Main topic: Numerical methods in nonlinear structural dynamics


My academic journey in Aerospace Engineering has led me to a PhD focused on tackling the complex challenges in nonlinear structural dynamics. I develop robust computational frameworks to simulate and analyse systems exhibiting strong nonlinear behaviour. My expertise lies at the intersection of several advanced numerical techniques: I employ nonlinear solvers like the Harmonic Balance and Shooting methods for periodic solutions, implement nonlinear Finite Element Analysis (FEA) for spatial discretisation, and research nonlinear model order reduction. Specifically, I use invariant manifold theory, such as Spectral Submanifolds (SSM), to construct minimal-order models that capture the essential nonlinear dynamics of large-scale structures, enabling faster and more accurate simulations for structural dynamics.

Important Publications:

A Python Implementation of a Robust Multi-harmonic Balance with Numerical Continuation and Automatic Differentiation for Structural Dynamics
Journal of Computational and Nonlinear Dynamics
2023-04-27 | Journal article
DOI: 10.1115/1.4062424
Contributors: Tiago Martins; Francesco Trainotti; Andreas Zwölfer; Frederico Afonso
https://asmedigitalcollection.asme.org/computationalnonlinear/article-abstract/18/7/071008/1163157/A-Python-Implementation-of-a-Robust-Multi-Harmonic?redirectedFrom=fulltext

An Investigation of Nonlinear Solution Techniques for SSM-Reduced Mechanical Systems
Nonlinear Structures & Systems, Vol. 1
2025 | Conference paper
DOI: 10.13052/97887-438-0146-7_14
Contributors: Tiago Martins; F. Trainotti; L. Kreuzer; D. J. Rixen
https://www.riverpublishers.com/pdf/ebook/chapter/RP_9788743801580C14.pdf

Theses:

Non-intrusive Direct Parametrisation of Invariant Manifolds for Reduced Order Modelling in Nonlinear Structural Dynamics
Author: Joana Maria Ramos Vardasca Pereira
(internacional collaboration with IST Lisbon and Exeter University, UK)
TUM Supervisors: Tiago Martins; Francesco Trainotti

A Shooting Algorithm with Numerical Continuation and Automatic Differentiation for Structural Dynamics
Author: Leo Kreuzer
Supervisors: Francesco Trainotti; Tiago Martins

Application of Parametric-based Proper Generalized Decomposition in Nonlinear Structural Dynamics
Author: Philipp Reer
Supervisors: Tiago Martins, Francesco Trainotti

Automatic Mesh Quality Analyser and Visualiser for Nonlinear Finite Elements
Author: Caglar Ayberk Saglik
Supervisors: Tiago Martins