nlirma.v2001, Inertia Relief Added to Static Nonlinear Analysis, Readme Note M. A. Gockel, May 12, 2003 Revised June 13, 2003 1. SUMMARY A method is provided to apply inertia relief effects in SOL 106. Inertial loads are automatically computed that balance the applied loads. Constraint equations that measure deflections relative to the c.g. of the assemblage are applied with Lagrange Multiplier techniques (LMT). This is a method to analyze a partially or totally free structure in large displacement nonlinear analysis. The constraints are removed before finding the real modes of the system. This is a research capability, and has been checked only with the class of problem described for the test problem. Other paths through the solution sequence have not yet been checked. This alter also functions in the experimental Version 2004 of today's date. The theory is described in "THEORY OF INERTIA RELIEF IN NONLINEAR STATIC ANALYSIS.doc", included in the same zip file as this note. This alter also functioned in the experimental version 2004 of today's date. 2. INPUT The LMT variables are stored on an extra GRID entry added to the structure. Its geometry is ignored, and no CORDI or SPC data should be present on this entry. The alter does not support superelements, so this GRID by default is in the residual structure. Add "include 'nlirma.v2001' " before the CEND entry. Add a USET, U2 entry that list the DOFs of LMT grid point. Use a conventional SOL 106 input file, set up for large displacement analysis. A param, grdpnt, [gidi] input is optional but recommended. It defines the point in space where resultant loads are measured, and rigid body accelerations are listed. If placed near the c. g. of the structure it provides more understandable output. If an eigensolution is also desired add a PARAM, NLLOOP, 1 entry, and a METHOD command that selects an EIGR* entry, for the subcase where the eigensolution is desired. Both the modal and statics analysis results will be produced. If the rigid body modes are desired in the eigensolution add param, rbmodes, yes in Case Control. When this parameter is not present the contraints remove the rigid body modes in a manner that does not affect the flexible modes. If it is desired to measure all deflections in direction Ti with respect to one grid point, list its GID in a SET command, and select that set with the PARTN command. Add param, scdir, [Ti], where Ti = 1, 2, or 3. The computed inertial loads can be printed with a MPCFORCE command. 3. OUTPUT The conventional SOL 106 output is produced. Some UWM 4698 messages ("high ratios") may appear in the first few iterations, as the structure converges on an answer. These messages should stop before the converged solution is approached. After the modal solution (if selected) and the static solution output, matrix VG1D lists the GID and Ti component of the reference DOF used to shift the reference axes, if selected. The values of the displacement vectors for that DOF are listed in matrix UC6N. The rigid body mass matrix M22 used to calculate the acceleration vector MQ2 and the acceleration vector Q2RB are all listed. The automatically-generated inertial loads caused by the acceleration can be requested with an MPCFORCE request when there is no m-set (no rigid elements present or MPCs selected). If there is an m-set all inertial forces are printed out with a MATGPR module option that produces output similar to other output formats, but unfortunately is not available to PATRAN or other results processors. Other output is conventional for SOL 106. 4. LIMITATIONS An o-set (caused by ASETi or OMITi entries) is not allowed, and will cause a fatal error exit. Superelement analysis is not supported. The USET, U2 entry is required. A fatal error exit results when it is not present. Point masses will provide better behavior than coupled masses. This alter has been tested for only the class of problem described in the example problem. While some of the structure may be planar, there must be structure and mass on part of the structure that defines a 3-dimensional structure. 5. EXAMPLE PROBLEMS This capability was developed for Solar Sail analysis. This structure is an interesting application of inertia relief. A large sail is deployed in space, attached by booms to a payload structure. Solar pressure loads the sail, causing the structure to accelerate at a constant rate. This leads to inertial loads that react the pressure loads. A small 2-dimensional model is used to demonstrate use of the alter. Rather than use a 2-dimensional sail, a line of rod elements modeling a chain is used to produce a minimum size model for rapid turnaround of model development exercises. File nlirm1.dat has a chain modeled by rods hanging from a beam, subjected to loads normal to the rods. The beam is tied to a payload structure at its center. FORCE2 loads with follower forces (param,lgdisp,1) cause loads normal to the rods, analogous to pressure loads on a surface. The chain starts in the shape of a squared-off "U", and changes to a "U" with a rounded bottom. The modes of the free structure and its static analysis using inertia relief are output. This is a mininmal planar model that serves as the pilot model for larger 3 dimensional solar sail models. This pilot model has 36 DOFs in its analysis set. The Case Control Section requests all possible types of outputs, and output options. This chain model is a rigorous test of the large displacement techinque. The center links, which are 4 units long, have almost 2 units of deflection normal to the beam. The solution requires 24 iterations to converge. File nlirm11.dat is the same model with all non-essential input commented out, to demonstrate the minimum modeling required to use this alter package. File nlirm1m.dat is the same model with an MPC equation added to a grid point not connected to the model. It demonstrates that the MPC path through the iterative process is working correctly, but does not change results in any way. File nlirm11x.dat is the same model converted to SOL 101. BAR elements are placed in parallel with the RODs, to provide static stability. An inertia relief analysis is performed. The solution follows the same trends as the non-linear analysis, providing some assurance on sign conventions and other output features that should be the same order of magnitude.