Mechanical Engineering

PART I – THEORETICAL AND METHODOLOGICAL BACKGROUND - Fundamentals of matrix structural analysis and definition of discrete systems. - The displacement method of solid mechanics. - Definition of nodal displacement and force vectors. Introduction of element stiffness matrix, boundary and loading conditions. - Structure stiffness matrix and step-by-step procedure to solve the discrete system by matrix structural analysis. THE FINITE ELEMENT METHOD - Mathematical formulation of the Finite Element Method. - Discrete equivalent of the mechanical continuum: elements, shape functions, stress and strain evaluation. - Main categories of finite elements suitable for 1D, 2D, 3D analyses: trusses, beams, triangular and quadrilateral plane elements, brick and tetrahedral elements, axisymmetric elements and shell elements. - Implementation and solution of basic examples in a Matlab environment. PART II - APPLICATIONS (Solution of exercises in classroom, using a personal computer and a FE code) STRUCTURAL ELASTIC PROBLEMS - Modelling the elastic constitutive behaviour. - Analysis of isostatic and hyperstatic truss and beam structures. - 2D plane stress and plane strain analysis. - 3D analysis of parts and mechanical systems subjected to complex multiaxial states of stress. - Axysimmetric analysis. ELASTO-PLASTICO PROBLEMS - Modelling the elasto-plastic constitutive behavior. Isotropic plasticity, bilinear, multilinear and nonlinear models. Large displacement analysis. - Solution of typical plastic problems: cold forming and evaluation of residual stresses. THERMAL AND TERMO-MECHANICAL PROBLEMS - Linear thermal analysis: thermal properties of materials, thermal boundary conditions (adiabatic, or fixed temperature constraints) and loads (conduction, convection, heat fluxes and the like). - Coupled thermo-mechanical analysis and thermal stresses. DYNAMIC PROBLEMS (highlights) - Transient analysis under time varying loads, inertial effects, impacts. - Modal analysis. ADVANCED TOPICS - modelling of contact between parts. - Scripting and programming capabilities of the FE code.

There are no prerequisites for this course.

Pdf material of the lectures and exercises, available at: www.costruzionedimacchine.it. Reference books and teaching material (not mandatory, to be used for an optional in-depth study): G. Santucci, Dispense del Corso di Costruzione di Macchine. O. C. Zienkiewicz , R L Taylor, Finite Element Method: Volume 1, The Basis, Butterworth-Heinemann. O. C. Zienkiewicz , R L Taylor, Finite Element Method: Volume 2, Solid Mechanics, Butterworth-Heinemann. K.J.Bathe. Finite Element Procedures in Engineering Analysis. Prentice-Hall.

The first part of the course consists of theoretical lectures explained with the aid of the blackboard and the projection of powerpoint slides. In the second (more extended) part practical exercises are carried out using a pc and the ANSYS Academic Teaching Introductory FEM code. As for this second part, the students can use the PCs of the classroom, which have the software preinstalled, or they can use a personal laptop, downloading a free ANSYS Student version that can be freely download from the ANSYS website. A text editor (Notepad++) Matlab/Octave will be also used throughout the course.

The course is organized in typical classroom lectures, with lectures on theoretical subjects, and practical computer based exercises.

Practical exercise on a personal computer, using a Finite Element code. Oral exam on theoretical and methodogical topics of the Finite Element Method.

The first part of the course consists of theoretical lectures explained with the aid of the blackboard and the projection of powerpoint slides. In the second (more extended) part practical exercises are carried out using a pc and the ANSYS Academic Teaching Introductory FEM code. As for this second part, the students can use the PCs of the classroom, which have the software preinstalled, or they can use a personal laptop, downloading a free ANSYS Student version that can be freely download from the ANSYS website. A text editor (Notepad++) Matlab/Octave will be also used throughout the course.

PART I – THEORETICAL AND METHODOLOGICAL BACKGROUND - Fundamentals of matrix structural analysis and definition of discrete systems. - The displacement method of solid mechanics. - Definition of nodal displacement and force vectors. Introduction of element stiffness matrix, boundary and loading conditions. - Structure stiffness matrix and step-by-step procedure to solve the discrete system by matrix structural analysis. THE FINITE ELEMENT METHOD - Mathematical formulation of the Finite Element Method. - Discrete equivalent of the mechanical continuum: elements, shape functions, stress and strain evaluation. - Main categories of finite elements suitable for 1D, 2D, 3D analyses: trusses, beams, triangular and quadrilateral plane elements, brick and tetrahedral elements, axisymmetric elements and shell elements. - Implementation and solution of basic examples in a Matlab environment. PART II - APPLICATIONS (Solution of exercises in classroom, using a personal computer and a FE code) STRUCTURAL ELASTIC PROBLEMS - Modelling the elastic constitutive behaviour. - Analysis of isostatic and hyperstatic truss and beam structures. - 2D plane stress and plane strain analysis. - 3D analysis of parts and mechanical systems subjected to complex multiaxial states of stress. - Axysimmetric analysis. ELASTO-PLASTICO PROBLEMS - Modelling the elasto-plastic constitutive behavior. Isotropic plasticity, bilinear, multilinear and nonlinear models. Large displacement analysis. - Solution of typical plastic problems: cold forming and evaluation of residual stresses. THERMAL AND TERMO-MECHANICAL PROBLEMS - Linear thermal analysis: thermal properties of materials, thermal boundary conditions (adiabatic, or fixed temperature constraints) and loads (conduction, convection, heat fluxes and the like). - Coupled thermo-mechanical analysis and thermal stresses. DYNAMIC PROBLEMS (highlights) - Transient analysis under time varying loads, inertial effects, impacts. - Modal analysis. ADVANCED TOPICS - modelling of contact between parts. - Scripting and programming capabilities of the FE code.

There are no prerequisites for this course.

Pdf material of the lectures and exercises, available at: www.costruzionedimacchine.it. Reference books and teaching material (not mandatory, to be used for an optional in-depth study): G. Santucci, Dispense del Corso di Costruzione di Macchine. O. C. Zienkiewicz , R L Taylor, Finite Element Method: Volume 1, The Basis, Butterworth-Heinemann. O. C. Zienkiewicz , R L Taylor, Finite Element Method: Volume 2, Solid Mechanics, Butterworth-Heinemann. K.J.Bathe. Finite Element Procedures in Engineering Analysis. Prentice-Hall.

The first part of the course consists of theoretical lectures explained with the aid of the blackboard and the projection of powerpoint slides. In the second (more extended) part practical exercises are carried out using a pc and the ANSYS Academic Teaching Introductory FEM code. As for this second part, the students can use the PCs of the classroom, which have the software preinstalled, or they can use a personal laptop, downloading a free ANSYS Student version that can be freely download from the ANSYS website. A text editor (Notepad++) Matlab/Octave will be also used throughout the course.

The course is organized in typical classroom lectures, with lectures on theoretical subjects, and practical computer based exercises.

Practical exercise on a personal computer, using a Finite Element code. Oral exam on theoretical and methodogical topics of the Finite Element Method.

The first part of the course consists of theoretical lectures explained with the aid of the blackboard and the projection of powerpoint slides. In the second (more extended) part practical exercises are carried out using a pc and the ANSYS Academic Teaching Introductory FEM code. As for this second part, the students can use the PCs of the classroom, which have the software preinstalled, or they can use a personal laptop, downloading a free ANSYS Student version that can be freely download from the ANSYS website. A text editor (Notepad++) Matlab/Octave will be also used throughout the course.