Three-Dimensional Effect of Flutter in a Real Fluid

The highest order encountered in this study was 529 and resulted from an analysis of the B-58 3/8-scale model. As reported in Ref. 2, the inversion time was about 15 hours. A reciprocity check of deflections for a number of unit loadings indicated a mathematical precision to about four significant figures. In summary, the writer would like to express the following opinions. (1) The findings of Ref. 2, rather than indicating a hopeless situation, give every encouragement to the prospects of solving at least certain types of problems involving very large structural matrices. As a matter of fact, the results showed that for the sort of problems being treated, the time and cost of inverting the very large matrix tended to become the primary considera­ tion, since the highest-order matrix considered was inverted with a precision quite in accord with engineering requirements. (2) One must be careful in using matrix size as a measure of relative problem complexity. Mixed force-displacement systems of equations produce matrix sizes considerably larger than those resulting from a displacement analysis. For example, a stiffness-matr ix analysis of the same B-58 3/8-scale model of Ref. 2 would involve something less than half the order of matrix encountered in the consistent-distortion solution. Nevertheless, the writer questions whether any penalty is suffered by working with the larger matrices generated by mixed force-displacement expressions. Based on experience in using this sort of formula­ tion, the writer's opinion is that considerable promise exists for this general approach. This seems to be in accord with the conclusions reached by Klein as a result of his studies. While initially one may feel overwhelmed by the large size of the structural matrix, the great number of zero elements which characteristically arises and the facility with which modern computers handle such problems often combine to produce a relatively simple solution. (3) It seems very likely that the capability of future com­ puters will lead to lower costs of large-matrix inversions and permit more exhaustive studies of limitations associated with various types and sizes of structural matrices.