TABLE OF CONTENTS Effective simulation of the pattern of behavior of discrete structural systems requires the solution of equilibrium, eigenvalue, or propagation problems, depending on the type of external excitation. Under static loading, it is necessary to solve the equilibrium problem involving the solution of a set of simultaneous algebraic equations. For stability and free vibration problems, the relevant analysis involves the eigenvalue problem solution of a pair of mostly symmetric matrices. A vital preliminary for the computation of the response of a structure because of time-dependent loading is the solution of the eigenvalue problem of matrices, with distinctive characteristics, if the modal superposition method is used for the calculations. Alternatively, a suitable step-by-step integration technique may be adopted for the dynamic problem. This involves the repeated solution of a set of simultaneous algebraic equations. In general, though, this latter technique is reserved for nonlinear problems because for linear problems the modal superposition method proves to be more efficient.
For efficient analysis of static and dynamic problems, it is vital to generate economical solution schemes for a set of algebraic simultaneous equations. Section 8.2 provides details of such conventional analysis schemes followed by more advanced techniques pertaining to sparse matrices, in Sec. 8.3.
These problems are characterized by the matrix formulation
in which the stiffness matrix K is usually symmetric and positive definite in nature; p is the external load vector consisting of mechanical and thermal forces, and q is the...
