SIMULATION: Transactions of The Society for Modeling and Simulation International

Wieneke, Robert G.

doi: 10.1177/003754976600700401pmid: N/A

Gold, Robert C.

doi: 10.1177/003754976600700402pmid: N/A

Ross, Lawrence W.

doi: 10.1177/003754976600700403pmid: N/A

Ben Clymer, A.

doi: 10.1177/003754976600700404pmid: N/A

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.

Vidal, Jacques J.

doi: 10.1177/003754976600700405pmid: N/A

Howard, Bernard E.

doi: 10.1177/003754976600700406pmid: N/A

The ideas presented in this paper have evolved gradually over the past 10 to 15 years. Their genesis may be ob served in the three reports in the bibliography, covering work the author contributed to and directed. The approach has been used in many practical problems, including the simulation of guided missile systems at the large analog computer facility at Wright-Patterson Air Force Base, Ohio. The ideas have further evolved during the teaching of courses in numerical analysis at the University of Miami, a two week session at the EAI Princeton Computation Center in 1964, and extensive use of the Milgo Computa tion Center in Miami.The paper itself was prepared specifically for the meet ing at which it was presented. It was couched in general phase-space terminology, but the examples were all two dimensional. The reviewer kindly suggested that either the discussion be directed toward the phase plane, or higher dimensional examples be included. Following his sug gestion, higher dimensional examples have been solved which will be presented as a sequel, to avoid making this paper too long. In addition, one of the author's graduate students, Mr. Alex Koler, has been producing some inter esting results on the global topology of the phase plane of quadratic systems, which will be presented separately. The field appears fruitful for further investigations.