The Large Mass/Spring approach is actually a modeling technique in which the user places an element with a large mass or stiffness at the points of known acceleration or
displacement. In effect, this large element acts as a constraint on the connected point. The user then supplies a corresponding large force via RLOADi or TLOADi inputs to produce the desired motion. If the added element is sufficiently stiff or heavy, the reaction forces from the actual structure will not affect the input motions. The actual input data and controls are described in “Enforced Motion” on page 197 of the MSC.Nastran Basic
Dynamic Analysis User’s Guide. Refer to them for modeling details. More advanced
applications of both large mass and large spring techniques are discussed below.
Using a large mass to enforce boundary motions is a standard practice in MSC.Nastran. It works well on a simply supported structure when a single grid point is excited by a well defined acceleration input. A typical example is the earthquake analysis of a tall building where a single base input is assumed. However the method may be abused when other types of boundary conditions are attempted.
Some additional considerations for the advanced analyst are listed below:
1. If enforced motion is applied to a redundant set of boundary points, a danger exists that the large masses (or springs) may create fictitious forces and stresses in the structure. This occurs when the enforced displacements inputs are not precisely synchronized. Also, in a modal formulation, the extra masses will cause fictitious low frequency modes to occur. The recommended procedure is to connect the redundant points with RBE (rigid) elements to prevent their
independent motions. The Lagrange Multiplier method is much better, but will not correct for errors in the loading functions. (See next note.)
2. Small errors in the loading history may cause large errors in the structural response. When using enforced accelerations in a transient solution, a small bias in the inputs (from instrumentation or processing) may cause a large spurious drift where the structure displaces a large amount as a rigid body. Solutions to remove the drift are as follows:
•
Supply a corrective load function, obtained from an initial run, to cancel the measured drift;•
Add dampers and springs in parallel with mass and tuned to filter the input signal; or•
Use the modal method and drop the zero-frequency modes. (See item 4 below.)An example of a mechanical filter is shown in the sketch below. A large mass, , is attached to the base of a structure to allow enforced accelerations. For control of the spurious displacements and velocities, attach a scalar spring, , and damper element, , between the mass and ground for each direction. If the first modal frequency is then set for a filter frequency approximately one tenth of the first vibration mode frequency, . Set the damping coefficient to a value near critical to eliminate spurious oscillations.
3. In the nonlinear transient solutions, large springs can affect the error tests and convergence logic. The internally calculated error ratios are dimensionless numbers obtained by dividing the errors by an average force or total energy. The forces and energy created by the large mass/spring approach will dominate these values, resulting in underestimates of the errors and false convergence. The solution is to decrease the error allowables on the TSTEPNL Bulk Data inputs. 4. Using these methods in a modal formulation requires some attention. For output
of total displacements, the user should retain the zero or low frequency modes that the large masses produce (i.e., set the parameter LFREQ = – .01). Note that if the low frequency modes are dropped from the dynamic solution, the output will be the correct relative motion.
Large springs for enforced displacements are not recommended for the modal formulations. They should generate high frequency modes that are usually missing from the system. The resulting dynamic solution is not valid since the large springs are not included in the modal stiffness matrix.
5. Numerical conditioning of the matrix solution may be affected by the method used to connect the large mass or spring. Numerical roundoff of the results may occur. MPCs, RBEi’s, and ASET operations all use a matrix elimination procedure that may couple many degrees-of-freedom. If a large mass or spring is not retained in the solution set, its matrix coefficient will be distributed to other solution points. Then, matrix conditioning for decomposition operations
M0 K B f1 K = 0.4 Mf12 f1 Structure Seismic Mass B K Filter M0
becomes worse, when the large terms dominate the significant finite element coupling terms). On the other hand, if the degrees-of-freedom with the large terms remain in the solution set, they remain on the diagonal of the matrix and the matrix decomposition is unaffected.
In summary, the large mass method is recommended for cases with known accelerations at a single point. It works well with the modal formulation, providing good stress and forces near the mass, and is easy to understand and use. In many cases, the structure is actually excited by the motions of a large, massive, base (for instance, the geological strata) which can actually be used as a value for the mass.
The large spring method is recommended for cases in which displacements are known at one point and a direct formulation is used. The primary advantage is its simplicity. However, the inertial loads approach or Lagrange Multiplier technique, described below, are more general and have better reliability.