scholarly journals THE FINITE STRIP METHOD FOR ACOUSTIC AND VIBROACOUSTIC PROBLEMS

2011 ◽  
Vol 19 (04) ◽  
pp. 353-378 ◽  
Author(s):  
J. POBLET-PUIG ◽  
A. RODRÍGUEZ-FERRAN
Keyword(s):  
Three Dimensional ◽  
The Finite Element Method ◽  
Frequency Range ◽  
Acoustic Boundary Conditions ◽  
Structure Interaction ◽  
Computational Costs ◽  
Finite Strip ◽  
Strip Method ◽  
Finite Strip Method ◽  
Dimensional Domain

The finite strip method, widely employed in structural mechanics, is extended to solve acoustic and vibroacoustic problems. The acoustic part of the formulation, including how to handle the most typical acoustic boundary conditions and the fluid structure interaction, is presented. Several realistic problems where the three-dimensional domain of interest has extrusion symmetry are solved. These examples illustrate the advantages of the method: it has smaller computational costs than the finite element method and consequently the analyzed frequency range can be increased.

Improved finite strip method for nonlinear analysis of long-span cable-stayed bridges

1990 ◽  
Vol 17 (1) ◽  
pp. 87-93 ◽  
Author(s):  
M. S. Cheung ◽  
Wenchang Li ◽  
L. G. Jaeger
Keyword(s):  
Three Dimensional ◽  
Structural Response ◽  
Finite Strip ◽  
Strip Method ◽  
Cable Stayed Bridge ◽  
Long Span ◽  
Finite Strip Method ◽  
Nonlinear Solutions ◽  
Raphson Iteration ◽  
Cable Stayed Bridges

As the spans of cable-stayed bridges increase, the degree of nonlinearity of structural response increases markedly. For future spans greater than (say) 800 m, existing three-dimensional software then becomes very time consuming and costly, and a finite strip approach becomes more attractive and preferable. An improved finite strip method using two types of longitudinal shape functions is developed in this paper for the analysis of girders of such bridges. The nonlinearities due to sag and angle change of the cables are taken into account by means of catenary theory. The substructuring technique and the modified Newton–Raphson iteration method are used for nonlinear solutions. A number of numerical examples are given to show the accuracy and efficiency of this method. Key words: finite strip, continuous structure, cable-stayed bridge, substructuring, catenary, nonlinearity, iteration.

An Efficient Sparse Finite Element Solver for the Radiative Transfer Equation

2009 ◽  
Author(s):  
Gisela Widmer
Keyword(s):  
Linear System ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Degrees Of Freedom ◽  
Radiative Transfer Equation ◽  
Three Dimensional ◽  
Discrete Ordinates ◽  
Five Dimensions ◽  
Computational Costs ◽  
Dimensional Domain

The stationary monochromatic radiative transfer equation (RTE) is posed in five dimensions, with the intensity depending on both a position in a three-dimensional domain as well as a direction. For non-scattering radiative transfer, sparse finite elements [1, 2] have been shown to be an efficient discretization strategy if the intensity function is sufficiently smooth. Compared to the discrete ordinates method, they make it possible to significantly reduce the number of degrees of freedom N in the discretization with almost no loss of accuracy. However, using a direct solver to solve the resulting linear system requires O(N3) operations. In this paper, an efficient solver based on the conjugate gradient method (CG) with a subspace correction preconditioner is presented. Numerical experiments show that the linear system can be solved at computational costs that are nearly proportional to the number of degrees of freedom N in the discretization.

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