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Course Criteria
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3.00 Credits
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.
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3.00 Credits
Introduces 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.
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3.00 Credits
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.
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3.00 Credits
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.
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3.00 Credits
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.
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3.00 Credits
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.
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3.00 Credits
Subject matter varies from year to year depending on students’ interest and needs. Typical topics may include geophysics, astrodynamics, water waves, or nonlinear methods.
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3.00 Credits
Develops the tools necessary for fatigue and fracture control in structural materials. Continuum fracture mechanics principles are presented. Fracture modes are discussed from the interdisciplinary perspectives of continuum mechanics and microscopic plastic deformation/fracture mechanisms. Cleavage, ductile fracture, fatigue, and environmental cracking are included, with emphasis on micromechanical modeling. Cross-listed as MSE 732.
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3.00 Credits
Analyzes 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.
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1.00 - 12.00 Credits
Detailed study of graduate course material on an independent basis under the guidance of a faculty member.
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