ME 400. Applied Boundary-Value Problems
(Same as ME 201)
Formulation of partial differential equations for physical problems; Fourier series; separation of variables leading to Fourier series; Sturm-Liouville theory; eigenfunction expansions and separation of variables; Fourier transform; similarity methods; Fourier-Bessel expansions and separation of variables in cylindrical coordinates; Legendre polynomials and separation of variables in spherical coordinates. Equations dealt with in the course are the Laplace equation, the heat equation, the wave equation, and related equations. Applications are to such areas as heat conduction, fluid flow, diffusive mass transport, electrostatics, and acoustics. Requires significant extra work at the 400 level.
ME 401. Methods of Applied Mathematics
Prerequisites: ME 201 or MTH 281; MTH 282.
Advanced ordinary differential equations (ODEs), boundary layer theory, WKB method, multiple-scale analysis, asymptotic expansion of integrals, renormalization group.
ME 402. Partial Differential Equations
Prerequisites: ME 201 or MTH 281 and ME 202/MTH 282.
Green’s functions and eigenfunction expansions; application to the Laplace, diffusion, and wave equations. First-order equations and the theory of characteristics; Green’s functions for wave propagation; dispersive waves. Boundary layers and matched asymptotic expansions.
ME 404. Computational Methods Applied to Biological Systems
Prerequisites: MTH 163, MTH 165
Computational methods to solve analytically intractable mathematical problems in biological research. Using matlab as a programming language; Numerical methods for linear algebra, ODE and PDE; Case studies such as biodynamics of human locomotion, ion channel kinetics, ionic diffusion in cells and finite element analysis of cells/tissues.
ME 403. Computational Methods for Engineering and Science
Prerequisite: ME 402 or PHY 401 or OPT 411, or consent of the instructor. Some FORTRAN experience desirable.
Computational solutions to coupled nonlinear partial differential equations arising in engineering and physics. Emphasis on current problems and techniques.
ME 406. Dynamical Systems
Prerequisite: MTH 165.
Plane autonomous systems: phase plane, stability of equilibrium by linearization; stability by Liapunov methods; periodic solutions and their stability; global phase portraits; bifurcations. Higher order autonomous systems: matrix methods for linear systems; local behavior near equilibrium points; Lorenz equations and chaotic solutions; tent map and Lorenz equations; Liapunov exponents. Driven systems: Duffing’s equation; the driven pendulum.
ME 407. Advanced Dynamics
Prerequisites: ME 121, 213, and ME/MTH 163.
Review of principles of mechanics; generalized coordinates and constraints; calculus of variations; Lagrange’s equations; Hamilton’s equations; rigid body dynamics; applications.
ME 408. Phase Transformation in Metals and Alloys
Prerequisite: ME 460.
The physical, chemical, and mechanical properties of metals and alloys can be varied drastically by thermal and mechanical treatments. This phase transformation course is concerned with a description of how atomic rearrangements occur and how they are associated with kinetic and crystallographic features.
ME 411. Mechanical Properties of Polymers
Prerequisite: permission of the instructor.
Structure of polymers,
elastic behavior, finite strain elasticity,
viscoelastic behavior of polymers, time-temperature superposition, free
volume theory, relaxation processes, nonlinear and anisotropic behavior,
yielding and fracture.
ME 424. Introduction to Robust Design and Quality Engineering
(Same as ME 222, MSC 424)
Prerequisite: MTH 164 or equivalent.
Definition and pursuit of “quality” as a design criterion. The concept of robust design. Selection of the quality characteristic and experimental design to improve quality. Cross-listed as ME 222, but requires significant extra work.
ME 432. Optomechanics
Prerequisites: ME 226 and 204.
Design of structures to support optical components such as
lenses, mirrors and telescopes for UV, visible and IR optical applications.
Extensive use of finite element methods in opto-
mechanical design and optimization.
ME 434. Introduction to Plasma Physics I
Prerequisite: EE 231 or PHY 217.
Orbit theory, adiabatic invariants, collective effects, two-fluid and MHD equations, waves in plasma, transport across magnetic fields and in velocity space.
ME 435. Introduction to Plasma Physics II
Prerequisite: ME 434.
Vlasov equation, Landau damping, Van-Kampen modes, shield clouds, two-stream instability, microinstabilities, drift instability, nonlinear instability theory, radiation from plasma.
ME 436. Compressible Flow
Prerequisites: ME 225 and ME 201 or MTH 281.
Equations of motion, acoustics; linearized equations for homogeneous media; mathematical theory of linear waves; geometrical acoustics. Nonlinear simple waves, Riemann invariants. Finite amplitude compressible flow; one-dimensional waves and the theory of characteristics; shock waves; steady two-dimensional flow. Dimensional analysis, self-similar flows. Combustion and detonation.
ME 437. Incompressible Flow
Prerequisites: ME 225 and ME 201 or MTH 281.
Conservation equations. Bernoilli’s equation, Navier-Stokes equation. Inviscid flows; vorticity; potential flows; stream function; complex potential. Viscosity and Reynolds number; some exact solutions with viscosity; boundary layers; low Reynolds number flows. Selected applications from aerodynamics. Waves.
ME 440. Mechanics of Structures
Prerequisite: ME 226.
Application of direct and indirect methods of the calculus of variations to the stress, deflection, and dynamic analysis of beam, ring, plate, and shell elements. Strain energy and complementary strain energy; variational principles; Lagrange multipliers. Rayleigh-Ritz method; Galerkin method; Reissner’s variational principle.
ME 441. Finite Elements
(Same as BME 486)
Prerequisites: ME 226 and programming capability in Matlab.
The theory and application of finite element analysis to linear problems in structural mechanics and other disciplines. Topics: matrix analysis concepts; element formulation methods; element behavior; global analysis aspects; isoparametric elements. Term project requires the implementation of a finite element program in Matlab.
ME 443. Applied Vibrations
Prerequisite: ME 213.
One, two, and many degrees-of-freedom systems. Complex representation; free and forced vibration; transient vibration; damping. Vibration of strings, beams, and membranes.
ME 444. Continuum Mechanics
Prerequisites: ME/MTH 164, ME 201, ME 225, ME 226.
The mechanics of continuous media. Introduction to tensors. Study of stress and strain. Constitutive laws for solids and fluids. Balance of mass, momentum, angular momentum, and energy. Entropy production. Internal variables. Applications to boundary value problems.
ME 445. Plates and Shells
Prerequisites: ME 226; ME 201 or MTH 281.
Analysis of stress and deformation in rectangular and circular plates bent by transverse loads. Axisymmetric deformation of shells of revolution. Asymptotic expansions; membrane and bending stress. Application to pressure vessels, tanks, and domes with various support and load conditions.
ME 446. Wave Propagation in Elastic Media
Prerequisites: ME 121, 226; ME 201 or MTH 281.
Physical phenomena (reflection, dispersion) and mathematical techniques (Green’s functions, Fourier analysis, stationary phase) are studied for waves on strings. Concepts are then used to study waves in infinite, semi-infinite, and layered structures and waves in layers and cylinders.
ME 448. Structural Stability
Prerequisite: ME 226. Strongly recommended: ME 201 or MTH 281.
Concepts of equilibrium and stability of deformable solid structures. Applications to elastic columns, plates, and shells. Interactions with fluids. Static and dynamic systems.
ME 449. Elasticity
Prerequisites: ME 226; ME/MTH 163.
Analysis of stress and strain; equilibrium; compatibility; stress-strain relations. Torsion and bending of bars. Plane stress and plane strain; Airy stress functions. Half-plane problems. 3-D elasticity; Papkovich-Neuber, Love potentials. Applications to problems for the half-space.
ME 450. Optimum Design
Prerequisites: ME 226, ME 204 (or equivalent), and
some
programming experience.
Nonlinear programming techniques are applied to optimize the mechanical design problem. Both constrained and unconstrained techniques are discussed. Students use state-of-the-art software to solve a variety of problems. The combination of optimization with finite elements is addressed.
ME 451. Crystallography and X-Ray Diffraction
Prerequisite: permission of instructor.
Crystallography, symmetry elements, point groups, space groups, X-ray diffraction, single crystal diffraction, powder patterns, Fourier transforms, grain size effects, residual stress and cold work, diffuse and small-angle scattering, Bragg and Laue, X-ray topography. Weekly laboratory.
ME 452. Electron Microscopy
(Same as BME 454)
Prerequisites: ME 451 and permission of instructor.
Microstructural features and their effect on mechanical, electrical, and optical properties. Point, line, and planar defects; kinematical theory of diffraction; reciprocal space; single crystal diffraction patterns; dynamical theory of diffraction; direct observations of dislocations and stacking faults. Weekly laboratory involving use of electron microscope.
ME 453. Intro to Nuclear Engineering
(Same as ME 253)
A first course in nuclear engineering with emphasis on the fundamental physics and technology of modern water-cooled power reactors, the nuclear fuel cycle, and the regulatory environment surrounding nuclear power in the United States.
ME 458. Nonlinear Finite Element Analysis
(Same as BME 487)
Prerequisite: ME 441 or equivalent.
The theory and application of nonlinear finite element analysis in solid and biosolid mechanics. Topics: generalization of FE concepts, review of solid mechanics, nonlinear incremental analysis, displacement-based FE formulation for large displacements and large strains, nonlinear constitutive relations, incompressibility and contact conditions, hyperelastic and viscoelastic materials, biomechanical materials, solution methods.
ME 459. Applied Finite Elements
Prerequisite: ME 441 or permission of instructor.
The course addresses practical topics in finite elements, including vibrations, buckling, structural symmetry, superelements, and fracture mechanics. Modeling techniques and applications to problem solving are stressed using commercial FEA codes.
ME 460. Thermodynamics of Solid Materials
Prerequisite: ME 123 or CHE 225.
Review of basic thermodynamic quantities and laws; phase transformations and chemical reactions; partial molar and excess quantities; electrochemical reactions; free energy of binary systems; surfaces and interfaces; nucleation of neophases; stressed solids; irreversible thermodynamics.
ME 461. Fracture and Fatigue
Prerequisites: ME 280, 226, and 442.
Linear elastic fracture mechanics. Griffith theory. K and J approaches to toughness measurements. Low-cycle fatigue. Crack nucleation and fatigue crack growth. Failure analysis. Emphasis on the role of microstructure in determining fracture and fatigue behavior. This is a course taught to bring the student at or near the level of current research.
ME 462. Solids and Materials Laboratory
(Same as ME 242}
Prerequisite: permission of instructor.
Design, planning, execution, and reporting of laboratory experiments, including both existing experiments and a significant independent research project. Cross-listed as ME 242, but requires significant extra work.
ME 463. Microstructure
Prerequisite: ME 280.
Crystal structure and Miller indices. Atomic vibration and interstitial diffusion. Vacancy and vacancy-atom exchanges. Diffusion-induced stresses. Dislocation walls and pileup. Disclinations. Surfaces and interfaces. Precipitates and inclusions.
ME 466. Electrochemistry and Corrosion
A scientific approach to understanding and thereby controlling metallic corrosion. Starting from general principals of materials science, this course explores the physics that controls chemical degradation.
ME 483. Biosolid Mechanics
Prerequisite: ME 226.
Application of engineering mechanics to biological tissues including soft tissue and bone. Experimental and computational methods and material models of biological structures.
ME 491. Reading Course on Mechanical Engineering
Credit to be arranged
Supervised reading on topics beyond those available in existing courses, or on specialized topics. The student in general makes a thorough search and study of the literature dealing with the current research in a given field.
ME 493. Master’s Essay
Supervised preparation of the master’s essay for Plan B candidates.
ME 495. Research in Mechanical Engineering
Credit to be arranged
ME 532. Magnetohydrodynamics
Basic equations of magnetohydrodynamics (MHD), boundary conditions. The induction equation and kinematic MHD. Magnetohydrostatic equilibrium and stability. Incompressible, viscous MHD flows. Alfven waves, magneto-acoustic waves, and magneto-acoustic-gravity waves. Dynamo theory, mean-filed theory of turbulent dynamos. Applications in engineering and astrophysics.
ME 533. Inertial Confinement Fusion
(Same as PHY 558)
Fusion energy. Lawson criterion for thermonuclear ignition. Fundamentals of implosion hydrodynamics. Temperature and areal density in spherical implosions. Laser light absorption. Implosion stability. Thermonuclear energy gain.
ME 535. Laser-Plasma Interactions
Prerequisite: ME 434 or permission of instructor.
Coronal plasmas in inertial confinement fusion. Inverse bremsstrahlung and resonant absorption. Parametric instabilities. Nonlinear plasma waves and collapse. High-intensity laser beams in plasmas.
ME 537. Advanced Topics in Fluid Mechanics
Credit—two to four hours
Content of the course varies from year to year, but may include such topics as perturbation methods in fluid mechanics, flow phenomena involving ionizing, dissociating, or reacting gases, higher approximations in boundary layer theory, the study of water waves, rotating flows, and solar magnetohydrodynamics.
ME 540. Advanced Topics in Materials Science
Credit—two to four hours
Topics vary from year to year. Examples are as follows: deformation of amorphous solids, dislocation dynamics, defect mechanisms in polymers, micromechanics of fracture and fatigue, structure and properties of grain boundaries and interfaces, disclinations, deformations of glasses with applications to optics manufacturing.
ME 544. Advanced Topics in Solid Mechanics
Credit—two to four hours
Content of the course varies from year to year but may include such topics as advanced experimental design, wave propagation, nonlinear elasticity, biomechanics, composite materials, and finite elements.
ME 545. Advanced Topics in Plasma Physics
Credit—two to four hours
The course content varies from year to year but includes topics which introduce the student to problems of immediate interest in the field. Examples are controlled fusion reactor concepts, including laser fusion, energy in the future, space plasmas, and astrophysical plasma phenomena.
ME 591. Reading Course in Mechanical Engineering
Credit to be arranged
Supervised reading on topics beyond those available in existing courses, or on specialized topics.
ME 595. Research in Mechanical Engineering
Credit to be arranged