### Orientation

### Reading for Martin Luther King Day

- 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

### Assignments (note: due dates are subject to change)

- guideline and template for completing assignments
- Homework 1 (due 1/17/2020): Design: open-ended problems requiring creative ideas and iterative solutions.
- Homework 2 (due 1/24/2020): Optimization: search methods.
- Homework 3 (due 1/31/2020): Optimization: gradient methods.
- Homework 4 (due 2/7/2020): Uncertainty: analysis and simulation.
- Homework 5 (due 2/14/2020): Real Work
- Homework 6 (due 2/21/2020): Minimum energy equilibrium and constraints.
- Project 1 (due 3/6/2020): Optimize a statically determinate truss.
- Take Home Midterm (due 3/27/2020)
- Project 2 (due 4/10/2020): Supply enough clean drinking water.
- Homework 7 (due 4/17/2020): Structural dynamics.
- Project 3 (due 4/22/2020): Protect buildings and contents from earthquakes.

### Course Notes

- 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

### Matlab functions for optimization

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

### Matlab functions for random variables

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 |

GEV
| GEV_pdf.m | GEV_cdf.m | GEV_inv.m | GEV_rnd.m |

### Additional References

### 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