By Alan Jennings
A e-book for engineers who desire to use matrices in electronic computation. the most subject is matrix numerical research, fairly the answer of linear simultaneous equations and eigen-value difficulties. chosen purposes were brought and likely gains of computing device implementation were mentioned
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Example text
6. Analysis of framed structures The analysis of framed structures can be considered as an extension of the network analysis principle by considering the joints and members of the frame to be nodes and branches respectively. e. three displacements in mutually perpendicular directions and also rotations about each of these directions as axis. Hence the number of equations may be quite large. However, if all of the displacement variables for each particular node are placed consecutively in the displacement vector, then the stiffness matrix can be divided into a submatrix form which has the same pattern of non-zero sub matrices as the pattern of non-zero elements occurring in an electrical resistance network with the same node and branch configuration.
2 is H= [Hp Hq1 = [-~ ~ ~ -~ -~] -1 2 3 -1 (1. 3) found by matrix addition of A and H is G = [Gp Gq 1 = [Ap Aq1 + [Hp Hq1 (1. 77). 76) can be expanded as if the submatrices are elements of the supermatrices. 9). Since the first three rows of matrix B refer to coins of denomination 5 p or less and the last two rows refer to coins of denomination greater than 5 p. e. the sub matrices may be treated as elements of the supermatrix provided that the order of multiplication in the sub matrix products is retained.
1 AN ELECTRICAL RESISTANCE NETWORK This chapter provides a selection of examples in which matrix computation is relevant. All of the problems presented here have the solution of a set of linear simultaneous equations as a key part of the computation. Examples which involve the computation of eigenvalues have been left to Chapter 7. 1. The battery in branch EA prov\des a constant voltage V across its terminals, and as a result current passes through all the branches of the circuit. The object of an analysis might be to determine how much current passes through each branch.