Department of Civil and Environmental Engineering

Edmund T. Pratt School of Engineering

Duke University - Box 90287, Durham, NC 27708-0287

- The King Center
- The Martin Luther King Jr. Papers Project at Stanford University
- Letter from a Birmingham Jail, Rev. Dr. Martin Luther King, Jr., April 16, 1963
- Acceptance Speech at the 1964 Nobel Peace Prize Ceremony, Rev. Dr. Martin Luther King, Jr., December 10, 1964

- Homework 1 (due 1/22/2016): Design: open-ended problems requiring creative ideas and iterative solutions.
- Homework 2 (due 1/29/2016): Optimization: search methods.
- Homework 3 (due 2/5/2016): Optimization: gradient methods.
- Homework 4 (due 2/12/2016): Uncertainty: analysis and simulation.
- Homework 5 (due 2/19/2016): Review of structural analysis.
- Project 1 (due 2/26/2016): Optimize a statically determinate truss.
- Homework 6 (due 3/4/2016): Real Work.
- Homework 7 (due 3/11/2016): Minimum Total Potential Energy.
- Take Home Midterm (due 3/25/2016)
- Project 2 (due 4/1/2016): Supply enough clean drinking water.
- Project 3 (due 4/8/2016): Trade stocks to make as much money as possible.
- Homework 8 (due 4/15/2016): Structural dynamics.
- Project 4 (due 4/27/2016): Protect buildings and contents from earthquakes.

- Links to some Matlab tutorials
- The Nelder-Mead Algorithm in Two Dimensions
- Constrained Optimization using Lagrange Multipliers
- Review of Matrix Math
- Constrained Linear Least Squares
- Summary of some Rules of Probability with Examples
- Summary of some probability distributions
- Solid Mechanics Review Questions
- A review of truss analysis
- A review of beam analysis
- A review of buckling analysis
- Oar Loom Optimization
- Introductory Example of Uncertainty, Design, and Optimization
- The Three Moment Equation, three_moment.m
- Strain Energy in Linear Elastic Solids
- Carlo Alberto Castigliano
- Theorems of Castigliano
- Summary of the Theorems of Castigliano
- Four Strain Energy Concepts in Pictures
- Minimum Total Potential Energy - example
- Minimum Total Potential Energy, Quadratic Programming, and Lagrange Multipliers
- Introduction to Water Supply and Treatment Project
- Plastic Design of a Fixed-Fixed Beam-Column, MP.m
- Linear SDOF Structural Dynamics: Free and Forced Response
- Elastic and Inelastic SDOF Structural Dynamics: Matlab/Simulink Demo's Matlab code

These Matlab functions implement methods for minimizing a function of several parameters subject to a set of inequality constraints:

minimize *f(x)* such that *g(x) ≤ 0*,

where *x* is a vector of design variables,
*f(x)* is a scalar-valued objective function,
and *g(x)* is a vector of constraints.

- Examples of running constrained minimization codes
- ORSopt.m implements an optimized step-size random search algorithm.
- NMAopt.m implements a Nelder-Mead algorithm.
- SQPopt.m implements a sequential quadratic programming algorithm.
- avg_cov_func.m calculates average and coefficient of variation of a random penalized objective function.
- box_constraint.m determines the box constraint scaling factor
*a>0*to the perturbation vector*r*from*x*such that: max(*x+ar*) < +1 and min(*x+ar*) > -1 - optim_options.m is needed for ORSopt.m, NMAopt.m, and SQPopt.m
- plot_surface.m plots the cost function as a surface over two of the parameter values, ORSopt, NMAopt, or SQPopt
- plot_cvg_hst.m plots the convergence history for the solution computed by ORSopt, NMAopt, or SQPopt

These Matlab functions can be used to compute probability distribution functions and to generate samples of random variables.

Distribution |
PDF, f _{X}(x) |
CDF, F _{X}(x) |
inverse CDF, F _{X}^{-1}(p) |
generate sample, x _{1} ... x_{N} |

uniform
| unifpdf.m | unifcdf.m | unifinv.m | rand.m |

triangular
| triangular_pdf.m | triangular_cdf.m | triangular_inv.m | triangular_rnd.m |

normal
| normpdf.m | normcdf.m | norminv.m | randn.m |

log-normal
| logn_pdf.m | logn_cdf.m | logn_inv.m | logn_rnd.m |

Poisson
| Poisson_pmf.m | Poisson_cdf.m | Poisson_rnd.m | |

exponential
| exp_pdf.m | exp_cdf.m | exp_inv.m | exp_rnd.m |

Rayleigh
| Rayleigh_pdf.m | Rayleigh_cdf.m | Rayleigh_inv.m | Rayleigh_rnd.m |

gamma
| gamma_pdf.m | gamma_cdf.m | gamma_inv.m | gamma_rnd.m |

Laplace
| Laplace_pdf.m | Laplace_cdf.m | Laplace_inv.m | Laplace_rnd.m |

#### Optimization

- A Sucker Is Optimized Every Minute, Virginia Heffernan, New York Times, March 17, 2015.
- Nonlinear Optimization with Engineering Applications, Michael Bartholomew-Biggs, Springer Optimization and Its Applications, vol 19, 2008.
- An Optimized Step Size Random Search (OSSRS), Sheela, B.V., Computer Methods in Applied Mechanics and Engineering, 19 (1979): 99-106.
- Adaptive Step Size Random Search, Schumer, M.A. and Steiglitz, K., IEEE Transactions on Automatic Control, AC-13, No. 3 (1968): 270-276.
- Evaluation of Adaptive Step Size Random Search, White, L.J. and Day, R.G., IEEE Transactions on Automatic Control, AC-16, No. 5 (1971): 475-478.
- Valuation of some Random Search Methods, Ugray, C., Optimization, 10(1) (1979): 57-65
- Introduction to Analyses of Adaptive Stochastic Search Methods for Global Optimization, by Zelda B. Zabinsky, University of Washington
- A General-Purpose Global Optimizer: Implementation and Applications, Pronzato, L., and Walter, E., Mathematics and Computers in Simulation XXVI (1984): 412-422.
- A simplex method for function minimization, J.A. Nelder and R. Mead, Computer Journal, 7(4) (1965): 308-313.
- Nelder-Mead method(Wikipedia)
- Animation of the Nelder-Mead algorithm, Grabitech Solutions AB, Sweden
- Animation of the Nelder-Mead algorithm, Practical Optimization: A Gentle Introduction, by John W. Chinneck, Carleton University.
- Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions by J.C. Lagarias et al., SIAM J. Optim., vol. 9, no 1, pp 112-147.
- Nonlinear Programming, Becerra, Victor M., University of Reading
- Numerical Optimization, Ascher, Uri M., University of British Columbia
- Matlab Optimization Toolbox, The MathWorks.
- Sequential quadratic programming, Boggs, P.T., Acta Numerica, (1995): 1-51.

#### Uncertainty Analysis

- For Todayâs Graduate, Just One Word: Statistics, Steve Lohr, New York Times, August 5, 2009.
- Introduction to Randomness and Random Numbers (random.org)
- A Probability Tutorial, West Texas A and M University.
- Bayes' Theorem for the curious and bewildered; an excruciatingly gentle introduction, Eliezer Yudkowsky, The Singularity Institute for Artificial Intelligence
- Introduction to Probability and Statistics, John Walker, Fourmilab, Switzerland.
- Uncertainty in Probabilistic Risk Assessment, A.R. Daneshkhah, University of Sheffield, UK (2004).
- Aleatory and Epistemic Uncertainty Quantification for Engineering Applications, L.P. Swiler, A.A. Giunta, Sandia labs.
- Uncertainty Modeling and Analysis in Civil Engineering, Bilal M. Ayyub, CRC Press, 1997.
- Quantitative Analysis of Variability and Uncertainty in Energy and Environmental Systems H.C. Frey, N.C. State University.
- Engineering Design Reliability, Efstratios Nikolaidis, Dan M. Ghiocel, Suren Singhal, CRC Press, (2004)
- Uncertainty in Structural Engineering, William M. Bulleit,
*Practice Periodical on Structural Design and Construction, ASCE*,**13**(1): 24-30. (2008) - Dealing with Uncertainty: From Health Risk Assessment to Environmental Decision Making,
Louis A. Cox, Jr. and Paolo F. Ricci,
*Journal of Energy Engineering, ASCE*,**118**(2): 77-94. (1992) - Superfund Decision Analysis in the Presence of Uncertainty,
Aaron A. Jennings, Neel Mehta, and Sumeet Mohan,
*Journal of Environmental Engineering, ASCE*,**120**(5): 1132-1150. (1994)

#### Solid Mechanics Review, References, and Software

- MecMovies: Review of Solid Mechanics
- MDSolids: Educational Software for Mechanics of Materials from the University of Alberta
- Mechanics of Solids from the University of Sydney
- Examples of Truss Types
- truss_plot.m Plot a truss configuration.
- On-line (Java) Structural Analysis Software from Dr. D.J.Rao
- Beam-bending Java Applet from Virginia-Tech
- On-Line Bridge-Design applet from Johns Hopkins University
- MS-Windows Truss Analysis Software from Method Computing
- Cross section relationships for Wide-Flange Sections

#### Prestressed Concrete Beam Design

#### Water Supply and Treatment System

- RDU Airport Rainfall statistics, WRAL weather
- Big Rain Events in the Southeast, Florida Climate Center, Florida State University.
- Real Time Water Supply Status, City of Durham, NC
- Little River Reservoir and Lake Michie Elevations, City of Durham, NC.
- Water Supply and Treatment, City of Durham, NC.
- Annual Water Quality Reports, City of Durham, NC.
- The Story of Drinking Water, City of Durham, NC.
- Falls Lake Data, USGS
- Falls Lake Data, US Army Corps of Engineers
- Charting Our Water Future, McKinsey&Company
- Average Daily Water Use in North Carolina Cities, by week, North Carolina Department of Environment and Natural Resources
- The Future of Water in North Carolina, Strategies for Sustaining Clean and Abundant Water, Conference Report, August 2007.
- Comparison of Methods Used to Estimate Lake Evaporation for a Water Budget of Lake Sminole, Southwestern Georgia and Northwestern Florida, by Melinda S. Mosner and Brnet T. Aulenbach
- Evaporatoin Rates, by David Cook, Argonne National Labs
- Rain Water Solutions, Inc., Raleigh, NC

#### Structural Dynamics and Vibration Response

- Vibration Response Plotter from Dr. D.J.Rao
- Structural Dynamic Vibrations Prof. B.J. Stone, University of Western Australia

- Frequency Response Functions from Dr. C.W.deSilva
- Acoustics and Vibrations Animations, Dr. Dan Russel, Kettering University
- Nonlinear SDOF Structural Dynamics: Experimental Data (2008):

16apr08.zip | 17apr08.zip | 18apr08.zip

#### Miscellaneous

This course has achieved Duke's Green Classroom Certification. The certification indicates that the faculty member teaching this course has taken significant steps to green the delivery of this course. Your faculty member has completed a checklist indicating their common practices in areas of this course that have an environmental impact, such as paper and energy consumption. Some common practices implemented by faculty to reduce the environmental impact of their course include allowing electronic submission of assignments, providing online readings and turning off lights and electronics in the classroom when they are not in use. The eco-friendly aspects of course delivery may vary by faculty, by course and throughout the semester. Learn more at sustainability.duke.edu

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.© 2001-2015 Henri P. Gavin; updated: 9-27-2001, 12-15-2003, 1-7-2004, 1-6-2005, 1-22-2005, 2-1-2005, 2-14-2005, 1-11-2006, 2-14-2008, 2-28-2008, 3-24-2008, 1-8-2009, 8-7-2009, 1-5-2011, 1-8-2014, 1-7-2015, 1-13-2016