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# FEM in sloshing

Hi all,

I am working on a sloshing problem. I have a cylinder filled with water partially, I willl place it on the shake table. Say we have only horizontal movement of the table no vertical movement. I want to analyze the problem using FEM. In there I want to calculate mass matrix, stiffness matrix and load vector. Here in the problem, loading is due to horizontal velocity of the earth. Now my question is, while calculating the load vector do I need to take the nodes at the bottom of the cylindrical tank? I have taken two noded elements on the walls of the tank. Total 15 elements, 31 nodes.5 elements on each wall. I have taken 11 nodes on left wall, 11 nodes at the bottom and 11 nodes on the right wall. I need to consider those 11 nodes on the bottom wall or not? If I need not to consider, why not required to consider? And what should be the order of load vector? 15X1 with zero at the elemental positions of bottom or 10X1 excluding the elements of bottom wall........?

Thanks in advance

Regards

sreenu

## Hey all......

Hey all......

I got the answer for that load vector thing. As the base of the tank is fixed the load at the bottom wall should be zero. But I have doubt regarding the order of the load vector.

Any further explanations please......?

Sreenu

Inspiration and genius--one and the same.

_______________________________________

http://sites.google.com/site/kolukulasivasrinivas/

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Siva Srinivas Kolukula

Junior Research Fellow

## Could you be more specific

Could you be more specific about whether the structure or the fluid is analyzed by FEM?

## Hi........

Hi........

It is the fluid which I wanted to analyze. I will consider the tank to be rigid. Also if tank is flexible how the loading vector differs? I want to know in both the cases.......

Next to that I have a major problem. I have evaluated mass matrix, stiffness matrix and load vector. In sloshing to evaluate mass matrix we consider only free surface of the fluid coz sloshing taking place on free surface only. For stiffness matrix we consider whole fluid elements and for load vector elements on the interface with with solid. The following are the orders of matrices I have:

M - 11X11

K - 96X96

F - 31X1

On assembling them we have to get set of linear, coupled, second order, ordinary differential equations. Where I have to solve them for nodal variable. (nodal variable is velocity potential). And then I have to apply newmarks step by step integration. Now my major problem is how I can assemble them? All of them are of different order? If this is solved I can continue with my further calculations.

I got struck up here.......Any one can please guide me through this.........?

Thanks in advance...

Inspiration and genius--one and the same.

_______________________________________

http://sites.google.com/site/kolukulasivasrinivas/

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Siva Srinivas Kolukula

Junior Research Fellow

## Well, maybe I am missing

Well, maybe I am missing something here, but assuming your flow is potential and you are solving laplace equation in the tank, I am not sure what mass matrix you are refering to. To me the stiffness matrix would have entries as integral of (grad(φi).grad(φj)), and your 'load' vector comes from the boundary condition at wall and free surface. During the time updating, free surface is updated using kinematic boundary condition, and potential is updated using dynamic boundary condition. Likewise, boundary condition at, say rigid, walls would be inhomogneous Neumann b.c. defined by the prescribed tank motion.

On the other hand, if your flow is modeled through Navier-Stokes eqn, with field velocities as unknowns, I still don't see the origin of mass matrix. The solution scheme would depends on specific time splitting plan, but the boundary condition argument above remains valid.

Yi

## Some reference

I don't know what the scale would be for your problem, for ocean and naval architecture sloshing problem, some interesting reference could be found among ISOPE 2009 sloshing mini-symposium. And some data there could be frustrating for someone trying to reach the same time and space scale through simulation as the tests.

Yi

## Inspiration and genius--one

Hi

Yes the boundary questions are absolutely perfect. I am using Laplace Equation with velocity potential as unknown. The mass matrix has come from free surface layer of the fluid.

Inspiration and genius--one and the same.

_______________________________________

http://sites.google.com/site/kolukulasivasrinivas/

----------------------------------------------------------------------

Siva Srinivas Kolukula

Junior Research Fellow