GEOMETRICALLY NONLINEAR ANALYSIS OF PLANE TRUSSES AND FRAMES USING AN AUTOMATIC DERIVATION ALGORITHM

Resumo

Structural analysis requires the derivation of complex functions usually of many variables,
especially when nonlinearities are considered. From a computational standpoint, to derivate can be a
great challenge due to a series of limitations inbuilt in the usual derivation techniques. Surmising both
these factors, this work presents the development of an automatic differentiation (AD) algorithm in
Python 3.x and its application to structural analysis, aiming at preventing possible compatibility and
truncation errors inherent to other derivation processes. The software implemented both the forward and
reverse modes of differentiation and is able to work with algorithms written as string or def Python
classes. Later, the package was used to obtain the local stiffness (tangent) matrices for plane trusses and
frames in linear and geometrically nonlinear analysis, derived through energy methods. The results were
compared with benchmarks found in the literature. Excellent results were found for the stiffness
matrices, nodal displacements and internal forces, supporting that this technique can be used for solid
mechanics problem with ease.