Research

Topics

The course contents are delivered through lectures, practices, lab activities.

The course covers the following topics divided in modules as per the description below:

Module 1:

Structural analysis:

- Statically undetermined systems: Force Method.

- Axisymmetric problems: thin and thick cylinders loaded by internal and external pressure and centrifugal loads.

- Stress analysis in plastic field: notched members, bending application over elastic limit.

- Finite element modelling: basic formulation, definition of stiffness matrix, main shape functions, selection of element types, load and boundary conditions, evaluation of results, type of analysis (static, dynamic, etc.).

Module 2:

Strength of materials and assessment criteria:

- Methods for fatigue design: Safe Life, Fail Safe, Damage Tolerance

- Cyclic response of materials: high cycle fatigue, endurance limit, fatigue strength, modifying factors, stress concentration and notch sensitivity, multiaxial fatigue, variable amplitude loading, cumulative fatigue damage.

- Linear Elastic Fracture Mechanics: energy approach (Griffith), stress intensity factor, K IC, fatigue crack propagation, plastic zone, overload effect.

Module 3:

Design of machine elements

- Mechanical transmissions and Shaft. Materials, layout, design for stress, deflections, critical components, bearings.

- Bolted joints. Stresses in bolted joints, design and assessment according with Standard.

Module 4:

Case studies:

- Railway axle application

- Pressure vessel

- Hydraulic cylinder

- Strcutural Health Monitoring theory and applications

Topics

- Introduction to the structural design of machine elements and systems under extreme loading conditions;

- Mechanical behavior of materials (metal, composite, ceramic, multilayers) under extreme loading conditions: modeling approaches, calibration by inverse methods, constitutive law, equation of state, failure mechanisms, etc;

- Numerical methods: nonlinear approaches for impact engineering;

- Terminal ballistic: tests, standards, modeling approaches;

- Low velocity impacts;

- Explosions: blast loading, modeling approaches;

- Stress waves and applications;

- Discussion of relevant examples;

- Laboratory activities: Numerical modeling lab for “virtual testing”;

- Laboratory activities: Low velocity impact lab (in collaboration with HSR lab,). https://www.mecc.polimi.it/en/about-us/news/high-strain-rate-a-new-interdepartmental-lab / https://www.polimi.it/ricerca/la-ricerca-al-politecnico/laboratori/laboratori-interdipartimentali/high-strain-rate-lab ).

Topics

The course contents are delivered through lectures, exercise courses, lab activities.

The course covers the following topics as per the description below:

- Stress-strain analysis in plastic field - Notched members and plasticity in bending

- Finite element modelling: basic formulation, definition of stiffness matrix, main shape functions, selection of element types, load and boundary conditions, evaluation of results.

- Cyclic response of materials: high cycle fatigue, endurance limit, fatigue strength, modifying factors, stress concentration and notch sensitivity, multiaxial fatigue.

- Linear Elastic Fracture Mechanics: energy approach (Griffith), stress intensity factor, KIC, fatigue crack propagation.

- Basic principles of Welding and the Design of Permanent Joints.

- Basic rules for writing a FEM report.

- Relevant example of Machine design applications close to the fields of Micro-Nano, Defense and Security and Material design will be discussed during the course.

- Laboratory activities: experimental activities on mechanical components

- Laboratory activities: numerical modelling lab

Topics

The course is organized in lectures and tutorials. Theoretical concepts will be applied during application in order to show an engineering approach to the design and assessment of actual and relevant components.

Internal forces: definition of slender members, definition of internal forces and equations of equilibrium, frames;

Axial and bending problem in beams: hypotheses and basic assumptions for the Euler-Bernoulli beam; state of stress due to normal force and bending moment;

Shear in beams: relationship between bending moment and shear force; shear stress distribution in case of solid section; torsion in beam: distribution of torsional stresses for a circular solid beam;

State of stress: definition of equilibrium for deformable bodies; Cauchy tetrahedron; principal stresses and directions; stress invariants; hydrostatic stress tensor and stress deviator tensor; Mohr’s circles for plane stress; three-dimensional description of Mohr’s circles;

Material behaviour: tensile test devices and specimens; engineering stress-strain curve; true stress-strain curve; ductile and brittle failure mechanisms; ideal material models;

Influence of notch for ductile and brittle materials: phenomenological aspects; definition of Kt and Ks parameters.

Stress-strain relations: general expression of the elastic tensor; elastic tensor for isotropic materials; derivation of the generalised Hooke’s law; stress-strain relationships for plane stress and plane strain.

Failure criteria for isotropic materials: Galileo-Leibniz-Rankine-Navier criterion for brittle materials; Guest-Saint Venant-Tresca criterion for ductile materials; Huber-Hencky-von Mises criterion for ductile materials; general considerations about the definition of the safety factor;

Fatigue: fatigue phenomena; fatigue testing; definition of fatigue cycles; Wöhler diagram; finite and infinite life regime; relationship between fatigue limit and tensile strength; influence of mean stress with Haigh diagrams; notch effect on fatigue; influence of surface finishing; size effect and influence of stress gradient; damage accumulation with Miner-Palmgren rule; Gough-Pollard and Sines criteria for multi-axial loading condition.

Several applications of the previously defined concepts will be carried out.

Topics

Main topics are:

- functional description of the most common machine elements with aeronautical application (shafts, bearings, gears, frames, riveted and welded joints);

- fatigue design methodologies (Safe Life, Fail Safe, Damage Tolerant and Flaw Tolerant);

- mechanical behaviour of materials (static and fatigue behaviour, variable amplitude loadings, nucleation and propagation of cracks, defects);

- structural integrity assessment (static and fatigue assessment, multiaxial state of stress);

- application on mechanical and aeronautical components.

Course organization

Lessons and practices: lessons and practices, integrated together, will be developed during the course.

Laboratory activities : during the course, some numerical and experimental (to be confirmed during the course) lab experiences on aeronautical components and systems will be carried out. A report on the labs experiences is requested and is compulsory.

The course will merge the multidisciplinary inputs from energy, mechanical, electrical, control and management engineering in a unique and coherent virtual framework that can be used for design, operation and monitoring optimizations.

The course will introduce students to the field of industrial system monitoring, specifically focusing on the role of models (and Digital-Twins) in the diagnosis and prognosis of industrial systems and components, exploiting statistical pattern recognition and machine learning to interpret changes in their measured features.

The course will provide additional insight to the modelling of energy plant systems, with laboratory experiences focused on realistic application scenarios, also involving national and/or international industrial representatives.

Topics

The course contents are delivered through lectures and hands-on computer laboratory practices with professors and/or a tutor.

The course covers the following topics divided in modules as per the description below:

Module 1 - Introduction

Topic 1.1 - Introduction and motivation for the rapid growth of Digital-Twins for industrial applications. Real case examples will be provided as input to the students, thus setting the motivation and goal of the course. Specific attention will be devoted to the application of Digital-Twins for system health management and maintenance optimization.

Topic 1.2 - Design and maintenance criteria evolution (from safe life to damage tolerant design, from fault driven to predictive maintenance). Introduction of Health and Usage Monitoring Systems as a means toward process automatization.

Module 2 – Physics-based modelling

Topic 2.1 - Physics-based modelling : application of time-based simulation with MATLAB SIMULINK-SIMSCAPE. Hand-on practices on energy system simulation.

Topic 2.2 - Degradation and failure mechanisms : an overview of different degradation and failure mechanisms occurring on the most widely used components in the energy field of application is provided, including fatigue, creep, corrosion, pitting, lubricant degradation, battery State of Charge, including an overview of failure and degradation mechanisms. The students will particularly focus on the analytical and numerical modelling strategies for predicting damage progression.

Topic 2.3 - Time-based modelling of system degradation : simulation is used to predict in a virtual environment the effect of a potential damage over the system features observed by a sensor.

Module 3 – Event-based modelling

Topic 3.1 - Event-based modelling : Discrete Event Simulation (DES) is introduced as a means to simulate systems depending on discrete time, with particular focus on event-based degradation modelling. Practical laboratories using MATLAB SimEvents (in combination to Simulink) will be provided, e.g. modelling scenarios typical of the operation research discipline.

Topic 3.2 - Decision logic modelling : concepts and instruments will be provided to simulate the decision logics in an operative framework. Practical laboratories using MATLAB State-Flow will be provided, simulating realistic scenarios of industrial systems’ management, e.g. the battery management system and the operation and monitoring of energy systems.

Module 4 – Surrogate modelling

Topic 4.1 – Surrogate modelling : for most application, the Digital-Twin should be fast enough to be run in real-time. This is not feasible with direct simulation, while surrogate models can be used for approximating input-output relations. Different methods based on Machine Learning (e.g. Artificial Neural Networks, Gaussian Processes, etc.) will be considered for the definition of surrogate models.

Module 5 – Model updating

Topic 5.1 - Basics of Monte-Carlo sampling : the concept of Monte-Carlo sampling will be recalled as a mean to implement repeated and efficient (forced sampling) simulation of the Digital-Twin.

Topic 5.2 – Digital-Twin updating : the Digital-Twin must be updated during service life based on observations by sensors. Various methods for parameter identification and tracking based on Bayesian inference and Monte-Carlo sampling will be implemented in the framework of damage identification and operation optimization, including the Metropolis-Hastings Monte-Carlo Markov Chain and the Particle Filter.

The theoretical aspects introduced in the course will be correlated with laboratories, for a direct implementation of the methods, e.g. including the implementation of a digital-twin for the Health and Usage Monitoring and Prognostic Health Management of energy systems and components, e.g. including pressure vessels, pumps, batteries, etc..

- The students will apply the concepts developed during the course to real-case studies.

- Students will analyze the industrial system, modelling its components in their operative scenario, including potential degradation and failure mechanisms and the logistic support to guarantee their operability.

- Students will perform trade-off analysis to support management decisions

- Finally, the students will provide a report in the form of a presentation of their results, that will be evaluated as part of their final score.

- The course is aimed at providing the Students with practical concepts and instruments for modelling complex systems in their operative environment or asset, including degradation phenomena through the Digital-Twin.

- The course will merge multidisciplinary inputs from different sectors (mechanical, materials, data science, management engineering, etc.) in a unique and coherent virtual framework that can be used for design, operation and monitoring optimizations.

- The course will introduce students to the field of health and usage monitoring of structures and systems, specifically focusing on the role of models (and Digital-Twins) in the diagnosis and prognosis of mechanical (and, in general, industrial) systems and components, exploiting statistical pattern recognition and machine learning to interpret changes in their measured features.

Topics

In the era of digitalization, Digital-Twins have been proposed as a mean to mimic the system life cycles in a virtual scenario. Specifically, a Digital-Twin is a virtual replica that mirrors the real system condition, resulting from the combination of a master model (typically developed during design) with real-time data (digital shadow) potentially captured during system operation. In this context, the digital-twin, constantly updated and refined during operation, can include information about potential damage/faulty scenarios and, thus, be used to simulate new information that is necessary for real-time assessment of the actual system condition (e.g. for structural damage identification) and for predictive asset optimization (e.g. for operation and maintenance optimization). This makes the Digital-Twin a crucial element in the development of any health and usage monitoring system.

To this aim, the following topics are treated throughout the course:

Introduction: the role of the Digital-Twin within system operation. Evolution of design and maintenance criteria (from safe life to damage tolerant design, from fault driven to predictive maintenance). Introduction of Health and Usage Monitoring Systems as a means toward predictive maintenance. Application of Digital-Twins for system health and usage monitoring as input to the operation and maintenance optimization.

Operational evaluation: review of different degradation processes affecting mechanical components in their operative environment. Models for prediction of damage progression and failures (fatigue, fracture, corrosion, creep, etc.) and general system performance degradation (e.g. fouling, battery state of life/charge, etc.). Motivation to the development of Digital-Twins for health and usage monitoring.

Digital master model creation. In this practical module the student will model continuous degradation processes and discrete system failures into the physical model of the component/system (within the Matlab Simulink/Simscape/Simevents framework). Realistic application scenarios will be considered, with final goal to simulate either changes in signal features captured by potential sensors or, in general, system performance degradation.

Improve simulation speed. In this module the students will learn how to use machine learning (specifically artificial neural networks) to approximate input-output relationships simulated with a detailed model. The resulting surrogate model is a requirement enabling the stochastic adaptiveness within the following Monte-Carlo sampling framework.

Development of an adaptive and stochastic Digital-Twin. In this module the student will use Bayesian inference to fuse the information from models with the continuous stream of information by sensors, resulting in a real-time statistical adaptation of model parameters to fit the real component or system subject to degradation. The Bayesian Model Updating will also offer a natural framework for combination of prior knowledge on the system parameters (including potential damage) with the new information from sensors.

- Overview of conditional probability distributions and Bayes theorem

- Monte-Carlo sampling strategy for approximated Bayesian inference in multiple-parameter updating. The need for an efficient sampling strategy: forced sampling.

- Metropolis-Hastings Markov Chain Monte-Carlo methods for statistical pattern recognition

- Sequential Importance Sampling/Resampling (particle filter) for tracking and prognosis of non-linear non-Gaussian systems subject to degradation

- Sensor installation

- Signal acquisition

- Execution of damage tests

- Post-processing and data interpretation

- Implementation of algorithms for load identification (real-time)

- Implementation of algorithms for structural health monitoring (real-time)

Topics

The laboratory contents are delivered through introductory lectures followed by laboratory activities. Specifically, the course allows student to work on application scenarios related to active and past international projects in which the Department of Mechanical Engineering was involved. Students will be divided into groups (based on their application scenario preferences) and each group will focus on one application scenario, covering different topics of the structural health monitoirng discipline, from sensor installation, to the acquisition system setup, data acquisition and processing, modelling and the development and implementation of diagnostic and prognostic algorithms.

Focussing on diagnostics and prognostics, topics can include:

Usage monitoring

- Topic 1.1: Load identification and full field strain reconstruction

- Topic 1.2: Shape sensing based on inverse FEM for full-field displacement and strain reconstruction in real-time

Diagnostics

- Topic 2.1: Outlier analysis for damage detection

- Topic 2.2: Artificial neural networks and surrogate modelling for fatigue crack identification on a plate subject to fatigue load cycles

- Topic 2.3: Impact damage detection on a rotating helicopter transmission shaft

Prognostics

- Topic 3.1: Surrogate modelling and Bayesian updating for structural/system degradation monitoring

Application scenarios can include:

- diagnostics and prognostics of structural elements subject to fatigue damage degradation (measure: optical strain sensor; methods: machine learning, monte-carlo sampling, outlier analysis, Bayesian inference)

- diagnostics of a reduced scale bridge subject to changing boundary conditions (measure: optical strain sensor; methods: inverse FEM)

- diagnostics of rotating shafts subject to imbalance (measure: optical strain sensor, accelerometers; methods: inverse FEM, convolutional neural networks, recurrent neural networks, etc.)

- diagnostics of composite plates subject to impact (measure: piezoelectric transducers, carbon nanotubes, etc.; methods: machine learning, outlier analysis, Bayesian inference)

- other, depending on running projects.

- Introduce students with generic background (mainly mechanical engineers) to the field of ship structural design and analysis. To this aim, the first part of the course is devoted to the general definitions and illustration of structural components of a generic steel ship.

- Provide students with theoretical concepts and practical instruments for design and analysis of ship structures.

- Provide students with practical examples of application, referring to realistic case studies

- Illustrate the most common problems affecting ship operation, from structural point of view, and new trends toward operation and maintenance optimization.

Topics

The course topics include:

- Overview of regulation authorities.

- General definitions and hull components.

- Main structural components of a ship.

- Classification of static and dynamic loads. Internal and external forces.

- Static bending moment (in still water).

- Weight distribution and weight diagram.

- Bending moment diagram in presence of wave loads

- Stress distribution due to internal forces (shear, bending, torsion)

- Verification of main ship section

The theoretical aspects introduced in the course will be correlated with practices and laboratories, for a direct implementation of the methods.

Topics

Engineering

This module provides a thorough introduction to mechanical design principles, focusing on machine systems and components. It starts with fundamental concepts of material strength and beam theory, essential for all mechanical engineering designs. The course then covers specialized design elements including the engineering of notched parts, which are crucial for understanding stress distribution and mechanical integrity. It also examines the design of springs and bearings, vital for machinery efficiency and durability, and discusses common joining techniques like bolted and welded joints. A key component of the module is an introduction to the fatigue design of metal parts, teaching students how to predict and improve the endurance of components under repetitive stress.

The course includes practical sessions where students apply these theories through numerical case study analysis. These sessions ensure students not only grasp the theoretical aspects of mechanical design but also gain practical skills in addressing real-world engineering design challenges.

Manufacturing

This module presents a comprehensive overview of the fundamentals of the most common manufacturing processes for metallic alloys and plastic materials, spanning from principles to applications and technology trends. Students will learn the key factors of manufacturing processes for different industrial products in metal and metallic alloys and will realize how process capabilities (production rate, cost, quality) are determined by the material characteristics, process parameters, and machine design.

In particular, the course assists the designers in the process selection, since the beginning of the design process of industrial products.

The selection of processes starts with the definition of the project specifications and their relationship with the process variability (mainly roughness and dimensional tolerances).

The relevant issues about the economic feasibility are introduced for each process.

Relevant manufacturing processes are presented (i.e. casting, sheet metal working, chip removal processes, extrusion of plastic materials, injection moulding, welding and assembly) with their manufacturing best practices, design options, and product aesthetics.

Topics

The course deals with the design methods used in the different phases of the product development and their practical implementation in engineering design.

It is a mix of frontal theory lectures and case studies descriptions, interactive practical exercises using different commercial softwares (Fusion 360, Abaqus, Altair-Inspire, etc.) and autonomous development of a project on a relevant case study, possibly in collaboration with an important company.

LECTURES

Introduction to Engineering Design. From customer requirements to production: concept, embodiment, detail design. The role of codes and standards in Engineering Design: Design by Rules and Design by Analysis.

Design methodologies

Design for Assembly (DfA) Assembly efficiency. Joints for plastic and metal parts: screws, press-fit, rivets, focus on snap-fits. Critical evaluation of the assembly method in the overall design process with respect of performance and cost.

Design for Manufacturing (DfM) – Methods to assess the cost related to manufacturing and to orient to correct choice of the process. The case of injection molding.

Design for Environment (DfE) – The natural and the industrial product life cycles; conditions for sustainability. Life Cycle Analysis (LCA): a) the functional unit, the reference flow and the eco-indicator concepts, b) goal and scope definition, inventory, assessment of the EI, interpretation of the results. Implementation of DfE and LCA in the product design.

Design for Disassembly (DfD ) - Choice of materials: the concept of Material Removal Rate (MRE), Architecture of the system and component design, joining methods, new methods for active disassembly (smart materials).

Design for Reliability (DfR) - Basic concepts, improving the reliability of systems. Risk Analysis: Failure Mode and Effects Analysis (FMEA), Failure mode, Effects and Criticality Analysis (FMEA), Fault Tree Analysis (FTA).

Design optimization and Robust Design – Basic concepts

PRACTICES

Quantitative and in-depth analyses of some of the topics of the course.

Interactive practical exercises using different commercial softwares (Fusion 360, Abaqus, Altair-Inspire, etc.)

A part of the practices is dedicated to a project to be developed in team, where the students are requested to work on the design of an engineering system (real case study to be carried out in collaboration with an important company) and to apply methods and techniques illustrated during the lectures.

This course focuses on providing a systematic approach to the design and management of mechanical/structural, and, more generally, engineering components and systems, with an emphasis on ensuring their reliability, availability, resilience and safety. The course covers probabilistic modeling, computational methods and advanced machine learning tools for evaluating the risk of failure due to uncertainties in design, manufacturing, and environmental and operating conditions. The objective is to equip participants with the skills and knowledge expected of a reliability and safety analyst and manager responsible for managing and controlling risk in complex industries relying on mechanical and structural components and systems.

Topics

Main theoretical topics :

- Basics of probability theory for applications to reliability and risk analysis.

- Reliability of simple systems : series, parallel, redundancies, standby.

- Reliability, availability and resilience of complex mechanical systems subject to realistic procedures of inspection, maintenance, repair, renewal. MonteCarlo simulation.

- Estimation of reliability parameters from experimental data (accelerated tests, censored tests, etc.). Analysis of reliability data and statistics of Extremes. Structural applications to loads and defects.

- Definition of Risk : the risk triplet, the risk matrix, risk acceptability.

- FMEA/FMECA

- Fault Trees : logical construction (operators, gates), structure function, minimal cut sets, quantitative analysis.

- Event Trees for qualitative and quantitative accidental scenario analysis.

- Dependent failures : cascading failures in interconnected systems, common cause failures.

- Uncertainty and Sensitivity analyses, Structural reliability. Importance measures, principles of structural/mechanical reliability: machine learning-based AI applications.

- Practical case studies related to the automotive, the mechatronics and other energy, mechanical and structural fields.

Practices :

Practice sessions will involve the development of exercises by the teacher and/or by the students working in groups, possibly involving the use of suitable calculation software (e.g., MATLAB, etc.)

Topics

The course covers the following key topics through laboratory activities:

- Anomaly detection on thin-walled structures

- Enabling touch screen capabilities on multiple materials

- Physics-informed surrogate model for wave propagation problems

- Improving anomaly detection through metamaterials

- Deep learning-based design of hierarchical structures for custom structural response

- Self-sensing structures through fractalization

- Human-robot interaction

- Autonomous assembly/disassembly using cobots

- Autonomous picking using industrial robots

- Autonomous navigation

- Machine vision for robotics

- Task learning

Topics

This course aims to help you determine the future application of your design. The main objective is to introduce students to the finite element method (FEM) in structural analysis and guide them in using relevant software for analysis. The course will provide a brief overview of structural analysis, focusing on general analysis and product design rather than complex mathematical formulas. Furthermore, the course will cover the fundamentals of the FEM and guide students in developing FEM models suitable for specific applications. Finally, the course will validate and analyze the results based on the FEM calculations. Students will be required to complete a product project in collaboration with the instructor.

Detailed Plan:

Introduction to Structural Analysis: Primarily covers material properties; beam structures and their reliability; stress states under tensile, bending, shear, and torsional loads; plane stress, plane strain, and three-dimensional stress states; material and structural evaluation: definition of permissible stress and feasible criteria for material failure; performance and reliability under complex stress states.

Introduction to the Finite Element Method: Finite element discretization of structures; shape functions; stiffness matrix; constraint discretization; application of boundary conditions and loads; different types of elements (rods, beams, shells, and three-dimensional elements); selection of element type based on analysis objectives.

Finite Element Modeling Techniques: Meshing techniques; the relationship between CAD models and the finite element method.

Result Computation and Visualization: Solutions to common errors; deformation visualization; stress/strain distribution profiling.

Result-Based Analysis: Model validation; determining model capabilities; convergence calculations; subsequent plotting/utilization of numerical data.

Exercises: Topics related to the application of the finite element method will be presented during the course and discussed with students.

Numerical Lab: Students will collaborate with the instructor to complete projects related to industrial/everyday design products.