Ae/AM/CE/ME 102 abc
Mechanics of Structures and Solids
9 units (3-0-6)
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first, second, third terms
Prerequisites: ME 35 abc or equivalent.
Static and dynamic stress analysis. Two- and three-dimensional theory of stressed elastic solids. Analysis of structural elements with applications in a variety of fields. Variational theorems and approximate solutions, finite elements. A variety of special topics will be discussed in the third term such as, but not limited to, elastic stability, wave propagation, and introductory fracture mechanics.
Instructors:
Bhattacharya, Ravichandran
CE/Ae/AM 108 ab
Computational Mechanics
9 units (3-0-6); first, second terms
|
Prerequisite:Ae/AM/ME/CE 102 abc or Ae/GE/ME 160 ab, or instructor's permission.
Numerical methods and techniques for solving initial boundary value problems in continuum mechanics (from heat conduction to statics and dynamics of solids and structures). Finite difference methods, direct methods, variational methods, finite elements in small strains and at finite deformation for applications in structural mechanics and solid mechanics. Solution of the partial differential equations of heat transfer, solid and structural mechanics, and fluid mechanics. Transient and nonlinear problems. Computational aspects and development and use of finite element code.
Instructor:
Dennis Kochmann
AM 125 abc
Engineering Mathematical Principles
9 units (3-0-6)
|
first, second, third terms
Prerequisites: ACM 95/100 abc.
Topics include linear spaces, operators and matrices, integral equations, variational principles, ordinary and partial differential equations, stability, perturbation theory, stochastic system analysis and Bayesian updating. Applications to problems in engineering and science are stressed.
Instructor:
Beck
AM/ACM 127
Calculus of Variations
9 units (3-0-6)
|
third Term
Prerequisites: ACM 95/100.
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
AM/CE/ME 150 abc
Graduate Engineering Seminar
1 unit
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each term
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
AM/CE 151 ab
Dynamics and Vibration
9 units (3-0-6)
|
first, second terms
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
AM/ME 165 ab
Elasticity
9 units (3-0-6)
|
second, third terms
Prerequisites: Ae/Ge/ME 160 a and registered in Ae/Ge/ME 160 b.
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.
AM 200
Special Problems in Advanced Mechanics
Hours and units by arrangement
By arrangement with members of the staff, properly qualified graduate students are directed in independent studies in mechanics.
Ae/AM/MS/ME 213
Mechanics and Materials Aspects of Fracture
9 units (3-0-6)
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second term
Prerequisites: Ae/AM/CE/ME 102 abc (concurrently) or equivalent and instructor's permission.
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.
Ae/AM/CE/ME 214 abc
Computational Solid Mechanics
9 units (3-0-6)
|
first, second, third terms
Prerequisites: AM 125 abc or equivalent; ACM 100 abc or equivalent; CE/AM/Ae 108 abc or equivalent or instructor's permission; Ae/AM/CE/ME 102 abc or equivalent; Ae/Ge/ME 160 ab desirable or taken concurrently.
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.
Ae/AM/ME 215
Dynamic Behavior of Materials
9 units (3-0-6)
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first term
Prerequisites: ACM 100 abc or AM 125 abc; Ae/AM/CE/ME 102 abc.
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.
Ae/AM/ME 223
Plasticity
9 units (3-0-6)
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first term
Prerequisites: Ae/AM/CE/ME 102 abc or instructor's permission.
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
Ae/AM/ME 225
Special Topics in Solid Mechanics: Linear and nonlinear waves in periodic media
9 units (3-0-6)
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second term
Prerequisites: Ae/AM/CE/ME 102 abc or permission of the instructor.
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.
AM 250
Research in Applied Mechanics
Hours and units by arrangement
Research in the field of applied mechanics. By arrangement with members of the staff, properly qualified graduate students are directed in research.
Published Date:
July 28, 2022