Graduate Courses in Engineering Mechanics

801 Analytical Methods in Engineering I, 3 cr.  Basic topics in real analysis and linear algebra with examples of applications from diverse branches of engineering and applied physics.

802 Analytical Methods in Engineering II, 3 cr.  Continuation of ENGM 801 topics in complex analysis, linear algebra, ordinary and partial differential equations, and other areas of applied mathematics, with examples of applications from diverse branches of engineering and applied physics.  Prereq: ENGM 801 or permission.

843 Introduction to Piezoelectricity with Applications, 3 cr.  Covers the basics of piezoelectricity and some of its applications. Topics may vary with the interest of the instructor and the students. Topics may include:  phenomena of piezoelectricity, equations of linear piezoelectricity, some static problems, some dynamic problems, equations for piezoelectric beams and plates, piezoelectric devices, finite element numberical analysis of piezoelectric problems by ANSYS. Prereq:  ENGM 325 and ENGM 373 or permission.

847 Advanced Dynamics, 3 cr. Particle dynamics using Newton's laws, energy principles, momentum principles. Rigid body dynamics using Euler's equations and Lagrange's equations. Variable mass systems. Gyroscopic motion. Prereq: ENGM 373 and MATH 821. Cross-listed with ENGM 447.

848 Advanced Mechanics of Materials, 3 cr. Stresses and strains at a point. Theories of failure. Thick-walled pressure vessels and spinning discs. Torsion of noncircular sections. Torsion of thin-walled sections, open, closed, and multicelled. Bending of unsymmetrical sections. Cross shear and shear center. Curved beams. Introduction to elastic energy methods. Prereq: ENGM 325 or 375. Cross-listed with ENGM 448.

850 Introduction to Continuum Modeling, 3 cr. The basic concepts of continuum modeling. Development of models and solutions to various mechanical thermal and electrical systems.  The thermo-mechanical and electro-mechanical coupling effects.  Differential equations, dimensional methods and similarity.  Prereq:  MATH 821, ENGM 325, 373.

851 Introduction to Finite Element Analysis, 3 cr (also CIVE 851). Matrix methods of analysis. The finite element stiffness method. Computer programs. Applications to structures and soils. Introduction to finite element analysis of fluid flow. Prereq: ENGM 325 and 880 or permission. Cross-listed with ENGM 451.

852 Experimental Stress Analysis I, 3 cr. Investigations of the basic theories and techniques associated with the analysis of stress using mechanical strain gages, electric strain gages, brittle lacquer, photoelasticity and membrane analogy. Lect 2 lab 2. Prereq: ENGM 325. Cross-listed with ENGM 452.

875 Vibration Theory and Applications,  3 cr. Variational principles, Lagrange's equation. Equations of motion for multi-degree of freedom systems.  Free vibrations eigenvalue problem: modal analysis.  Forced vibrations: general solutions, resonance, effect of damping, and superposition. Vibrations of continuous systems: vibrations frequencies and mode shapes for bars, membranes, beams, and plates. Experimental methods and techniques. Prereq: ENGM 373 and MATH 821.

880 Numerical Methods in Engineering Analysis, 3 cr. Application of numerical methods to the solution of engineering problems using computational software. Roots of algebraic and transcendental equations. Simultaneous algebraic equations--linear and non-linear, homogeneous and non-homogeneous. Curve fitting: polynomial, exponential, Fourier series, and cubic spline. Numerical integration and differentiation. Ordinary differential equations: initial and boundary value problems.  Eigenvalue/eigenvector problems. Partial differential equations: elliptical, parabolic, and hyperbolic. Prereq: MATH 821. Cross-listed with ENGM 480.

888 Nonlinear Optimization, 3 cr. Methods for solving constrained and unconstrained nonlinear optimization problems.  Practical numerical algorithms based on gradients or genetic algorithms for optimization will be emphasized.  Calculus of variations will provide the basis for design optimization and optimal control. Cross-listed with ENGM 488 and as IMSE 488/888.

891 Special Topics in Engineering Mechanics, 1-6 cr. Treatment of special topics in engineering mechanics by experimental, computational and/or theoretical methods. Topics will vary from semester to semester. See current schedule of classes for offerings. Prereq: Permission of instructor. Cross-listed with ENGM 491.

899 Masters Thesis, 6-10 cr.

910 Continuum Mechanics, 3 cr. The continuum. Geometrical foundations of continuum mechanics. Rectilinear and curvilinear coordinates. Elements of tensor analysis. Analysis of stress. Analysis of strain. Equations of motion. Constitutive equations. Fundamental laws. Applications to deformable systems. Prereq: ENGM 848, and permission of instructor.

915 Stress Waves in Solids, 3 cr. Waves in rods, beams, strings, and membranes. Sound waves in air. Dilatational and distortional waves. Reflection and refraction of waves. Rayleigh surface waves. Love waves. Applications of transform theory and the method of stationary phase to wave analysis. Waves in anisotropic and viscoelastic media. Lect 3. Prereq: ENGM 847, 848, or permission of instructor.

916 Theory of Plates and Shells I, 3 cr. Basic equations for the bending and stretching of thin plates with small deformations. General theory of deformation of thin shells with small deflections. Large deformation theories of plates and shells. Effect of edge conditions. Prereq: ENGM 848 and MATH 821.

917 Theory of Plates and Shells II, 3 cr. Continuation of ENGM 916 topics. Large deflection shell theory. Critical examination of effects of boundary conditions. Additional topics selected from folded plates, orthotropic plates and shells, sandwich plates and shells, use of complex transformations, etc. Lect 3. Prereq: ENGM 916.

918 Fundamentals of Finite Elements, 3 cr. Derivation and implementation of the finite element method.  Introduction to the theory of finite element methods for elliptic boundary-value problems. Applications to time-independent physical phenomena (e.g., deformation of elastic bodies,heat conduction, steady-state fluid flow, electrostatics, flow through porous media). Basic coding techniques. A basic understanding of ordinary differential equations and matrix algebra as well as some programming skills are assumed. Lect 3. Prereq: ENGM 848, 880, 851 or CIVE 851, or permission of instructor.

919 Nonlinear Mechanics, 3 cr. Study of physical systems in solid mechanics which lead to nonlinear differential equations. Graphical, numerical, and exact solutions of the governing differential equations. Physical interpretation of the solution. Lect 3. Prereq: ENGM 847, 848, or permission.

920 Theory of Elastic Stability, 3 cr. Lateral buckling of beams; failure of columns; bending and buckling of thin plates and shells. Consideration of classical and modern theories.  Prereq: ENGM 325 or 375, and MATH 821.

922 Theory of Elasticity I, 3 cr. Plane stress and strain. Solution of two-dimensional problems by polynomials. Two-dimensional problems in polar coordinates. Triaxial stress and strain. Torsion of noncircular cross section. Bending of prismatical bars. Hydrodynamical analogies. Prereq: ENGM 848 and MATH 821.

923 Theory of Elasticity II, 3 cr. ENGM 922 continued. Foundation of the theory of large deformation. Equations of linear elasticity. Complex representation of the general solution of the equations of plane theory of elasticity. Conformal mapping. Solutions of problems in three-dimensional elasticity in terms of potential functions. Axially symmetric problems. Variational methods. Prereq: ENGM 922.

925 Viscoelasticity, 3 cr. An introduction to linear and nonlinear viscoelastic material behavior. One dimensional response. Linearity of material response. Quasi-static and dynamic problems. Time-temperature superposition. Viscoelastic beams. Multidimensional response. Nonlinear response. Lect 3. Prereq: ENGM 848 or 910, and MATH 821 or 822; or permission of instructor.

930 Mechanics of Composite Materials, 3 cr. Introduction to composite materials. Properties of an anisotropic lamina. Laminated composites. Failure theories. Analysis of composite structures. Lect 3. Prereq: ENGM 848 or permission of instructor.

940 Fracture Mechanics, 3 cr. Modes of failure. Elastic stress field near cracks. Theories of brittle fracture. Elastic fracture mechanics. Elastic-plastic analysis of crack extension. Fracture toughness testing. Prereq: ENGM 848 or permission.

941 Mechanics of Dislocations and Cracks, 3 cr. Mathematical theory of straight dislocations in isotropic and anisotropic elastic media.  Dislocations on and near an interface.  Dislocation interactions.  Discrete and continuously distributed dislocations.  Applications to mechanics of materials:  grain boundaries and dislocation pile-ups.  Applications to fracture mechanics:  Griffith-Inglish crack, Zener-Stroh-Koehler crack, Bilby-Cottrell-Swinden-Dugdale crack. Prereq:  ENGM 848 or permission.

942 Theory of Plasticity, 3 cr. Basic concepts of plasticity. Yield conditions and yield surfaces. Torsion of cylindrical bars and Saint Venant-Mises and Prandtl-Reuss theories. General theory of plane strain and shear lines. Steady and pseudo-steady plastic flow. Extremum principles. Engineering applications. Prereq: ENGM 922.

951 Advanced Topics in Finite Element Methods, 3 cr.  Contemporary topics in the theory and application of finite element methods.  Topics may vary with interest of instructor and may include:  finite elements for the analysis of fracture; mixed variational formulations; hybrid stress elements; plasticity; non-linear elasticity; large deformations of structures; plate and shell elements; transverse shear effects in beams, plates and shells; "locking" phenomena; treatment of singularities; dynamics of large systems; "enhanced" strain methods; methods for solving non-linear algebraic systems; architecture of computer codes for non-linear finite element analysis; and treatment of constraints arising in nearly incompressible material models.  Prereq:  ENGM 851 or 918, or permission.

952 Experimental Stress Analysis II, 3 cr. Surface strains and their measurement, principally by bonded wire resistance strain gages. Static and dynamic measurements using both oscilloscope and direct writing oscillograph, associated electrical circuits. Use of brittle coating in conjunction with strain gages. Evaluation of stresses from strain data. Lect 2 lab 3. Prereq: ENGM 848 and 852.

975 Advanced Vibrations, 3 cr.  Variational mechanics, Hamilton's principle, and energy formulations for linearly elastic bodies.  Eigenvalue and boundary value problems.  non-self adjoint systems.  Approximate methods:  Ritz and Galerkin.  Gyroscopic systems.  nonconservative systems.  Perturbation theory for the eigenvalue problem.  Dynamics of constrained systems. Prereq:  ENGM 875.

991 Advanced Investigations in Engineering Mechanics, 1-12 cr. Treatment of advanced topics in engineering mechanics by experimental, computational, and/or theoretical methods. Topics will vary from semester to semester. See current schedule of classes for offerings. Prereq: Permission of instructor.

996 Seminar in Engineering Mechanics, 1 cr. per semester, maximum of 4. Presentation and discussion of topics in the various branches of engineering mechanics. (Previously ENGM 978).  Prereq: Permission of instructor.

999 Doctoral Dissertation, 1-24 cr.