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This book is intended as a study aid for the finite element method.
Based on the free computer algebra system Maxima, we offer routines
to symbolically or numerically solve problems from the context of
two-dimensional problems. For this rather advanced topic, classical
'hand calculations' are difficult to perform and the incorporation
of a computer algebra system is a convenient approach to handle,
for example, larger matrix operations. The mechanical theories
focus on the classical two-dimensional structural elements, i.e.,
plane elements, thin or classical plates, and thick or shear
deformable plate elements. The use of a computer algebra system and
the incorporated functions, e.g., for matrix operations, allows to
focus more on the methodology of the finite element method and not
on standard procedures. Furthermore, we offer a graphical user
interface (GUI) to facilitate the model definition. Thus, the user
may enter the required definitions in a source code manner directly
in wxMaxima or use the GUI which is able to execute wxMaxime to
perform the calculations.
This study aid on numerical optimization techniques is intended for
university undergraduate and postgraduate mechanical engineering
students. Optimization procedures are becoming more and more
important for lightweight design, where weight reduction can, for
example in the case of automotive or aerospace industry, lead to
lower fuel consumption and a corresponding reduction in operational
costs as well as beneficial effects on the environment. Based on
the free computer algebra system Maxima, the authors present
procedures for numerically solving problems in engineering
mathematics as well as applications taken from traditional courses
on the strength of materials. The mechanical theories focus on the
typical one-dimensional structural elements, i.e., springs, bars,
and Euler-Bernoulli beams, in order to reduce the complexity of the
numerical framework and limit the resulting design to a low number
of variables. The use of a computer algebra system and the
incorporated functions, e.g., for derivatives or equation solving,
allows a greater focus on the methodology of the optimization
methods and not on standard procedures. The book also provides
numerous examples, including some that can be solved using a
graphical approach to help readers gain a better understanding of
the computer implementation.
This book is intended as a study aid for the finite element method.
Based on the free computer algebra system Maxima, we offer routines
to symbolically or numerically solve problems from the context of
two-dimensional problems. For this rather advanced topic, classical
'hand calculations' are difficult to perform and the incorporation
of a computer algebra system is a convenient approach to handle,
for example, larger matrix operations. The mechanical theories
focus on the classical two-dimensional structural elements, i.e.,
plane elements, thin or classical plates, and thick or shear
deformable plate elements. The use of a computer algebra system and
the incorporated functions, e.g., for matrix operations, allows to
focus more on the methodology of the finite element method and not
on standard procedures. Furthermore, we offer a graphical user
interface (GUI) to facilitate the model definition. Thus, the user
may enter the required definitions in a source code manner directly
in wxMaxima or use the GUI which is able to execute wxMaxime to
perform the calculations.
This study aid on numerical optimization techniques is intended for
university undergraduate and postgraduate mechanical engineering
students. Optimization procedures are becoming more and more
important for lightweight design, where weight reduction can, for
example in the case of automotive or aerospace industry, lead to
lower fuel consumption and a corresponding reduction in operational
costs as well as beneficial effects on the environment. Based on
the free computer algebra system Maxima, the authors present
procedures for numerically solving problems in engineering
mathematics as well as applications taken from traditional courses
on the strength of materials. The mechanical theories focus on the
typical one-dimensional structural elements, i.e., springs, bars,
and Euler-Bernoulli beams, in order to reduce the complexity of the
numerical framework and limit the resulting design to a low number
of variables. The use of a computer algebra system and the
incorporated functions, e.g., for derivatives or equation solving,
allows a greater focus on the methodology of the optimization
methods and not on standard procedures. The book also provides
numerous examples, including some that can be solved using a
graphical approach to help readers gain a better understanding of
the computer implementation.
Diese Studienhilfe zu numerischen Optimierungsverfahren richtet
sich an Studierende des Maschinenbaus im Grundstudium und im
Hauptstudium. Optimierungsverfahren gewinnen zunehmend an Bedeutung
fur den Leichtbau, wo eine Gewichtsreduzierung z.B. im Automobilbau
oder in der Luft- und Raumfahrtindustrie zu einem geringeren
Kraftstoffverbrauch und einer entsprechenden Senkung der
Betriebskosten sowie zu positiven Auswirkungen auf die Umwelt
fuhren kann. Basierend auf dem freien Computeralgebrasystem Maxima
stellen die Autoren Verfahren zur numerischen Loesung
ingenieurmathematischer Probleme sowie Anwendungen aus
traditionellen Lehrveranstaltungen zur Festigkeit von Werkstoffen
vor. Die mechanischen Theorien konzentrieren sich auf die typischen
eindimensionalen Strukturelemente, d.h. Federn, Stabe und
Euler-Bernoulli-Balken, um die Komplexitat des numerischen Rahmens
zu reduzieren und den resultierenden Entwurf auf eine geringe
Anzahl von Variablen zu beschranken. Die Verwendung eines
Computeralgebrasystems und der darin enthaltenen Funktionen, z. B.
fur Ableitungen oder Gleichungsloesungen, ermoeglicht eine starkere
Konzentration auf die Methodik der Optimierungsverfahren und nicht
auf Standardverfahren. Das Buch enthalt auch zahlreiche Beispiele,
darunter einige, die mit Hilfe eines grafischen Ansatzes geloest
werden koennen, um dem Leser ein besseres Verstandnis der
Computerimplementierung zu vermitteln.
This book is intended as an essential study aid for the finite
element method. Based on the free computer algebra system Maxima,
the authors offer routines for symbolically or numerically solving
problems in the context of plane truss and frame structures,
allowing readers to check classical 'hand calculations' on the one
hand and to understand the computer implementation of the method on
the other. The mechanical theories focus on the classical
one-dimensional structural elements, i.e. bars, Euler-Bernoulli and
Timoshenko beams, and their combination to generalized beam
elements. Focusing on one-dimensional elements reduces the
complexity of the mathematical framework, and the resulting matrix
equations can be displayed with all components and not merely in
the form of a symbolic representation. In addition, the use of a
computer algebra system and the incorporated functions, e.g. for
equation solving, allows readers to focus more on the methodology
of the finite element method and not on standard procedures.
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