The course aims to improve and deepen the basic knowledge acquired in the course of Structural Mechanics at the Bachelor Degree. The fundamental tools necessary for the advanced modeling of the mechanical behavior of materials and structures will be provided. The student will study highly statically indeterminate beam-framed structures, will learn the basic concepts for the analysis of bi-dimensional elements (plates and shells) and will face the basic concepts of dynamics of beam systems.

The student will have to deepen the analytical and numerical topics presented during lectures, starting from the basic equations and choosing, for each problem, the most appropriate methodology to get the solution. The student must possess an appropriate scientific language. The knowledge of a finite element code will help the student to understand the difficulties for scientific/professional modeling.

Fundamental notions from the bachelor mathematical courses (Mathematical Analysis 1 and 2, Geometry, Linear Algebra, Analytical Mechanics, Numerical Methods) and engineering courses (Structural Mechanics: study of isostatic and statically indeterminate structures by the force method, differential equation of the elastica) are required.

1. ONE-DIMENSIONAL STRUCTURES. Statically Indeterminate Structures: Method of forces, Method of displacements, mixed Method. Structural symmetry. Rotating- and translating-node frames. Thermal loads and imposed displacements. Frames with non-orthogonal beams. Stiffness matrix of the beam. Automatic computation of beam systems. Beams with curvilinear axes. Beam on elastic foundation. 2. BI-DIMENSIONAL STRUCTURES: Plane stress and plane strain. Plates loaded in their plane: plates with a circular hole; concentrated force acting on a semi-infinite plane. Plates loaded orthogonally to their plane: Sophie Germain equation for plates in bending, boundary conditions. Symmetrically loaded shells of revolution: membranes and thin shells, circular plates, cylindrical shells. 3. DYNAMICS OF STRUCTURES: Single-degree-of-freedom linear systems. Free response. Damped response. Forced response to harmonic, periodic, impulsive or generic excitations. Non-linear elastic oscillator. Elasto-plastic oscillator. Multi-degree-of-freedom linear systems: modal analysis. Continuous systems: modal analysis of deflected beams. Dynamics of beam systems.

Approximately three fourth of the lectures are given in classroom (mainly at blackboard) whereas one fourth are held at LAIB to learn the use of a finite element software. This allows the student to check the results obtained analytically during the course. These lessons cover: (1) introduction of a finite element analysis on PC, thin or thick beam elements; (2) calculation of plane frames and trusses; (3) calculation of shear-type and spatial frames; (4) calculation of rectangular thin plates; (5) calculation of circular plates and hemispherical domes; (6) calculation of beam on elastic foundation and hydrostatic tanks; (7) free vibrations of a cantilever beam (mono-, bi-and tri-dimensional model); (8) modal analysis of plane and space frames; (9) Modal analysis of continuous systems (arc, circular plate, hemispherical dome).

Official textbook: - A. Carpinteri, "Advanced Structural Mechanics", CRC Press, 2017. (Chapter 1 to 6) Recommended books: – A. Carpinteri, "Structural Mechanics Fundamentals", CRC Press, 2013. (it covers what students are expected to know from the bachelor course in structural mechanics) -A. Carpinteri, G. Lacidogna, C. Surace, "Calcolo dei telai piani – Esempi ed esercizi", Pitagora Editrice, Bologna, 2002 (useful for the written examination). -S. Timoshenko, "Theory of Plates and Shells", McGraw-Hill, Singapore, 1959. (world-wide known structural mechanics book) As regards numerical and analytical practice lessons, material will be uploaded on the teaching internet site.

Modalità di esame: Prova orale obbligatoria; Elaborato scritto individuale;

The exam is aimed at ascertaining the knowledge of the topics listed in the course syllabus and the ability to apply the theory and the relative calculation methods to the solution of structural systems (see Expected Learning Outcomes). The exam consists of three parts: (1) the numerical solution of a structure to check the knowledge of the finite element code (see Expected Learning Outcomes), either at the Informatic Laboratory at the end of the course or at home; Then, the oral test will consist of: (2) solving a statically indeterminate frames (3) an examination on the theoretical topics The ability to solve the frame is a necessary condition to access to part 3. For the exercise students can only use the formularies provided during the course. Oral questions will assess the knowledge level and the scientific language of student. The final mark will properly take into account the results obtained in all the three steps.

Modalità di esame: Prova scritta (in aula); Prova orale obbligatoria; Elaborato scritto individuale;

he exam is aimed at ascertaining the knowledge of the topics listed in the course syllabus and the ability to apply the theory and the relative calculation methods to the solution of structural systems (see Expected Learning Outcomes). The exam consists of three parts: (1) the numerical solution of a structure to check the knowledge of the finite element code (see Expected Learning Outcomes), either at the Informatic Laboratory at the end of the course or at home; (2) solving a statically indeterminate frames, either online or onsite (3) an examination on the theoretical topics The ability to solve the frame is a necessary condition to access to part 3. For the exercise, students can only use the formularies provided during the course. Oral questions will assess the knowledge level and the scientific language of student. The final mark will properly take into account the results obtained in all the three steps.