Brownian motion and classical potential theory by Rao M.

By Rao M.

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5. Analysis of Large Systems by Method of Tearing this structure would also be symmetrical. This in turn conditions that the deflections of poinfs on the symmetry axis could be in the direction of this axis. In structure (b), on the other hand, the points on the symmetry axis will not be displaced in the direction of that axis. Consequently, only one half of the original structure need be analyzed under the boundary conditions shown in Fig. 3. w 2 Fig. 3 The analysis of two sub-structures in this fashion may not seem to have any advantages; nevertheless it is advantageous and such an advantage becomes more appreciable as the structure gets larger.

W 2 Fig. 3 The analysis of two sub-structures in this fashion may not seem to have any advantages; nevertheless it is advantageous and such an advantage becomes more appreciable as the structure gets larger. Especially one pays attention to the fact that after the analysis of either one of the two sub-structures, the next one can be analyzed in shorter time by the modification of the previous analysis according to the method presented in Chapter 4. Chapter 6 EQUIVALENT STIFFNESS-:f'LEXIBILITY MATRICES FOR SERIES, PARALLEL AND CLOSED-LOOP SYSTEMS Quite often, in practice, systems contain series and parallel connected members or closed loops.

In other words, the well-known analogy between elastic systems and electric circuits is encountered. R (Resistance) B (Flexibility) I (Current) P (Force) (Volt). , Introduction to Matrices and Vectors. McGraw-Hill, New York, 1961. [2] Ayres, F. , Theory and Problems of Matrices. , New York, 1962. , Matrix Methods for Engineering. , 1963. , "Inversion of Band Matrices", 2nd ASCE Conf. Electronic Computations, 1960. E. and N. Ohanian, "Tro-Diagonal Matrix Method for Complex Structures", J. Structural Division, ASCE 91, No.

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