POINT_MASS — single-node lumped translational mass

A diagonal 3 × 3 contribution to the global mass matrix at a single grid node. The translational counterpart of MASS21 KEYOPT(3) = 2 in MAPDL. No stiffness contribution.

• MAPDL alias: MASS21 (KEYOPT(3) = 2 variant)

• Spec: ELEMENTS.POINT_MASS

Mass

The full element contribution to the global mass matrix is

\[\mathbf{M}^{\mathrm{loc}} = m\, \mathbf{I}_{3 \times 3},\]

acting only on the three translational DOFs of the host node; zero on all rotational DOFs (this kernel does not model rotational inertia). The diagonal structure makes assembly trivial — no Gauss quadrature, no shape-function evaluation.

Stiffness

None. POINT_MASS is a mass-only kernel.

Real constants

• REAL[0] — \(m\), the lumped mass in kg.

Verification cross-references

• MASS21 — single-DOF spring-mass oscillator — spring + lumped mass single-DOF oscillator, \(\omega = \sqrt{k / m}\).

Implementation: femorph_solver.elements.point_mass.

References

• Cook, R. D., Malkus, D. S., Plesha, M. E., Witt, R. J. (2002) Concepts and Applications of Finite Element Analysis, 4th ed., Wiley, §11.3 (lumped mass).

• Bathe, K.-J. (2014) Finite Element Procedures, 2nd ed., §11.4.1 (concentrated-mass elements).