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
Cross-vendor mapping#
Solver |
Element name |
Notes |
|---|---|---|
femorph-solver |
|
translational only; rotational inertia not modelled |
ANSYS Mechanical APDL |
|
KEYOPT(3)=2 → translational only (matches our model) |
NX / MSC Nastran |
|
CONM2 = standard concentrated mass with inertia tensor |
Abaqus |
|
scalar mass element |
LS-DYNA |
|
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
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#
POINT_MASS — 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).