These analyses test the family of hydrostatic fluid elements. For the two-dimensional and three-dimensional cases, a “block” of incompressible fluid is subjected to a system of loads, as shown in Figure 1.3.39–1. The downward force causes the fluid to compress vertically and expand horizontally, while maintaining the original fluid volume (since the fluid is incompressible). The spring resists the horizontal expansion of the fluid, thus generating internal pressure in the fluid. The first axisymmetric problem is similar: the fluid volume is now a cylinder, compressed axially, with a spring resisting the radial expansion. In the second axisymmetric problem the pressure inside the fluid is specified. No external loading is applied, and the “walls” bounding the fluid are fixed.

The two-dimensional fluid block measures 1 × 1 and has unit thickness, while the three-dimensional fluid block measures 1 × 1 × 1. Node 1 is the cavity reference node for the fluid cavity. In each case a single grounded spring acting in the x-direction is attached to a node on the outermost face of the model perpendicular to the x-direction. In addition, all nodes on this face are constrained to displace equally in the x-direction. The downward force is applied as a concentrated load to a single node on the uppermost face of the model perpendicular to the y-direction. All nodes on this face are constrained to displace equally in the y-direction. Finally, a grounded spring of negligible stiffness acting in the y-direction is attached to a single node on this face to preclude solver problems in the solution.

*ELEMENT, TYPE=F2D2, ELSET=CAV1
1, 2, 3
2, 3, 4
*FLUID PROPERTY, ELSET=CAV1, REFNODE=1, TYPE=HYDRAULIC
1.0

*ELEMENT, TYPE=F3D3, ELSET=CAV1
1, 2, 3, 6
2, 3, 7, 6
3, 7, 3, 4
4, 4, 8, 7
5, 6, 7, 8
6, 5, 6, 8
*FLUID PROPERTY, ELSET=CAV1, REFNODE=1, TYPE=HYDRAULIC

*ELEMENT, TYPE=F3D4, ELSET=CAV1
1, 2, 3, 7, 6
2, 3, 4, 8, 7
3, 6, 7, 8, 5
*FLUID PROPERTY, ELSET=CAV1, REFNODE=1, TYPE=HYDRAULIC

The axisymmetric fluid cylinder has a radius of 1 and a height of 1. Node 1 is the cavity reference node for the fluid cavity. In the first problem a single grounded spring acting in the r-direction is attached to a node on the outermost face of the model perpendicular to the r-direction. All nodes on this face are additionally constrained to displace equally in the r-direction. The downward force is applied as a concentrated load to a single node on the uppermost face of the model perpendicular to the z-direction. All nodes on this face are constrained to displace equally in the z-direction. Finally, a grounded spring of negligible stiffness acting in the z-direction is attached to a single node on this face to preclude solver problems in the solution. In the second problem all nodes are fixed in space, and the pressure inside the fluid is specified at node 1. No external force is specified, and no springs are used in the model.

*ELEMENT, TYPE=FAX2, ELSET=CAV1
1, 2, 3
2, 3, 4
*FLUID PROPERTY, ELSET=CAV1, REFNODE=1, TYPE=HYDRAULIC

Fluid: incompressible, density = 10.0 (arbitrary).

Spring: 400.

Loading:

The concentrated force applied to all models except the second axisymmetric analysis ( –600 at node 4) is ramped linearly from zero to the final value of –600 over a single static step. Results are reported at the end of the step.

1 for the second axisymmetric analysis.

Two-dimensional boundary conditions:

0 at node 4; is constrained to be equal at nodes 2 and 3.

0 at node 2; is constrained to be equal at nodes 3 and 4.

Three-dimensional boundary conditions:

0 at nodes 4, 5, and 8; is constrained to be equal at nodes 2, 3, 6, and 7.

0 at nodes 2, 5, and 6; is constrained to be equal at nodes 3, 4, 7, and 8.

0 at nodes 2 through 8.

Axisymmetric boundary conditions—Problem 1:

0 at node 4; is constrained to be equal at nodes 2 and 3.

0 at node 2; is constrained to be equal at nodes 3 and 4.

Axisymmetric boundary conditions—Problem 2:

0 at nodes 2, 3, and 4.

0 at nodes 2, 3, and 4.