General Information |
Degree Programs |
Program Descriptions |
**Course Descriptions** |
Faculty

Aerospace Engineering |
Applied Mathematics |
Applied Mechanics |
Biomedical Engineering

Chemical Engineering |
Civil Engineering |
Computer Science |
Electrical Engineering

Engineering Physics |
Materials Science and Engineering |
Mechanical and Aerospace Engineering

Nuclear Engineering |
Systems Engineering |

**AM 601 - (3) (Y)
Advanced Mechanics of Materials
**Prerequisites: Undergraduate mechanics and mathematics

Review of basic stress-strain concepts; constitutive relations. Study of unsymmetrical bending, shear center, and shear flow. Analysis of curved flexural members, torsion, bending, and twisting of thin walled sections. Theories of failure, other selected topics. Cross-listed as CE 601.

**AM 602 - (3) (Y)
Continuum Mechanics With Applications
**Introduction to continuum mechanics and mechanics of deformable
solids. Vectors and cartesian tensors, stress, strain, deformation,
equations of motion, constitutive laws, introduction to elasticity,
thermal elasticity, viscoelasticity, plasticity, and fluids. Cross-listed
as
APMA 602,
CE 602,
MAE 602.

**AM 603 - (3) (Y)
Computational Solid Mechanics
**Variational and computational mechanics of solids, potential
energy, complementary energy, virtual work, Reissner's principle,
Ritz and Galerkin methods. Displacement, force and mixed methods
of analysis. Finite element analysis, including shape functions,
convergence and integration. Applications in solid mechanics.
Cross-listed as
CE 603 and
MAE 603.

**AM 604 - (3) (E)
Plates and Shells
**Prerequisites:
APMA 541,
AM 601 or
602

Classical analysis of plates and shells. Plates of various shapes (rectangular, circular, skew) and shells of various shape (cylindrical, conical, spherical, hyperbolic, paraboloid). Closed-form numerical and approximate methods of solution governing partial differential equations. Advanced topics (large deflection theory, thermal stresses, orthotropic plates). Cross-listed as CE 604 and MAE 604.

**AM 606 - (3) (Y)
Applied Boundary Element Analysis
**Prerequisites:
AM 671 or
AM 603

Fundamental concepts of Green's functions, integral equations, and potential problems. Weighted residual techniques and boundary element methods. Poisson type problems, including cross-sectional analysis of beams and flow analyses. Elastostatics. Other applications.

**AM 612 - (3) (SI)
Theory of Elasticity
**Prerequisite: AM 602 or permission of instructor

Review of the concepts of stress, strain, equilibrium, compatibility. Hooke's law (isotropic materials). Displacement and stress formulations of elasticity problems. Plane stress and strain problems in rectangular coordinates (Airy's stress function approach). Plane stress and strain problems in polar coordinates, axisymmetric problems. Torsion of prismatic bars (semi-inverse method using real function approach). Thermal stress. Energy methods.

**AM 613 - (3) (Y)
Mathematical Foundations of Continuum Mechanics
**Prerequisites: linear algebra, vector calculus, elementary
PDE (or concurrently)

This course describes the mathematical foundations of continuum mechanics from a unified viewpoint. The relevant concepts from linear algebra, vector calculus and Cartesian tensors; the kinematics of finite deformations and motions leading to the definition of finite strain measures; the process of linearization; and the concept of stress. Conservation laws of mechanics yield the equations of motion and equilibrium and description of constitutive theory leading to the constitute laws for nonlinear elasticity, from which the more familiar generalized Hooke's law for linearly elastic solid is derived. Constitutive laws for a Newtonian and non-Newtonian fluid are also discussed. The basic problems of continuum mechanics are formulated as boundary value problems for partial differential equations. Cross-listed as APMA 613.

**AM 620 - (3) (Y)
Energy Principles in Mechanics
**Prerequisite: Permission of instructor

Derivation, interpretation, and application to engineering problems of the principles of virtual work and complementary virtual work. Related theorems such as the principles of the stationary value of the total potential and complementary energy, Castigliano's Theorems, theorem of least work, and unit force and displacement theorems. Introduction to generalized, extended, mixed, and hybrid principles. Variational methods of approximation, Hamilton's principle, and Lagrange's equations of motion. Approximate solutions to problems in structural mechanics by use of variational theorems. Cross-listed as CE 620 and MAE 620.

**AM 621 - (3) (Y)
Analytical Dynamics I
**Prerequisites: Differential equations, undergraduate dynamics
course

Kinematics of rigid body motion, Eulerian angles, Lagrangian equations of motion, inertia tensor, momental ellipsoid. Rigid body equations of motion, Euler's equation, force-free motion, polhode and herpolhode, theory of tops and gyroscopes, variational principles. Hamiltonian equations of motion, Poinsote representation. Cross-listed as MAE 621.

**AM 623 - (3) (SI)
Vibrations
**Prerequisite: Permission of instructor

Free and forced vibrations of undamped and damped single-degree-of-freedom systems and undamped multi-degree-of-freedom systems. Use of Lagrange's equations. Laplace transform, matrix formulation, and other solution methods. Normal mode theory. Introduction to vibration of continuous systems. Cross-listed as CE 623 and MAE 623.

**AM 629, 630 - (3) (IR)
Special Problems in Applied Mechanics
**Detailed study of special topics in mechanics.

**AM 631 - (3) (Y)
Fluid Mechanics I
**Prerequisite: Permission of instructor

Hydrostatics, including surface tension. Kinematics. Non-inertial reference frames. Rigorous formulation of conservation equations for mass, momentum, and energy. Euler and Bernoulli equations. Vorticity dynamics. Two-dimensional potential flow theory, complex potentials; applications to airfoils. The Navier-Stokes equations: selected exact and approximate solutions. Cross-listed as MAE 631.

**AM 632 - (3) (Y)
Fluid Mechanics II
**Prerequisite: AM 631

The laminar boundary layer equations, differential and integral. Elementary similar and integral solutions. Introduction to and modeling of turbulent flows. Surface waves. Quasi-one-dimensional compressible, perfect gas dynamic analysis. Practical applications. Cross-listed as MAE 632.

**AM 644 - (3) (SI)
Theoretical Acoustics
**Prerequisite: APMA 341

Theoretical description of sound-transmission processes. Derivation of basic gas dynamic equations, behavior of plane waves. The basic processes of transmission, reflection, and absorption. Transmission in non-uniform, shearing atmospheres. Sound waves in two and three dimensions; line sources, monopoles, dipoles, quadrupoles. The Heimholtz integral equation. Sound transmission in ducts and resonators. Cross-listed as MAE 644.

**AM 665 - (3) (Y)
Mechanics of Composite Materials
**Prerequisites:
ENGR 306,
APMA 206

Properties and mechanics of fibrous, laminated composites, 2D and 3D anisotropic constitutive equations, classical lamination theory, thermal stresses, material response and test methods, edge effects, design considerations, computerized implementation. Cross-listed as CE 665.

**AM 666 - (3) (Y)
Stress Analysis of Composites
**Prerequisite: AM 665

3-D anisotropic constitutive theory, interlaminar stresses, failure criteria, micromechanics, cylindrical bending, laminated tubes, laminated plates, damage mechanics, and hygro-thermal effects. Cross-listed as CE 666.

**AM 671 - (3) (Y)
Applied Finite-Element Analysis
**Prerequisite: Permission of instructor

Introduction to finite element methods for solving problems in heat transfer, fluid mechanics, solid mechanics, and electrical fields. Basics of one, two, and three-dimensional elements. Applications to bars, electrical networks, trusses, conduction and convection heat transfer, ideal and viscous flow, electrical current flow, plane stress, plane strain, and elasticity. Development of computer codes to implement finite element techniques. Cross-listed as MAE 671.

**AM 675 - (3) (SI)
Theory of Structural Stability
**Prerequisite: Permission of instructor

Introduction to the elastic stability of structural and mechanical systems. Classical stability theory and buckling of beams, trusses, frames, arches, rings and thin plates and shells. Derivation of design formulas. Computational formulation and implementation. Cross-listed as CE 675.

**AM 693 - (Credit as arranged) (Y)
Independent Study
**Detailed study of graduate course material on an independent
basis under the guidance of a faculty member.

**AM 695 - (Credit as arranged) (Y)
Supervised Project Research
**Formal record of student commitment to project research
under guidance of a faculty advisor. Registration may be repeated
if necessary.

**AM 703 - (3) (Y)
Thermal Structures
**Prerequisite: AM 602 or permission of instructor; corequisite:
AM 612

Fundamentals of thermal structural analysis. Mechanical and thermodynamic foundations. Formulation of heat transfer and thermal-structural problems. Heat transfer in structures. Thermal stresses in rods, beams, and plates. Thermally induced vibrations. Thermoelastic stability. Computational methods.

**AM 704 - (3) (SI)
Theory of Shells
**Prerequisites: AM 602, AM
604

Introduction to the nonlinear, thermoelastic theory of shells. Governing equations are derived by a mixed approach in which those equations of three-dimensional continuum mechanics that are independent of material properties are used to derive the corresponding shell equations, whereas the constitutive equations of shell theory which, unavoidably, depend on experiments, are postulated. Emphasizes efficient, alternative formulations of initial/boundary value problems, suitable for asymptotic or numerical solution, and discusses variational principles. Some comparisons made with exact, three-dimensional solutions.

**AM 708 - (3) (SI)
Inelastic Solid Mechanics
**Prerequisite: AM 602

Emphasizes the formulation of a variety of nonlinear models. Specific topics include nonlinear elasticity, creep, visco-elasticity, and elasto-plasticity. Solutions to boundary value problems of practical interest are presented in the context of these various theories in order to illustrate the differences in stress distributions caused by different types of material nonlinearities. Cross-listed as APMA 708.

**AM 712 - (3) (SI)
Advanced Theory of Elasticity
**Prerequisites: AM 602 or permission of instructor,
AM 612

Generalized Hooke's law, strain-energy density, uniqueness. Classes of boundary value problems (Navier's and Beltrami-Mitchell equations). Torsion (Dirlichlet and Neumann problems). Flexure. Complex variable formulation of torsional (Dirlichlet and Neumann problems) and two-dimensional problems. General solution methodologies based on complex variable techniques and elements of potential theory for torsional and two-dimensional problems. Three-dimensional problems. Wave propagation. Energy methods.

**AM 714 - (3) (SI)
Nonlinear Elasticity Theory
**Prerequisite: AM 602

Describes the theory of finite (nonlinear) elasticity governing large deformations of highly deformable elastic solids. New features not present in the linear theory are emphasized. These include instabilities (both material and geometric), normal stress effects, non-uniqueness, bifurcations and stress singularities. A variety of illustrative boundary value problems will be discussed which exhibit some of the foregoing features. Both physical and mathematical implications considered. The results are applicable to rubber-like and biological materials and the theory serves as a prototype for more elaborate nonlinear theories of mechanics of continuous media. Cross-listed as APMA 714.

**AM 722 - (3) (O)
Analytical Dynamics II
**Prerequisites: Differential equations, AM 621 or
permission of instructor

Formulation and application of the generalized principles of classical particle and continuum mechanics. Lagrangian mechanics; Hamiltonian mechanics. Cannonical transformation theory. Dynamics of variable-mass systems. Dynamics of connected, rigid-body systems. Stability analysis of dynamical systems. Analysis of nonlinear systems by perturbation methods. Applications to space and machine dynamics. Cross-listed as MAE 722.

**AM 724 - (3) (Y)
Advanced Vibrations
**Prerequisite: AM 623

Study of the motion of large scale systems including model testing and reanalysis theory. Shock and wave analysis. Shock and vibration isolation. Integration of linear and nonlinear governing equations. Use of general purpose analysis systems. Cross-listed as MAE 724.

**AM 725 - (3) (SI)
Random Vibrations
**Prerequisites: Background in probability theory and vibration
analysis

Review of probability theory. Stochastic processes, with an emphasis on continuous, continuously parametered processes. Mean square calculus, Markov processes, diffusion equations, Gaussian processes, and Poisson processes. Response of SDOF, MDOF, and continuous linear and nonlinear models to random excitation. Upcrossings, first passage problems, fatigue and stability the considerations. Monte Carlo simulation, analysis of digital time series data, and filtered excitation models. Cross-listed as CE 725.

**AM 728 - (3) (SI)
Skeletal Biomechanics
**Prerequisite: BIOM 603 or permission of instructor

The focus of this course is the study of forces (and their effects) which act on the musculoskeletal structures of the human body. Based on the foundations of functional anatomy and engineering mechanics (rigid body and deformable approaches), students are exposed to clinical problems in orthopaedics and rehabilitation. Cross-listed as BIOM 728.

**AM 729 - (3) (IR)
Selected Topics in Applied Mechanics
**Prerequisite: Permission of instructor

Subject matter varies from year to year depending on interest and needs of our students. Typical topics may include geophysics, astrodynamics, waterwaves, or nonlinear methods.

**AM 732 - (3) (Y)
Fracture Mechanics of Engineering Materials
**Prerequisite: MS 731 or permission of instructor

Development of the methods for fracture control through defect tolerant life prediction, materials characterization, mechanistic behavior modeling and metallurgical alloy development. Discussion of the continuum and microscopic mechanics of material fracture modes. Cross-listed as MS 732.

**AM 767 - (3) (SI)
Micromechanics of Heterogeneous Media
**Prerequisite: AM 602

Averaging principles, equivalent homegencity, effective moduli, bounding principles, self-consistent schemes, composite spheres, concentric cylinders, three phase model, repeating cell models, inelastic and nonlinear effects, thermal effects, isotropic and anistropic media, strength and fracture. Cross-listed as APMA 767 and CE 767.

**AM 793 - (Credit as arranged) (Y)
Independent Study
**Detailed study of graduate course material on an independent
basis under the guidance of a faculty member.

**AM 822 - (3) (SI)
Biomechanics**

Prerequisite: Permission of instructor

Rheological properties of biological tissues and fluids, with emphasis on methods of measurement and data organization. Basic principles of continuum mechanics and their application to mechanical problems of the heart, lung, and peripheral circulation. Criteria for selecting either lumped or continuous models to simulate mechanical interaction of biological systems (and mechanical prostheses) and application of such models under static and dynamic loading conditions. Cross-listed as BIOM 822.

**AM 895 - (Credit as arranged) (Y)
Supervised Project Research**

Formal record of student commitment to project research for Master of Engineering degree under the guidance of a faculty advisor. Registration may be repeated as necessary.

**AM 897 - (Credit as arranged) (S)
Graduate Teaching Instruction
**For master's students.

**AM 997 - (Credit as arranged) (S)
Graduate Teaching Instruction
**For doctoral students.

Continue to: Biomedical Engineering Courses

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