Kinematics of rigid bodies; momentum and energy methods; vibrations of discrete and continuous systems; eigen-value problems, natural frequencies and modes. Basics of computer simulation of dynamics problems using MATLAB or Mathematica.
Material behavior and constitutive relations. Mechanical properties of metals and cement composites. Structural materials. Modern construction materials. Experimental investigation of material properties and behavior of structural elements including fracture, fatigue, bending, torsion, buckling.
Research training course. Recommended in preparation for laboratory related research.
Numerical and symbolic (algebraic) problem solving with Mathematica. Formulation for graphics application in civil, mechanical, and bioengineering. Example of two-and three-dimensional curve and surface objects in C++ and Mathematica; special projects of interest to electrical and computer science.
Analysis of aerospace structures (solid and thin-walled structures), including bending, shear, and torsion; aircraft loading bearing members; introduction to aerospace materials; analysis of structural instability; experimental method in aerospace structures.
Stress and deformation formulation in two-and three-dimensional solids; viscoelastic and plastic material in one and two dimensions energy methods.
Elastic stresses at a crack; energy and stress intensity criteria for crack growth; effect of plastic zone at the crack; fracture testing applications. Fatigue characterization by stress-life and strain-life; damage index; crack propagation; fail safe and safe life analysis.
Overview of composite materials, including history, background, and manufacturing processes. Macro-mechanics: anisotropic elasticity and stress transformation. Micro-mechanics: Rule of Mixture, Composites Cylinder Model (CCM) and other models. Macro-mechanics: Classic Lamination Theory (CLT). Hygrothermal effects, residual stresses, Composite mechanical testing, fabrication. Failure modes and lamina-based failure theories. Bending and Buckling of composite plates. ICME of Composites (nano-, micro-, meso- and macro-scale analysis, experimental validation, process modeling, integration).
Static flexural response of thin, elastic, rectangular, and circular plates. Exact (series) and approximate (Ritz) solutions. Circular cylindrical shells. Axisymmetric and non-axisymmetric membrane theory. Shells of arbitrary shape.
Research training course. Recommended in preparation for laboratory related research.
Principles of traditional and emerging sensors, data acquisition and signal processing techniques, experimental modal analysis (input-output), operational modal analysis (output-only), model-based diagnostics of structural integrity, data-based diagnostics of structural integrity, long-term monitoring and intelligent maintenance. Lectures and demonstrations, hands-on laboratory experiments.
Review of random variables. Random process theory: stationary and ergodic processes, correlation functions and power spectra, non-stationary, non-white and non-Gaussian processes. Uncertainty quantification and simulation of environmental excitations and material/media properties, even when subject to limited/incomplete data: joint time-frequency analysis, sparse representations and compressive sampling concepts and tools. Stochastic dynamics and reliability assessment of diverse engineering systems: complex nonlinear/hysteretic behaviors and/or fractional derivative modeling. Emphasis on solution methodologies based on Monte Carlo simulation, statistical linearization, and Wiener path integral. Examples from civil, marine, mechanical and aerospace engineering.
A fluid infiltrating porous solid is a multiphase material whose mechanical behavior is significantly influenced by the pore fluid. Diffusion, advection, capillarity, heating, cooling, and freezing of pore fluid, buildup of pore pressure, and mass exhanges among solid and fluid constituents all influence the stability and integrity of the solid skeleton, causing shrinkage, swelling, fracture, or liquefaction. These coupling phenomena are important for numerous disciplines, including geophysics, biomechanics, and material sciences. Fundamental principles of poromechanics essential for engineering practice and advanced study on porous media. Topics include balance principles, Biot’s poroelasticity, mixture theory, constitutive modeling of path independent and dependent multiphase materials, numerical methods for parabolic and hyperbolic systems, inf-sup conditions, and common stabilization procedures for mixed finite element models, explicit and implicit time integrators, and operator splitting techniques for poromechanics problems.
FE formulation for beams and plates. Generalized eigenvalue problems (vibrations and buckling). FE formulation for time-dependent parabolic and hyperbolic problems. Nonlinear problems, linearization, and solution algorithms. Geometric and material nonlinearities. Introduction to continuum mechanics. Total and updated Lagrangian formulations. Hyperelasticity and plasticity. Special topics: fracture and damage mechanics, extended finite element method.
Ordinary and partial differential equations. Turbulence phenomenology; spatial and temporal scales in turbulent flows; statistical description, filtering and Reynolds decomposition, equations governing the resolved flow, fluctuations and their energetics; turbulence closure problem for RANS and LES; two equation turbulence models and second moment closures.