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TAM 539: Fluid Mechanics Seminar
1.00 Credits
University of Illinois at Urbana-Champaign
Weekly seminar on current research topics in turbulent and other complex flows: theoretical modeling, numerical analysis, computational techniques, and experimental investigations. Recommended for graduate students in fluid mechanics. Approved for S/U grading only.
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TAM 539 - Fluid Mechanics Seminar
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TAM 541: Mathematical Methods I
4.00 Credits
University of Illinois at Urbana-Champaign
Vector and tensor algebra, introduction to complex-variable methods; ordinary differential equations, qualitative questions of existence and uniqueness; analytic solution methods, numerical methods, power-series solution and special functions; eigenvalue problems, Green's functions, Laplace transforms, stability of solutions; engineering applications drawn from mechanics. Prerequisite: MATH 241 or MATH 380; MATH 285.
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TAM 541 - Mathematical Methods I
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TAM 542: Mathematical Methods II
4.00 Credits
University of Illinois at Urbana-Champaign
Continuation of TAM 541. Modeling, inequalities, elements of functional analysis; partial differential equations, existence and uniqueness, second-order equations; hyperbolic conservation laws; numerical methods, eigenfunction expansions, integral transforms, and fundamental solutions; engineering applications drawn from mechanics. Prerequisite: TAM 541.
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TAM 542 - Mathematical Methods II
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TAM 545: Advanced Continuum Mechanics
4.00 Credits
University of Illinois at Urbana-Champaign
Unified treatment of modern continuum mechanics: mathematical preliminaries; review of kinematics and general balance laws; general theory of mechanical constitutive equations, including material constraints and material symmetry. Prerequisite: TAM 551.
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TAM 545 - Advanced Continuum Mechanics
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TAM 549: Asymptotic Methods
4.00 Credits
University of Illinois at Urbana-Champaign
Advanced methods of perturbation theory and asymptotic analysis, with examples drawn from classical dynamics, fluid mechanics, and wave propagation: asymptotics of integrals, singular perturbation theory (boundary layers, matched asymptotic expansions, and composite expansions), multiple scales, summation of series; special topics. Same as MATH 559, NPRE 559, and PHYS 522. Prerequisite: MATH 446 and TAM 541.
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TAM 549 - Asymptotic Methods
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TAM 551: Solid Mechanics I
4.00 Credits
University of Illinois at Urbana-Champaign
Mechanics of elastic deformable bodies, based on the fundamental concepts of modern continuum mechanics: kinematics, balance laws, constitutive equations; classical small-deformation theory; formulation of initial boundary-value problems of linear elastodynamics and boundary-value problems of linear elastostatics; variational formulations, minimum principles; applications of theory to engineering problems. Prerequisite: MATH 241 or MATH 380; MATH 285; TAM 251.
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TAM 551 - Solid Mechanics I
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TAM 552: Solid Mechanics II
4.00 Credits
University of Illinois at Urbana-Champaign
Continuation of TAM 551. Selected topics in linear elasticity (including St. Venant beam theory and plane problems of elastostatics), plasticity (including yield surfaces, von Mises and Tresca yield criteria, Drucker's stability postulate, J-flow theory, perfect plasticity, limit analysis, and slip-line theory), and fracture mechanics (including linear elastic analysis, fracture criteria for elastic brittle fracture, and elastic-plastic fracture). Prerequisite: TAM 551.
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TAM 552 - Solid Mechanics II
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TAM 554: Plasticity
4.00 Credits
University of Illinois at Urbana-Champaign
Phenomenological and mathematical formulation of the constitutive laws of plasticity; yield criteria and their experimental verification; plastic stress-strain relations and their associated flow rules; correspondence between rate-independent and rate-dependent plasticity; solutions to basic boundary-value problems, including plane problems and those involving cylindrical and spherical symmetries; variational and minimum principles; limit analysis; plane-strain problems and crystal plasticity; finite-strain theory. Prerequisite: TAM 552.
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TAM 554 - Plasticity
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TAM 555: Fracture Mechanics
4.00 Credits
University of Illinois at Urbana-Champaign
Unified analytical treatment of modern fracture problems: macroscopic theories used to determine the static strength of bodies containing cracks; Griffith criterion, linear-elastic fracture mechanics, elastic-plastic fracture mechanics models; small-scale yielding results and their implications; general yielding; interfacial fracture; fracture control; micromechanisms of fracture. Prerequisite: TAM 424 or MSE 440; TAM 541; TAM 552.
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TAM 555 - Fracture Mechanics
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TAM 570: Computational Fluid Mechanics
4.00 Credits
University of Illinois at Urbana-Champaign
Highly accurate and reliable techniques for large-scale numerical simulations of fluid flows: spectral numerical methods, including Fourier and other functional expansions, Galerkin and collocation projections, domain decompositions and the solution of partial differential equations, especially the Navier-Stokes equations; high-resolution methods for the solution of hyperbolic conservation laws with discontinuous solutions, and issues related to implementation on supercomputers. Same as CSE 560. Prerequisite: TAM 470 and TAM 542.
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TAM 570 - Computational Fluid Mechanics
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