Browsing 3. Tεχνικές Αναφορές by Subject "Applied mechanics"
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- ItemOpen AccessComputer algebra and symbolic computational mechanics
Γενικό Τμήμα (Τεχνικές Αναφορές)Ioakimidis, Nikolaos; Ιωακειμίδης, ΝικόλαοςAlthough, undoubtedly, numerical computations are the computations of primary importance in computational mechanics, nevertheless, symbolic computations also constitute a significant related tool. Here at first an extensive review of the major computer algebra systems is made, i.e. (in alphabetical order) of Derive, Macsyma, Maple, Mathematica and Reduce. Next, several applications of symbolic computations to computational mechanics are mentioned in brief (including the computer algebra system used in each of them) as well as the related very recent research results by the author. Extensive conclusions with respect to the usefulness of computer algebra systems in computational mechanics are also mentioned and several comments concerning the trends and the possibilities in this very interesting application of computer algebra systems are made.
- ItemOpen AccessNumerical verification of equations in applied mechanics: comments on the inexpensive alternative to computer algebra
Γενικό Τμήμα (Τεχνικές Αναφορές)Ioakimidis, Nikolaos; Ιωακειμίδης, ΝικόλαοςComputer algebra methods play a continually increasing rôle in the proof of equations and theorems. Gröbner bases and characteristic sets have been extensively used in this task. Here we attempt a critical view of this approach, which is frequently extremely computer-memory- and time-consuming. In fact, we suggest the direct verification of our conclusions on the basis of the existing `hypotheses' numerically and not algebraically. This approach can be incorporated into `tomorrow's semi-rigorous mathematical culture' commented by Zeilberger although a strictly rigorous related approach can also be used on the basis of the parallel numerical method. Several examples from applied mechanics (including compatibility equations in plane elasticity, the classical Newton–Kepler and related movement problems for a particle and problems during movements in mechanisms) illustrate this extremely elementary approach and its advantages over computer algebra methods in the applied mechanics environment. The case of differential polynomials constitutes a standard part of the present method.