Finite Elements Using Python: Theory and Routines for Rods and Beams

This book is intended as a study aid for the finite element method in undergraduate well as postgraduate degree courses in engineering at universities. Based on the general-purpose programming language Python, we offer routines to symbolically or numerically solve problems from the context of plane truss and frame structures. This allows to check classical 'hand calculations' on the one hand and to understand the computer implementation of the method on the other hand. 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 are still possible to be displayed with all components and not only in a symbolic representation. The use of a general-purpose programming language and the available libraries, e.g. for equation solving or symbolic mathematics, allows to focus more on the methodology of the finite element method and not on standard procedures. Some of the provided examples should also be solved in a classical 'hand calculations' to better understand the computer implementation.