Abstract
This tutorial article is intended to convey the capability of simulating dynamically almost any structure by means of mathematical models of several types. It is intended also for reference.
The article follows a building-block approach, starting with treatment of the basic structural elements: bars, straight beams, columns, curved beams, rods, plates, shells, and soil and foundations. Then methods of modeling an assembly of elements, as well as methods of assembling models of elements, are discussed.
The methods covered include lumping, finite differenc ing, normal modes, and assumed modes. A road map is presented which shows many analytical routes from one type of model to another. It is shown that these methods may be regarded as special cases of the Lagrange assumed- mode method. Realization of this fact enhances under standing of each method and its relationships with other methods, thus affording a unified outlook upon the methods.
Examples are given which point out both the impor tance of matching each assumed mode to every boundary condition and the remarkable accuracy of the resulting modal models.
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