Finite Elements Using Maxima Theory and Routines for Rods and Beams - Öchsner, Andreas; Makvandi, Resam; SpringerLink (Online service) (Cham : Springer International Publishing : Imprint: Springer, 2019)
This book provides a study aid on the finite element method. Based on the free computer algebra system "Maxima", it presents routines to symbolically or numerically solve problems in the context of plane truss and frame structures. This allows readers to not only check classical "hand calculations" but also understand the computer implementation of the method. The mechanical theories focus on the classical one-dimensional structural elements, i.e. bars, Euler-Bernoulli and Timoshenko beams as well as their combination to generalized beam elements. Focusing on one-dimensional elements reduces the complexity of the mathematical framework and the resulting matrix equations can still be displayed with all components, and not only in a symbolic representation. The use of a computer algebra system and the incorporated functions, e.g. for equation solving, highlights the methodology of the finite element method rather than standard procedures. The book is based on the Springer Brief "Finite Elements for Truss and Frame Structures" (978-3-319-94940-6) by the same authors.
Introduction -- Maxima - A Computer Algebra System -- Rods and Trusses -- Euler-Bernoulli Beams and Frames -- Timoshenko Beams and Frames.
Keywords: Mechanics, Applied; Solids; Numerical analysis; Mathematics -- Data processing; Solid Mechanics; Numerical Analysis; Computational Science and Engineering