Boundary element method for buckling eigenvalue problem and its convergence analysis

2002 ◽  
Vol 23 (2) ◽  
pp. 155-168 ◽  
Author(s):  
Ding Rui ◽  
Ding Fang-yun ◽  
Zhang Ying
Keyword(s):  
Boundary Element Method ◽  
Eigenvalue Problem ◽  
Boundary Element ◽  
Convergence Analysis ◽  
Element Method

Anti-Sloshing Effects of Longitudinal Partial Baffles in a Partly-Filled Container Under Lateral Excitation

2014 ◽  
Author(s):  
Amir Kolaei ◽  
Subhash Rakheja ◽  
Marc J. Richard
Keyword(s):  
Free Surface ◽  
Boundary Element Method ◽  
Eigenvalue Problem ◽  
Boundary Element ◽  
Lateral Force ◽  
Computational Time ◽  
Generalized Coordinates ◽  
Liquid Slosh ◽  
Lateral Excitation ◽  
Element Method

This study is aimed at analysis of transient lateral slosh in a partially-filled cylindrical tank with different designs of longitudinal partial baffles using a coupled multimodal and boundary-element method. A boundary element method is initially formulated to solve the eigenvalue problem of free liquid slosh, assuming inviscid, incompressible and irrotational flows. Significant improvement in computational time is achieved by reducing the generalized eigenvalue problem to a standard one involving only the velocity potentials on the half free-surface length using the zoning method. The generalized coordinates of the free-surface oscillations under a lateral excitation are then obtained from superposition of the natural slosh modes. The lateral slosh force is also formulated in terms of the generalized coordinates and hydrodynamic coefficients. The validity of the model is illustrated through comparisons with available analytical solutions. Two different designs of longitudinal baffles are considered: bottom- and top-mounted baffles. The effect of different baffle designs on the normalized slosh frequencies, modes and lateral force are investigated. It is shown that the multimodal method yields computationally efficient solutions of liquid slosh within moving baffled containers. The results suggest that the effectiveness of baffles in suppressing the liquid oscillations is strongly affected by the baffle length relative to the free-surface height. The top-mounted baffle yields the greatest effectiveness, when it pierces the free-surface. The bottom-mounted baffle, however, may not be considered as an efficient mean for controlling the liquid slosh in tank vehicles where the liquid fill height is above 50%.

Natural Frequencies of Submerged Structures Using an Efficient Calculation of the Added Mass Matrix in the Boundary Element Method

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Luis E. Monterrubio ◽  
Petr Krysl
Keyword(s):  
Boundary Element Method ◽  
Eigenvalue Problem ◽  
Boundary Element ◽  
Numerical Integration ◽  
Natural Frequencies ◽  
Mass Matrix ◽  
Computational Cost ◽  
Added Mass ◽  
Computational Time ◽  
Element Method

This work presents an efficient way to calculate the added mass matrix, which allows solving for natural frequencies and modes of solids vibrating in an inviscid and infinite fluid. The finite element method (FEM) is used to compute the vibration spectrum of a dry structure, then the boundary element method (BEM) is applied to compute the pressure modes needed to determine the added mass matrix that represents the fluid. The BEM requires numerical integration which results in a large computational cost. In this work, a reduction of the computational cost was achieved by computing the values of the pressure modes with the required numerical integration using a coarse BEM mesh, and then, interpolation was used to compute the pressure modes at the nodes of a fine FEM mesh. The added mass matrix was then computed and added to the original mass matrix of the generalized eigenvalue problem to determine the wetted natural frequencies. Computational cost was minimized using a reduced eigenvalue problem of size equal to the requested number of natural frequencies. The results show that the error of the natural frequencies using the procedure in this work is between 2% and 5% with 87% reduction of the computational time. The motivation of this work is to study the vibration of marine mammals' ear bones.

Sign in / Sign up

Export Citation Format

Share Document