THREE-DIMENSIONAL MODELING

Course objectives

The teaching “Mechanics applied to Solids and Structures”, given at the 2nd year of the Bachelor Degree in Clinical Engineering, aims at learning the skills to analyze the mechanical behaviour of elastic beams with straight axis, to check the resistance of thin open sections subjected to axial and transverse eccentric forces, and to assess the state of global displacement, local strain and stress, for verification of functionality and durability. It is a preparatory course of "Strength of Biomaterials" for the Master Degree in Biomedical Engineering, where it finds its natural application to the mechanical behaviour of biological tissues and biomaterials, and of the main bone joints of the human body, and to the structural analysis of the prostheses that replace these joints. Expected results of learning. We expect that the candidate engineer acquires the skills to analyze the mechanical behaviour of elastic beams with straight axis, to check the resistance of thin open sections subjected to axial and transverse eccentric forces, and to assess the state of global displacement, local strain and stress, for verification of functionality and durability.

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ANTONINO FAVATA Lecturers' profile

Program - Frequency - Exams

Course program
Kinematics and Statics of Rigid Bodies Definition of a rigid body. Translation, exact and infinitesimal rotation. Properties of the infinitesimal displacement field. Planar constraints: hinge, pendulum, slider, double pendulum, clamped support. Constraint reactions. Static problem. Systems of rigid bodies. Internal constraints. Method of partial equilibrium. Rigid Beams with Straight Axis Geometry and loads. Stress resultants. Differential equilibrium equations. Diagrams of stress resultants. Deformable Beams Extensional deformations in straight-axis beams, compatibility equation, constitutive equation, differential equation of the elastic line. Strain measurements in beams. Compatibility equations. Euler–Bernoulli model. Constitutive equations, identification of axial and flexural stiffness. Flexural deformations. Differential equation of the elastic line. The principle of virtual work. Applications of the virtual work equation: calculation of displacements in isostatic structures. Determination of hyperstatic unknowns. Continuum Mechanics Deformations, displacements, geometric variations. Strain measures, infinitesimal strain tensor. Forces, stress, and work. Body and surface forces; stress; Cauchy stress tensor; pointwise equilibrium equations; principal stresses and directions. Elasticity tensor; isotropic and anisotropic materials; interpretation of elastic constants. Formulation of the elastic problem and solution strategies. Displacement-based, stress-based, and semi-inverse approaches. The Saint-Venant Problem Geometry and loads. Review of area geometry. Normal and shear stresses. Navier’s formula. Axial force, straight bending, oblique bending, eccentric axial force. Shear stresses. Shear center. Torsion, circular section and thin rectangular section, thin-walled open sections, torsional inertia, thin-walled closed sections, Bredt’s formulas. Approximate shear theory, Jourawski’s formula.
Prerequisites
Basic notions acquired in courses of mathematical analysis, geometry, and physics.
Frequency
In-presence lectures
Exam mode
Written exam with practical and theoretical components.
  • Academic year2025/2026
  • CourseClinical Engineering
  • CurriculumSingle curriculum
  • Year2nd year
  • Semester1st semester
  • SSDICAR/08
  • CFU6