Vector algebra, force systems, free-body diagrams; engineering applications of equilibrium, including frames, friction, distributed loads; centroids, moments of inertia.

Kinematics, dynamics, and energy and momentum methods for points as well as 2D/3D rigid bodies. Describe and predict the motion of different types of rigid bodies in space and time. Vibrations of simple systems.

Internal forces and deformations in solids; stress and strain in elastic and plastic solids; application to simple engineering problems.

Used to record credit the student earns while enrolled at another institution in a program administered by the University's Study Abroad Office or the school's International Engineering Education programs.

Curved beams, shear deformation, beam columns, beams on elastic foundations; inelastic behavior of members; elementary plate bending.

Advanced work in the various areas of engineering mechanics, based on recent developments.

Used to record credit the student earns while enrolled at another institution in a program administered by the University's Study Abroad Office or the school's International Engineering Education Programs.

Physical basis of plastic deformation; mathematical theory of incremental plasticity; total theories; numerical implementation; slip and physical theories of plastic deformation; rate dependent (viscoplastic) models; applications to several engineering problems.

Dynamics of systems of particles and rigid bodies; vibration theory; analytical dynamics, including Lagrangian and Hamiltonian formulations; dynamic stability; continuous systems.

Methods for analyzing various types of nonlinear differential equations of dynamical systems; exact methods, perturbation and averaging techniques, direct method of Liapunov.

Foundations of the general nonlinear theories of continuum mechanics; general treatment of motion and deformation of continua, balance laws, constitutive theory; particular application to elastic solids and simple materials.

Free and forced vibration of single-degree-of-freedom, multiple-degree-of-freedom, and continuous systems. Lagrange's equations and Hamilton's principle; discretization of continuous systems; numerical methods for response and algebraic eigenvalue problems.

Basic topics in real and complex analysis, ordinary and partial differential equations, and other areas of applied mathematics with application to applied mechanics.

Continuation of Engineering Mechanics 386K.

An introduction to modern concepts in functional analysis and linear operator theory, with emphasis on their application to problems in theoretical mechanics; topological and metric spaces, norm linear spaces, theory of linear operators on Hilbert spaces, applications to boundary value problems in elasticity and dynamical systems.

A study of methods for assessing the qualitative behavior of solutions to equations governing nonlinear continuum mechanics.

Governing equations in differential and integral forms; applications to both inviscid and viscous flow problems.

Mathematical description of stress, deformation, and constitutive equations of solid mechanics; boundary value problems of elasticity.

Griffith theory of brittle crack propagation, other theories, crack toughness testing concepts.

Continuation of Engineering Mechanics 388. Additional topics in elasticity, plasticity, viscoelasticity, variational methods, and other areas of solid mechanics.

Constitutive characterization of materials based on their microstructure. Relationships between internal structure and mechanical properties for composites, polycrystals, and polymers on the basis of linear elasticity, plasticity, and theories that account for rate-dependence.

Introduction to soft tissues and soft tissue mechanics; continuum mechanics (kinematics, stress, balance laws and hyperelasticity); and nonlinear finite element analysis in soft tissue mechanics.

Introduction to soft tissues and soft tissue mechanics; continuum mechanics (kinematics, stress, balance laws and hyperelasticity); and nonlinear finite element analysis in soft tissue mechanics.

Discuss an extensive overview of mechanics-related subjects including stress, strain, fracture, delamination, instability, characterization, and important applications of thin films.

Introduction to linear viscoelasticity; methods of characterizing viscoelastic material behavior; analytical and approximate solution techniques for engineering problems, including contact, wave propagation, and thermoviscoelastic problems.

Principles and techniques of measurement in mechanics; includes discussion of strain gauges, optical interference methods, photoelasticity, and dynamic measurements.

Continuum physics and thermodynamics including thermal, mechanical, electrical and magnetic behaviors of active/smart materials. Linear and non-linear behavior of ferroelectrics, ferromagnetic materials, and shape memory alloys. Crystal symmetry, domain structure, phenomenological constitutive models, phase-field modeling, and dielectric elastomers.

Introduction to probability theory and its application to random excitation of linear and nonlinear systems; a probabilistic discussion of failure and fatigue in structures.

Approximate solution methods for flow and transport problems in engineering and applied science. Finite element, finite difference, and residual methods for linear and nonlinear problems.

Fundamental theory of buckling of elastic structural elements such as bars, frames, rings, plates, and shells; also special stability topics including inelastic buckling, creep buckling, and buckling under dynamic loading.

Derivation and implementation of the finite element method; basic coding techniques; application to problems of stress and diffusion.

Organization and data management in finite element codes; element models and calculations; equation solving; preprocessing and postprocessing.

Contemporary topics in the theory and application of finite element methods.

Solutions of linear wave equations; waves in elastic media, including plates and cylinders; transient waves, transform methods, asymptotic approximation.

Discuss machine learning algorithms, including linear models, kernel machines, tree-based algorithms, density estimation, clustering, dimensionality reduction and deep neural networks; foundations of machine learning, including optimization theory, probability theory, advanced linear algebra, statistics; evaluation of machine learning methods; and convolutational neural networks.

Must be arranged by mutual agreement between student and faculty member.

Current topics in mechanics.

Current topics in computational mechanics.

Preparation of a report to fulfill the requirement for the master's degree under the report option.

Teaching methods and objectives, criteria for evaluating teaching effectiveness, procedures and regulations, laboratory teaching.