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

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 Interaction formulae for buckling and failure of orthotropic plates under combined axial compression/tension and shear

2021 ◽  
Author(s):  
Binwen WANG ◽  
Xiangming CHEN ◽  
Xiasheng SUN ◽  
Puhui CHEN ◽  
Zhe WANG ◽  
...  
Keyword(s):  
Axial Compression ◽  
Orthotropic Plates

scholarly journals A Revisit to CMFD Schemes: Fourier Analysis and Enhancement

Energies ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 424
Author(s):  
Dean Wang ◽  
Zuolong Zhu
Keyword(s):  
Fourier Analysis ◽  
Eigenvalue Problems ◽  
Neutron Transport ◽  
Coarse Mesh ◽  
Successive Overrelaxation ◽  
Computational Cell ◽  
Artificial Diffusion ◽  
Acceleration Method ◽  
The Stability ◽  
Partial Current

The coarse-mesh finite difference (CMFD) scheme is a very effective nonlinear diffusion acceleration method for neutron transport calculations. CMFD can become unstable and fail to converge when the computational cell optical thickness is relatively large in k-eigenvalue problems or diffusive fixed-source problems. Some variants and fixups have been developed to enhance the stability of CMFD, including the partial current-based CMFD (pCMFD), optimally diffusive CMFD (odCMFD), and linear prolongation-based CMFD (lpCMFD). Linearized Fourier analysis has proven to be a very reliable and accurate tool to investigate the convergence rate and stability of such coupled high-order transport/low-order diffusion iterative schemes. It is shown in this paper that the use of different transport solvers in Fourier analysis may have some potential implications on the development of stabilizing techniques, which is exemplified by the odCMFD scheme. A modification to the artificial diffusion coefficients of odCMFD is proposed to improve its stability. In addition, two explicit expressions are presented to calculate local optimal successive overrelaxation (SOR) factors for lpCMFD to further enhance its acceleration performance for fixed-source problems and k-eigenvalue problems, respectively.

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