Massenlements

Massenlements are discrete units used to represent mass distribution in mechanical models. In finite element analysis and multibody dynamics, continuous mass density is often replaced by a set of lumped mass elements, each with a specified mass and, in some cases, rotational inertia. They can be attached to nodes (point masses) or form small rigid bodies within the model. The main distinction is between distributed mass representation, which uses the actual density distribution across the domain, and lumped-mass representations, which simplify the mass into a finite number of elements to accelerate computation.

Two common approaches are lumped-mass elements and distributed mass elements (via a consistent mass matrix). Lumped masses lead to a diagonal mass matrix, enabling faster time integration; consistent mass matrices preserve the mass distribution more accurately but require more computation.

Applications of Massenlements include structural dynamics, vibration analysis, earthquake engineering, automotive and aerospace crash simulations, and biomechanics. In practice, each mass element has a mass value equal to the local density times the elemental volume, and its inertia is computed about its reference point. In multibody simulation, mass elements contribute to the total mass, the center of mass, and the inertia tensor of the system.

Limitations of using Massenlements involve the trade-off between accuracy and computational efficiency. The choice of mass distribution affects natural frequencies and mode shapes, and for high-frequency content or tight coupling, a finer distribution or more detailed representation may be required.

See also: mass matrix, lumped parameter model, finite element method, inertia.