POINT_MASS — single-node lumped translational mass#

A diagonal 3 × 3 contribution to the global mass matrix at a single grid node. Translational-only (3 DOFs per node); no stiffness contribution.

  • Spec: ELEMENTS.POINT_MASS

Verified vs single-DOF spring-mass oscillator natural frequency

Cross-vendor mapping#

Solver

Element name

Notes

femorph-solver

ELEMENTS.POINT_MASS

translational only; rotational inertia not modelled

ANSYS Mechanical APDL

MASS21

KEYOPT(3)=2 → translational only (matches our model)

NX / MSC Nastran

CONM1 / CONM2

CONM2 = standard concentrated mass with inertia tensor

Abaqus

MASS

scalar mass element

LS-DYNA

ELEMENT_MASS

lumped translational mass on a node

Restrictions#

Use a different approach when:

  • Rotational inertia is needed (e.g., flywheels, eccentric masses with offset CG) — currently un-modelled. Workaround: attach the mass via a stiff BEAM2 stub from the rotation axis.

  • Anisotropic mass (different in each direction) — the scalar \(m\, \mathbf{I}\) form is isotropic by construction; use multiple coupled springs + masses if directional inertia matters.

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#

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).