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No.9 (1975/03) >

 
Title :Analysis of Continuous Beams & Cable Nets by Finite Difference Calculus
Authors :Oshiro, Takeshi
Tokashiki, Naohiko
Authors alternative :大城, 武
渡嘉敷, 直彦
Issue Date :1-Mar-1975
Abstract :With the application of high-speed electronic computers, the matrix methods have become prominent means for analyzing complex engineering structures and the advantages of the matrix methods have been shown in many cases. While the techniques of the matrix methods are simple and straight forwards, a problem of large matrix orders becomes apparent in general caces, which results in the need for large storage facilities in a computer. Also the round-off error and the excessive computation time make the methods less applicable. Generally, many engineering structures are arranged in uniform (i. e., beams on equidistant supports, cables with equal spaces.) For such structures, the discrete field analysis gives more advantages and it will be shown that this method is superior to the matrix methods. This is the direct application of finite difference calculus and the mathematical models are difference equations. Exact closed form field solution can be found for many regular cases and such solutions are valid over entire structures. Therefore, the solutions are essentially independent of the size of structures, that is, the same solution form holds for the structure with a very small or a very large number of nodes or elements. For more complex structures with irregular patterns, this method also can be applied. A closed form solutions are not to be found easily for these cases. However, the numerical technique called as 〝walk through" gives solutions, which is out of presentation of this paper. This paper presents the application of the discrete field analysis using simple examples such as continuous beams and cable nets. The closed form solutions are obtained, which are in the forms of single and double finite Fourier series. While the same examples are analyzed by the first author using the variational technique(⁵), this paper presents the direct application of the force equilibrium on node points. It will be noticed that same difference equations are obtained. The validity of this technique can be proven theoretically by the general concept of the variational technique. Comparing with the variational technique, this method yields simple forms. This paper emphasizes on the numerical calculations, which were not presented in the previous paper(⁵).
Type Local :紀要論文
ISSN :0387-429X
Publisher :琉球大学理工学部
URI :http://hdl.handle.net/20.500.12000/26434
Citation :琉球大学理工学部紀要. 工学篇 = Bulletin of Science & Engineering Division, University of the Ryukyus. Engineering no.9 p.115 -129
Appears in Collections:No.9 (1975/03)

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