This command is used to add mass to a node or geometrical region.

Directional distribution

The option distribution=3 can be used to model added mass effects for bodies submerged in a liquid. The added node mass is then a vector $\mathbf{v}_m = \left[ v_{m,x} \; v_{m,y} \; v_{m,z} \right]^T$:

$\displaystyle{ \mathbf{v}_m = \left\{ \begin{array}{c} v_{m,x} \\ v_{m,y} \\ v_{m,z} \end{array} \right\} = m_{add} \cdot A \cdot \hat{\mathbf{n}} = m_{add} \cdot A \cdot \left\{ \begin{array}{c} n_x \\ n_y \\ n_z \end{array} \right\}}$

where $A$ is the surface area represented by the node and $\hat{\mathbf{n}}$ is the surface normal vector at the node. That is, the added mass effect is assumed to be proportional to the area (of the body) projected in the acceleration direction. The node acceleration $\mathbf{a}$ at a given node force $\mathbf{F} = \left[ F_x \; F_y \; F_z \right]^T$ becomes:

$\displaystyle{ \mathbf{a} = \left\{ \begin{array}{c} a_x \\ a_y \\ a_z \end{array} \right\} = \left\{ \begin{array}{c} F_x / (m + v_{m,x}) \\ F_y / (m + v_{m,y}) \\ F_z / (m + v_{m,z}) \end{array} \right\} = \left\{ \begin{array}{c} F_x / (m + m_{add} A n_x) \\ F_y / (m + m_{add} A n_y) \\ F_z / (m + m_{add} A n_z) \end{array} \right\} }$

where $m$ is the physical node mass. Note that it remains for the user to define $m_{add}$. As a rule of thumb it should be proportional to the smallest projected side length of the body (in the acceleration direction) multiplied by the liquid density.

One can take a rigid square plate with side length $L$ submerged in a liquid with density $\rho$ as an example. According to potential flow theory, $m_{add}$ should be (Patton K.T., Tables of Hydrodynamic Mass Factors for Translational Motion, ASME, 1965):

$\displaystyle{ m_{add} = 0.3758 \rho L }$

Node mass

The following command adds a point mass of 0.13kg to a node with ID=1001.

Time dependent mass

A mass of 2.5kg is distributed to a surface and then removed after 0.01s.