9: School of Graduate Engineering and Applied Science

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

Applied Mechanics

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

Analysis of 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; and 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
Topics include the 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; and 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
Analysis of the 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; and 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, and energy methods.

AM 613 - (3) (Y)
Mathematical Foundations of Continuum Mechanics

Prerequisites: linear algebra, vector calculus, elementary PDE (or concurrently)
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
Analysis of the 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
Topics include the 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)

Prerequisite: Permission of instructor
Topics include 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
Analysis of 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
Topics include 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
Topics include the 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; and sound transmission in ducts and resonators. Cross-listed as MAE 644.

AM 665 - (3) (Y)
Mechanics of Composite Materials

Prerequisites: ENGR 306, APMA 206
Analysis of the properties and mechanics of fibrous, laminated composites; 2-D and 3-D anisotropic constitutive equations; classical lamination theory; thermal stresses; material response and test methods; edge effects; design considerations; and computerized implementation. Cross-listed as CE 665.

AM 666 - (3) (Y)
Stress Analysis of Composites

Prerequisite: AM 565
Analysis of 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. Emphasizes the 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. Topics include 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
Topics include the 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; and 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
Topics include 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; and 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
Analysis of the 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; and applications to space and machine dynamics. Cross-listed as MAE 722.

AM 724 - (3) (Y)
Advanced Vibrations

Prerequisite: AM 623
Topics include the 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; and the 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
Topics include a 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
Focuses on 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 students’ interest and needs. Typical topics may include geophysics, astrodynamics, water waves, or nonlinear methods.

AM 732 - (3) (Y)
Fracture Mechanics of Engineering Materials

Prerequisite: MSE 731 or permission of instructor
Topics include the 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 MSE 732.

AM 767 - (3) (SI)
Micromechanics of Heterogeneous Media

Prerequisite: AM 602
Analysis of averaging principles, equivalent homogeneity, 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 anisotropic 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)

Prerequisite: Permission of instructor
Topics include the 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. 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
Return to: Chapter 9 Index