Godunov-Conte Method for Solution of Eigenvalue Problems and Its Applications

1977 ◽  
Vol 44 (4) ◽  
pp. 776-779 ◽  
Author(s):  
I. Elishakoff ◽  
M. Charmats
Keyword(s):  
Vibration Analysis ◽  
Eigenvalue Problems ◽  
Annular Plate ◽  
Initial Conditions ◽  
Isotropic Case ◽  
Orthotropic Plates ◽  
Elastic Bodies ◽  
Kronecker Delta ◽  
Parallel Integration ◽  
Polar Orthotropic

The method originally presented by Godunov and modified by Conte for solution of two-point boundary-value problems, is outlined here as applied to eigenvalue problems. The method (which avoids the loss of accuracy resulting from the numerical treatment, often associated with stability and vibration analysis of elastic bodies) consists of parallel integration of the set of k homogeneous equations under the Kronecker-delta initial conditions which are orthogonal (k being the number of “missing” conditions), after each step. Subject to Conte’s test, the set of solutions is reorthogonalized by the Gram-Schmidt procedure and integration continues. The procedure prevents flattening of the base solutions, which otherwise become numerically dependent. The method is applied to stability analysis of polar orthotropic plates, and as in the isotropic case (as shown by Yamaki), it is seen that assumption of symmetric buckling results in a stability overestimate for an annular plate.

scholarly journals Vibration Analysis of Circular and Annular Plate under different Boundary Conditions

2017 ◽  
Vol 10 (32) ◽  
pp. 1-7 ◽  
Author(s):  
G. V. R. Seshagiri Rao ◽  
U. Ramakanth ◽  
Suryaprakash ◽  
◽  
◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Annular Plate ◽  
Different Boundary Conditions

scholarly journals On a class of eigenvalue problems of orthotropic plates

1986 ◽  
Vol 44 (2) ◽  
pp. 277-292
Author(s):  
Chiruvai P. Vendhan ◽  
Subroto Kumar Bhattacharyya
Keyword(s):  
Eigenvalue Problems ◽  
Orthotropic Plates

Calculation of Non-Homogeneous Anisotropic Rectangular Plates with Arbitrary Fixation on the Contur

2019 ◽  
Vol 968 ◽  
pp. 444-449
Author(s):  
Nikolay Zavrak
Keyword(s):  
Main Idea ◽  
Isotropic Case ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Anisotropic Plates ◽  
Practical Applications ◽  
Internal Forces ◽  
The Relationship ◽  
Difficult Cases ◽  
Anisotropic Rectangular Plates

The developing of the effective methodic of elastic orthotropic plates’ calculation and the research on the base of their state under different boundary conditions are of great importance nowadays. The representation of the received results in the form, convenient for practical use, is also important. For practical applications in engineering are important tables for determining deflections and internal forces of structures. Such tables for the isotropic case under various conditions of plate support on the contour are given in many works. As for the anisotropic plates, there are no such tables, with the exception of one Huber table compiled for a freely supported rectangular orthotropic plate, depending on the relationship between the stiffness values. Here is a method of calculating the non-homogeneous anisotropic rectangular plates with arbitrary fixation on the contour is set forth, which is reduced to a boundary value problem. The main idea of a calculated general methodic of linear marginal differential tasks calculation is based on underlying of the main part of a solution. Such approach is proved by means of development and some generalization of common positions of a variational method of marginal tasks of mathematical physics of self-conjugated tasks solution. To solve a system of equations in terms of displacements using finite difference method (FDM) in combination with different variations of analytical solutions. It is advisable to construct a numerical solution of the problem so that in difficult cases the support fixing and uploading solution sought, not directly, but in the form of amendments to the known solution for simple cases of reference to consolidate and uploading at finding the solutions which the analytical methods or the FDM with sparse mesh may be used. Given as examples are the results of calculation for a series of square orthotropic plates with a fixed boundary under the action of uniformly distributed load.

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