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This method is based on the elastic theory, where it can be assumed that most structures behave like complex elastic springs, the load-displacement relationship of which is linear. Obviously, the analysis of such complex springs is extremely difficult, but if the complex spring is subdivided into a number of simpler springs, which can readily be analysed, then by considering equilibrium and compatibility at the boundaries, or nodes, of these simpler elastic springs, the entire structure can be represented by a large number of simultaneous equations. Solution of the simultaneous equations results in the displacements at these nodes, whence the stresses in each individual spring element can be determined through Hookean elasticity.
There are two methods in Matrix Methods:
1. Flexibility Method
2. Stiffness method.
I have found a good ebook on matrix method, which you can download and study on your own. Its very easy to understand.
Download from here
Also look at this file
Also you can read this; Matrix Methods, Calculators and Computers: Impact on Introductory Mechanics of Materials Courses*