Identification of the Impulsive Load on an Elastic Rectangular Plate

2003 ◽  
Vol 39 (10) ◽  
pp. 1199-1204 ◽  
Author(s):  
E. G. Yanyutin ◽  
A. V. Voropai
Keyword(s):  
Rectangular Plate ◽  
Impulsive Load ◽  
Elastic Rectangular Plate

Technical Theory of Bending of Elastic Rectangular Plate Pivotally Supported on the Perimeter or Pinched Along Two Adjacent Sides

2020 ◽  
Vol 35 (2) ◽  
pp. 73-82
Author(s):  
A.S. Kravchuk ◽  
A.I. Kravchuk ◽  
S.A. Tomilin ◽  
S.F. Godunov
Keyword(s):  
Rectangular Plate ◽  
Technical Theory ◽  
Elastic Rectangular Plate

Bifurcations near a multiple eigenvalue of the rectangular plate problem

1986 ◽  
Vol 103 (1-2) ◽  
pp. 35-62
Author(s):  
Zoltán Sadovský
Keyword(s):  
Aspect Ratio ◽  
Rectangular Plate ◽  
Small Perturbation ◽  
Perturbation Parameter ◽  
Multiple Eigenvalue ◽  
Bifurcation Problem ◽  
Operator Equations ◽  
Double Eigenvalue ◽  
Elastic Rectangular Plate ◽  
Degenerate Cases

SynopsisWe consider the bifurcation problem of the Föppl–Kármán equations for a thin elastic rectangular plate near a multiple eigenvalue allowing for a small perturbation parameter related to the aspect ratio of the plate. The first step in the study is to introduce equivalent operator equations in the energy spaces of the problem which explicitly contain the perturbation parameter. By dealing partially with a general formulation, we obtain the main results for the double eigenvalue and Z2 ⊓ Z2 symmetry of bifurcation equations. We are chiefly interested in the degenerate cases of bifurcation equations.

scholarly journals BUCKLING AND POSTBUCKLING BEHAVIOR COMPRESSED OF THE RECTANGULAR PLATE WITH INTERNAL STRESSES, LYING ON NON-LINEAR ELASTIC FOUNDATION

2019 ◽  
Vol 81 (2) ◽  
pp. 137-145
Author(s):  
I. M. Peshkhoev ◽  
B. V. Sobol
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Asymptotic Formulas ◽  
Internal Stresses ◽  
Postbuckling Behavior ◽  
Non Linear ◽  
Compressive Loads ◽  
Elastic Rectangular Plate ◽  
Non Linear Operator ◽  
Edge Dislocations

The problem of the effect of initial imperfections in the form of small transverse loads on the loss of stability and the post-critical behavior of a compressed elastic rectangular plate lying on a non-linearly elastic foundation is considered. The plate contains in a flat state continuously distributed edge dislocations and wedge disclinations or other sources of internal stresses. The research is conducted on the basis of a modified system of non-linear Karman equations for an elastic plate with dislocations and disclinations which additionally takes into account the reaction of the base in the form of a second or third degree polynomial in deflection. Two cases of boundary conditions are considered: free pinching and movable hinged support of the edges. The problem is reduced to solving a non-linear operator equation which is investigated by the Lyapunov-Schmidt method. The linearized equation is a multiparameter boundary value problem for eigenvalues which is solved by a finite-difference method. The coefficients of the system of ramification equations are calculated numerically. The post-buckling behavior of the plate is investigated and asymptotic formulas are derived for new equilibria in the neighborhood of critical loads. For different values of the parameters of compressive loads and the parameter of internal stresses, relations have been established between the values of the parameters of the base, at which its bearing capacity is preserved in the neighborhood of the classical value of the critical load.

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