On the solvability of geometrically nonlinear problem of sandwich plate theory

Badriev, I. B.; Banderov, V. V.; Garipova, G. Z.; Makarov, M. V.; Shagidullin, R. R.

doi:10.12988/ams.2015.54358

Cited by 33 publications

(18 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…To illustrate theoretical results of Theorems 1 and 2, we have solved the eigenvalue problem (9) for ( ) 1, p x = ( ) 1, r x = 1, l = using the finite difference scheme (23), (24) …”

Section: Finite Difference Approximation Of the Problemmentioning

confidence: 99%

See 1 more Smart Citation

Eigenvibrations of a bar with load

Samsonov

́ev

2017

MATEC Web Conf.

View full text Add to dashboard Cite

Abstract. The differential eigenvalue problem describing eigenvibrations of an elastic bar with load is investigated. The problem has an increasing sequence of positive simple eigenvalues with limit point at infinity. To the sequence of eigenvalues, there corresponds a complete orthonormal system of eigenfunctions. We formulate limit differential eigenvalue problems and prove the convergence of the eigenvalues and eigenfunctions of the initial problem to the corresponding eigenvalues and eigenfunctions of the limit problems as load mass tending to infinity. The original differential eigenvalue problem is approximated by the finite difference method on a uniform grid. Error estimates for approximate eigenvalues and eigenfunctions are established. Investigations of this paper can be generalized for the cases of more complicated and important problems on eigenvibrations of beams, plates and shells with attached loads.

show abstract

“…To illustrate theoretical results of Theorems 1 and 2, we have solved the eigenvalue problem (9) for ( ) 1, p x = ( ) 1, r x = 1, l = using the finite difference scheme (23), (24) …”

Section: Finite Difference Approximation Of the Problemmentioning

confidence: 99%

“…The theoretical basis for the study of nonlinear spectral problems is results obtained for linear eigenvalues problems [17][18][19][20][21][22][23]. In the papers [24][25][26][27][28][29][30], numerical methods for solving applied nonlinear boundary value problems and variational inequalities have been studied.…”

Section: Introductionmentioning

confidence: 99%

Eigenvibrations of a bar with load

Samsonov

́ev

2017

MATEC Web Conf.

View full text Add to dashboard Cite

show abstract

“…The theoretical basis for the study of nonlinear eigenvalue problems is results obtained for linear eigenvalues problems [17][18][19][20][21][22][23]. In the papers [24][25][26][27][28][29][30], numerical methods for solving applied nonlinear boundary value problems and variational inequalities have been studied. …”

Section: Introductionmentioning

confidence: 99%

Finite difference approximation of electron balance problem in the stationary high-frequency induction discharges

́ev

Chebakova

2017

MATEC Web Conf.

View full text Add to dashboard Cite

Abstract. The problem of finding the minimal eigenvalue corresponding to a positive eigenfunction of the nonlinear eigenvalue problem for the ordinary differential equation with coefficients depending on a spectral parameter is investigated. This problem arises in modeling the plasma of radio-frequency discharge at reduced pressures. The original differential eigenvalue problem is approximated by the finite difference method on a uniform grid. A sufficient condition for the existence of a minimal eigenvalue corresponding to a positive eigenfunction of the finite difference nonlinear eigenvalue problem is established. Error estimates for the approximate eigenvalue and the corresponding approximate positive eigenfunction are proved. Investigations of this paper generalize well known results for eigenvalue problems with linear dependence on the spectral parameter.

show abstract

“…Here had brought monographs [1][2][3][4][5][6] and articles [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] as classical examples, it should be noted that in all these mentioned works occurs large deformations. In these problems, one of the most apprehensions to build calculation contrivance is the decomposition of total deformations or their velocities into the elastic and plastic components.…”

Section: Introductionmentioning

confidence: 99%

Numerical modeling of mechanical behavior of clinch connections at breaking out and shearing

2017

View full text Add to dashboard Cite

Abstract. This article describes an approach to constructing the defining relationships between increment of true stresses and true deformations, with considering the contact interaction of elastoplastic deformed bodies among each other. Within the framework of finite element method, solving these problems in case of "breaking out" and "shearing" in the clinch joint, the stress fields in the zone of the clinch connection are defined, and recommendations are given for realizing the process of their creation.

show abstract

On the solvability of geometrically nonlinear problem of sandwich plate theory

Cited by 33 publications

References 23 publications

Eigenvibrations of a bar with load

Eigenvibrations of a bar with load

Finite difference approximation of electron balance problem in the stationary high-frequency induction discharges

Numerical modeling of mechanical behavior of clinch connections at breaking out and shearing

Contact Info

Product

Resources

About