value ◽  
Microwave Circuits ◽  
Algebraic Equations ◽  
Fine Grid ◽  
Preconditioning Techniques ◽  
Linear Algebraic Equations

Abstract. Field-oriented methods which describe the physical properties of microwave circuits and optical structures are an indispensable tool to avoid costly and time-consuming redesign cycles. Commonly the electromagnetic characteristics of the structures are described by the scattering matrix which is extracted from the orthogonal decomposition of the electric field. The electric field is the solution of an eigenvalue and a boundary value problem for Maxwell’s equations in the frequency domain. We discretize the equations with staggered orthogonal grids using the Finite Integration Technique (FIT). Maxwellian grid equations are formulated for staggered nonequidistant rectangular grids and for tetrahedral nets with corresponding dual Voronoi cells. The interesting modes of smallest attenuation are found solving a sequence of eigenvalue problems of modified matrices. To reduce the execution time for high-dimensional problems a coarse and a fine grid is used. The calculations are carried out, using two levels of parallelization. The discretized boundary value problem, a large-scale system of linear algebraic equations with different right-hand sides, is solved by a block Krylov subspace method with various preconditioning techniques. Special attention is paid to the Perfectly Matched Layer boundary condition (PML) which causes non physical modes and a significantly increased number of iterations in the iterative methods.

scholarly journals Hartman-Wintner-Type Inequality for a Fractional Boundary Value Problem via a Fractional Derivative with respect to Another Function

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Mohamed Jleli ◽  
Mokhtar Kirane ◽  
Bessem Samet
Keyword(s):  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Eigenvalue Problems ◽  
Boundary Value ◽  
Type Inequality ◽  
Fractional Boundary Value Problem

We consider a fractional boundary value problem involving a fractional derivative with respect to a certain function g. A Hartman-Wintner-type inequality is obtained for such problem. Next, several Lyapunov-type inequalities are deduced for different choices of the function g. Moreover, some applications to eigenvalue problems are presented.

scholarly journals Solvability of a fourth-order boundary value problem with periodic boundary conditions II

1991 ◽  
Vol 14 (1) ◽  
pp. 127-137 ◽  
Author(s):  
Chaitan P. Gupta
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Periodic Boundary ◽  
Eigenvalue Problems ◽  
Boundary Value ◽  
Periodic Boundary Conditions ◽  
Special Case

Letf:[0,1]×R4→Rbe a function satisfying Caratheodory's conditions ande(x)∈L1[0,1]. This paper is concerned with the solvability of the fourth-order fully quasilinear boundary value problemd4udx4+f(x,u(x),u′(x),u″(x),u‴(x))=e(x),   0<x<1, withu(0)−u(1)=u′(0)−u′(1)=u″(0)-u″(1)=u‴(0)-u‴(1)=0. This problem was studied earlier by the author in the special case whenfwas of the formf(x,u(x)), i.e., independent ofu′(x),u″(x),u‴(x). It turns out that the earlier methods do not apply in this general case. The conditions need to be related to both of the linear eigenvalue problemsd4udx4=λ4uandd4udx4=−λ2d2udx2with periodic boundary conditions.

scholarly journals Hartman-Wintner and Lyapunov-type inequalities for high order fractional boundary value problems

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2273-2281
Author(s):  
Şuayip Toprakseven
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Nontrivial Solution ◽  
Eigenvalue Problems ◽  
Boundary Value ◽  
High Order ◽  
Fractional Boundary Value Problem ◽  
Sturm Liouville ◽  
Fractional Boundary Value Problems

In this paper, we obtain Hartman-Wintner and Lyapunov-type inequalities for the three-point fractional boundary value problem of the fractional Liouville-Caputo differential equation of order ? 2 (2; 3]. The results presented in this work are sharper than the existing results in the literature. As an application of the results, the fractional Sturm-Liouville eigenvalue problems have also been presented. Moreover, we examine the nonexistence of the nontrivial solution of the fractional boundary value problem.

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