By Rolf Steinbuch
Die Finite Elemente Methode (FEM) ist heute ein gängiges Werkzeug der Ingenieurspraxis. Zahlreiche Programmpakete erlauben einen effektiven Einsatz des Verfahrens auch in kleineren und mittleren Betrieben. Ziel der Ausbildung ist es, einen Einblick in die dahinter stehenden Verfahren zu geben. Der Lernende soll Schwierigkeiten in manchen Anwendungen erkennen können und einen tiefen Einblick in neue Anwendungsmöglichkeiten bekommen. Dieses Werk vermittelt dem Leser used to be hinter der FEM steht, wie sie eingesetzt werden kann und worauf bei der Anwendung zu achten ist. Ein kurzer Ausblick auf nichtlineare Probleme und aktuelle Entwicklungen wird ergänzt durch Anhänge, in denen die mathematischen und elastomechanischen Grundkenntnisse wiederholt werden.
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Extra resources for Finite Elemente - Ein Einstieg (Springer-Lehrbuch) (German Edition)
3 First and Rest The ﬁrst element in a list has an enormous importance in Lisp since its combination of symbol and value determines if it is a list of data or a list with a call to a function. In fact, when Lisp ﬁnds a list, it immediately evaluates its ﬁrst element in order to know what to do with it. 3 First and Rest 25 temperatures for Berlin (-3 -2 1 4 8 11 13 12 9 6 2 -1) is “-3”, so Lisp identiﬁes it as a list where no function is called. On the other hand, the ﬁrst element of the list (add -3 -2 1 4 8 11 13 12 9 6 2 -1) is “add” and since it is included in the list of symbols of Lisp that represent functions then treats the rest of the list as arguments that must be provided to the function call.
3 First and Rest 25 temperatures for Berlin (-3 -2 1 4 8 11 13 12 9 6 2 -1) is “-3”, so Lisp identiﬁes it as a list where no function is called. On the other hand, the ﬁrst element of the list (add -3 -2 1 4 8 11 13 12 9 6 2 -1) is “add” and since it is included in the list of symbols of Lisp that represent functions then treats the rest of the list as arguments that must be provided to the function call. Having into account this grammatical rule of the language, it is not a surprise that Lisp incorporates two functions for accessing the ﬁrst element of a list and the rest of elements.
Fig. 1 A graphical representation of the relationships between the Lisp functions (ﬁrst), (rest) and (nth) 28 2 Lists Everywhere After arriving to this point, we are ready to learn how to build lists. Until now we have used the assignment function setq for linking a list to a symbol, and the symbols Berlin-lows and months were built this way. From these two symbols we are going to build a more complex list where every month and its correspondent low temperature will be paired in a sublist. Let us type the following: > (setq mt1 (cons (nth 0 months) (nth 0 Berlin-lows))) : (Jan -3) Here the new function is (cons).