Course Syllabus: Continuum Mechanics - ME 212A Division Course Number Course Title Academic Semester Physical Science and Engineering Division ME 212A Continuum Mechanics Fall Academic Year 2017/2018 Semester Start Date 08/20/2017 Semester End Date 12/12/2017 Class Schedule (Days & Time) 10:30 AM - 12:00 PM Mon Wed Instructor(s) Name Email Phone Office Location Office Hours Gaetano Magnotti GAETANO.MAGNOTTI@KAU ST.EDU.SA +966128082874 4335, 5, Al-Kindi (bldg. 5) Tuesday and Thursday 8:30 AM : 10:00 AM. Open Office policy: I am available outside office hours if I am not in the lab. Name Teaching Assistant(s) Email Course Information
Comprehensive Course Description Fundamental of Continuum Mechanics: -Continuum Hypothesis -Tensors: Indicial notation, operations with tensors, Orthogonal tensors, Transformation law for Cartesian components of a tensor, Symmetric and Anti-symmetric tensors, Principal values and Principal directions of a tensor -Tensor Calculus: Gradient, divergence, curl and Laplacian -Curvilinear coordinates: Polar, Cyclindrical and Spherical coordinates. -Kinematics of a Continuum: Material and Spatial description, Material derivative, Kinematic equation for rigid body rotation -Infinitesimal rotation tensor, rate of deformation tensor, spin tensor and angular velocity vector. -Equation of conservation of mass, Compatibility condition for Infinitesimal strain components, and for rate of deformation components. -Right Cauchy-Green Deformation tensor.- Lagrangian Strain Tensor -Left Cauchy-Green Deformation tensor -Eulerian Strain Tensor -Stress and Integral formulation of General Principles: Stress vector and Stress tensor, Symmetry of stress tensor, Principal Stresses -Equation of Motion: Principle of Linear Momentum, Equation of motion in cylindrical and spherical coordinates, Boundary conditions for the stress tensor -Piola Kirchhoff Stress tensor, Equation of motion with respect to a reference configuration, Stress Power, Stress Power in terms of Piola Kirchhoff Stress tensor -Energy Equation, Entropy Equation, Entropy Inequality Integral Formulations of the general Principles of Mechanics -The Elastic Solid: Fundamentals. Isotropic Linearly Elastic Solid, simple extension, torsion and pure bending. -Newtonian Viscous fluid: Definition of a fluid, Compressible vs incompressible, equation of Hydrostatics. Definition of a Newtonian fluid -Navier-Stokes equations: Navier-Stokes for incompressible fluids in cartesian, cylindrical and spherical coordinates. Buondary conditions. Streamline, pathlines, laminar and turbulent flows. Flows with algebraic solution of the NAvier Stokes equations. -Energy equation for Newtonian fluids, Vorticity, Irrotational flows, Buondary layers, Enthalpy equation, onedimensional compressible flows -Reynolds Transport Theorem and its application: Green's Theorem, Divergence Theorem, Integral over a fixed volume and a material volume, Reynolds Transport theorem. -Governing equations in Integral form: Principle of Conservation of mass, principle of linear momentum, principle of moment of momentum, principle of Conservation of Energy. Entropy inequality and second law of thermodynamics Course Description from Program Guide Goals and Objectives Required Knowledge Reference Texts Method of evaluation Nature of the assignments Course Policies Elements of Cartesian tensors. Configurations and motions of a body. Kinematicsstudy of deformations, rotations and stretches, polar decomposition. Lagrangian and Eulerian strain velocity and spin tensor fields. Irrotational motions, rigid motions. Kineticsbalance laws. Linear and angular momentum, force, traction stress. Cauchys theorem, properties of Cauchys stress. Equations of motion, equilibrium equations. Power theorem, nominal (Piola-Kirchoff) stress. Thermodynamics of bodies. Internal energy, heat flux, heat supply. Laws of thermodynamics, notions of entropy, absolute temperature. Entropy inequality (Clausius- Duhem). Examples of special classes of constitutive laws for materials without memory. Objective rates, corotational, convected rates. Principles of materials frame indifference. Examples: the isotropic Navier- Stokes fluid, the isotropic thermoelastic solid. Basics of finite differences, finite elements, and boundary integral methods, and their applications to continuum mechanics problems illustrating a variety of classes of constitutive laws. 1) To provide the students with a foundation in Continuum Mechanics. 2) To learn the conservation principles and derive the equations governing the mechanics of solids and fluids within the continuum hypothesis 3) To learn the constitutive equations for solid and fluids. 4) To develop practical skills in working with tensors 5) To develop problem solving skills, applying the conservation principles and the constitutive equations to solve practical engineering problems. Differential equations, undergraduate fluid mechanics or mechanics of materials. Lai W. M., Rubin D., Krempl E., "Introduction to Continuum Mechanics", Fourth Edition, Elsevier. R. Aris, Vectors, Tensors, and the Basic Equations of Fluid Mechanics, Dover Publications Paolucci S., Continuum Mechanics and Thermodynamics of Matter, Cambridge University Press Panton R. L., Incompressible Flows, Wiley 40.00% - Final exam 30.00% - Midterm exam 20.00% - Homework /Assignments 10.00% - Active participation Problem sets are assigned as homeworks. Midterm and final exams are closed book, closed notes. The exams will include few multiple answer questions, and problems similar to those assigned in the homeworks. In case of unjustified absence, the student will have a penality of 10 % reduction of the final score per missing class. In case of justified absences, additional homework can be asked to the student, in order to ensure that he/she will have go through the corresponding material. Late homeworks will not be accepted.
Additional Information
Tentative Course Schedule (Time, topic/emphasis & resources) Week Lectures Topic 1 Mon 08/21/2017 Introduction to Continuum Mechanics. The Continuum hypothesis. Indicial notation 1 Wed 08/23/2017 Tensors. Algebraic operation with tensors. Transformation laws for cartesian coordinates 2 Mon 08/28/2017 Symmetric and Anti-Symmetric tensors. Dual Vector of Antisymmetric tensors. Eigenvalues and eigenvectors of a tensor. Principal values and principal directions of real symmetric tensors.principal scalar invariants of a tensor. 2 Wed 08/30/2017 Tensor Calculus: gradient, curl, divergence and Laplacian. 3 Mon 09/04/2017 Eid holiday 3 Wed 09/06/2017 Eid Holyday 4 Mon 09/11/2017 Curvlinear coordinates: polar, cylindrical and spherical. 4 Wed 09/13/2017 Kinematics of continuum. Eulerian and Lagrangian description of motion. Material derivative. Acceleration of a particle. Equation of rigid body motion. 5 Mon 09/18/2017 Rate of deformation tensor Infinitesimal deformation. Strain tensor. Principal strain. Dilatation. Infinitesimal rotation tensor.rate of deformation tensor. Spin tensor and angular velocity vector. 5 Wed 09/20/2017 Conservation of mass. Compatibility conditions for strain and rate of deformation components.stretch and rotation tensors from the deformation gradient 6 Mon 09/25/2017 Left and Right Cauchy Green deformation tensors. Lagrangian and Eulerian strain tensors. Change of area and change of volume due to deformation.components od deformation tensor in other coordinates. 6 Wed 09/27/2017 Stress tensor. Symmetry of stress tensor. Principal Stresses. 7 Mon 10/02/2017 Equation of motion. Principle of linear momentum. Equation of motion in cylindrical and spherical coordinates. Piola Kirchhoff Stress Tensor. 7 Wed 10/04/2017 Energy equation and entropy inequality. Integral formulation of general principles of Mechanics. 8 Mon 10/09/2017 Reynolds Transport Theorem. Green's Theorem. Divergence's Theorem. Integrals over fixed and material volumes. 8 Wed 10/11/2017 Principle of Conservation of Mass in integral form. Principle of Linear Momentum in Integral form. Principle of moment of momentum in integral form. Principle of Conservation of Energy in Integral form. Second Law of Thermodynamics 9 Mon 10/16/2017 Review and in class problem-solving 9 Wed 10/18/2017 Review and in class problem-solving 10 Mon 10/23/2017 Midterm Exam 10 Wed 10/25/2017 The Elastic Solid. Isotropic linearly elastic solid. Equations of the infinitesimal theory of elasticity. Navier Equation of motion for elastic medium. 11 Mon 10/30/2017 Plane elastic waves. Plane equivoluminal waves.reflection of elastic waves. Vibration of an infinite plate. 11 Wed 11/01/2017 Simple extension, torsion and bending. Torsion of circulanr cylinder. St. Venant's problem. Prandtl's formulation of torsion problem. Pure bending. 12 Mon 11/06/2017 Plane stress and plane strain solutions. Thick walled circulanr cylinder under internal and external pressure. Stress concentration due to small hole in a plate under tension and under pure shear. 12 Wed 11/08/2017 Newtonian fluids. Compressible and incompressible fluids. Hydrostatics. Stokes' Hypothesis. 13 Mon 11/13/2017 Navier Stokes equations 13 Wed 11/15/2017 Some exact solutions of Navier Stokes equations. 14 Mon 11/20/2017 Dissipation function for Newtonian fluids. Energy equation for Newtonian fluids 14 Wed 11/22/2017 Vorticity vector. Irrotational flows. Bernouili equation.boundary layer. 15 Mon 11/27/2017 Compressible Newtonian fluid. Energy equation in terms of Enthalpy. Flow through a 1D convergingdiverging nozzle. Acoustic waves 15 Wed 11/29/2017 Introduction to Non-Newtonian fluids. Linear Maxwell fluids. 16 Mon 12/04/2017 Non-linear Viscoelastic fluids.
16 Wed 12/06/2017 Review 17 Mon 12/11/2017 Final Exam Note The instructor reserves the right to make changes to this syllabus as necessary.