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  • AM 127: Calculus of Variations

    9.00 Credits
    California Institute of Technology

    First and second variations; Euler-Lagrange equation; Hamiltonian formalism; action principle; Hamilton-Jacobi theory; stability; local and global minima; direct methods and relaxation; isoperimetric inequality; asymptotic methods and gamma convergence; selected applications to mechanics, materials science, control theory and numerical methods. Instructor: Bhattacharya. Prerequisite:    ACM 95/100.
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  • AM 150 abc: Graduate Engineering Seminar

    1.00 Credits
    California Institute of Technology

    Students are required to attend a graduate seminar, in any division, each week of each term. Students not registered for the M.S. and Ph.D. degrees must receive the instructor’s permission. Graded pass/fail. Instructor: Staff.
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  • AM 151 ab: Dynamics and Vibration

    9.00 Credits
    California Institute of Technology

    Equilibrium concepts, conservative and dissipative systems, Lagrange’s equations, differential equations of motion for discrete single and multi degree-of-freedom systems, natural frequencies and mode shapes of these systems (Eigen value problem associated with the governing equations), phase plane analysis of vibrating systems, forms of damping and energy dissipated in damped systems, response to simple force pulses, harmonic and earthquake excitation, response spectrum concepts, vibration isolation, seismic instruments, dynamics of continuous systems, Hamilton’s principle, axial vibration of rods and membranes, transverse vibration of strings, beams (Bernoulli-Euler and Timoshenko beam theory), and plates, traveling and standing wave solutions to motion of continuous systems, Rayleigh quotient and the Rayleigh-Ritz method to approximate natural frequencies and mode shapes of discrete and continuous systems, frequency domain solutions to dynamical systems, stability criteria for dynamical systems, and introduction to nonlinear systems and random vibration theory. Instructor: Staff.
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  • AM 165 ab: Elasticity

    9.00 Credits
    California Institute of Technology

    Fundamental concepts and equations of elasticity. Linearized theory of elastostatics and elastodynamics: basic theorems and special solutions. Finite theory of elasticity: constitutive theory, semi-inverse methods. Variational methods. Applications to problems of current interest. Not offered 2012–13. Prerequisite:    Ae/Ge/ME 160 a and registered in Ae/Ge/ME 160 b.
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  • AM 200: Special Problems in Advanced Mechanics

    1.00 - 9.00 Credits
    California Institute of Technology

    By arrangement with members of the staff, properly qualified graduate students are directed in independent studies in mechanics.
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  • AM 213: Mechanics and Materials Aspects of Fracture

    9.00 Credits
    California Institute of Technology

    Analytical and experimental techniques in the study of fracture in metallic and nonmetallic solids. Mechanics of brittle and ductile fracture; connections between the continuum descriptions of fracture and micromechanisms. Discussion of elastic-plastic fracture analysis and fracture criteria. Special topics include fracture by cleavage, void growth, rate sensitivity, crack deflection and toughening mechanisms, as well as fracture of nontraditional materials. Fatigue crack growth and life prediction techniques will also be discussed. In addition, “dynamic” stress wave dominated, failure initiation growth and arrest phenomena will be covered. This will include traditional dynamic fracture considerations as well as discussions of failure by adiabatic shear localization. Not offered 2012–13.
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  • AM 214 abc: Computational Solid Mechanics

    9.00 Credits
    California Institute of Technology

    Introduction to the use of numerical methods in the solution of solid mechanics and materials problems. First term: geometrical representation of solids. Automatic meshing. Approximation theory. Interpolation error estimation. Optimal and adaptive meshing. Second term: variational principles in linear elasticity. Finite element analysis. Error estimation. Convergence. Singularities. Adaptive strategies. Constrained problems. Mixed methods. Stability and convergence. Variational problems in nonlinear elasticity. Consistent linearization. The Newton-Rahpson method. Bifurcation analysis. Adaptive strategies in nonlinear elasticity. Constrained finite deformation problems. Contact and friction. Third term: time integration. Algorithm analysis. Accuracy, stability, and convergence. Operator splitting and product formulas. Coupled problems. Impact and friction. Subcycling. Space-time methods. Inelastic solids. Constitutive updates. Stability and convergence. Consistent linearization. Applications to finite deformation viscoplasticity, viscoelasticity, and Lagrangian modeling of fluid flows. Not offered 2012–13.
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  • AM 215: Dynamic Behavior of Materials

    9.00 Credits
    California Institute of Technology

    Fundamentals of theory of wave propagation; plane waves, wave guides, dispersion relations; dynamic plasticity, adiabatic shear banding; dynamic fracture; shock waves, equation of state. Not offered 2012–13.
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  • AM 223: Plasticity

    9.00 Credits
    California Institute of Technology

    Theory of dislocations in crystalline media. Characteristics of dislocations and their influence on the mechanical behavior in various crystal structures. Application of dislocation theory to single and polycrystal plasticity. Theory of the inelastic behavior of materials with negligible time effects. Experimental background for metals and fundamental postulates for plastic stress-strain relations. Variational principles for incremental elastic-plastic problems, uniqueness. Upper and lower bound theorems of limit analysis and shakedown. Slip line theory and applications. Additional topics may include soils, creep and rate-sensitive effects in metals, the thermodynamics of plastic deformation, and experimental methods in plasticity. Instructor: Andrade.
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  • AM 225: Special Topics in Solid Mechanics

    1.00 - 9.00 Credits
    California Institute of Technology

    The course will cover the basic principles of linear and nonlinear wave propagation in periodic media. It will introduce examples of periodic structural configurations at different length-scales and their relation to wave propagation. The course will cover the fundamental mathematical principles used to describe linear wave propagation and will describe the fundamentals of weakly nonlinear and highly nonlinear approaches. Selected recent scientific advancements in the dynamics of periodic media will also be discussed. Not offered 2012–13.
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