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Course Criteria
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3.00 Credits
Introduces continuum mechanics and mechanics of deformable solids. Topics include 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 and CE 602
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3.00 Credits
Analyzes 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.
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3.00 Credits
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.
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3.00 Credits
Analyzes 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.
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3.00 Credits
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. Cross-listed as CE 607.
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3.00 Credits
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.
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3.00 Credits
Analyzes the derivation, interpretation, and application of the principles of virtual work and complementary virtual work to engineering problems; 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. Introduces generalized, extended, mixed, and hybrid principles; variational methods of approximation, Hamilton’s principle, and Lagrange’s equations of motion. Uses variational theorems to approximate solutions to problems in structural mechanics. Cross-listed as CE 620.
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3.00 Credits
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.
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3.00 Credits
The topics covered are: plane waves; d’Alembert solution; method of characteristics; dispersive systems; wavepackets; group velocity; fully-dispersed waves; Laplace, Stokes, and steepest descents integrals; membranes, plates and plane-stress waves; evanescent waves; Kirchhoff’s solution; Fresnel’s principle; elementary diffraction; reflection and transmission at interfaces; waveguides and ducted waves; waves in elastic half-spaces; P, S, and Rayleigh waves; layered media and Love waves; slowly-varying media and WKBJ method; Time-dependent response using Fourier-Laplace transforms; some nonlinear water waves. Also cross-listed as MAE 622.
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3.00 Credits
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.
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