Preface. 1 Introduction to Optimization. 1.1 Introduction. 1.2 Historical Development. 1.3 Engineering Applications of Optimization. 1.4 Statement of an Optimization Problem. 1.5 Classification of Optimization Problems. 1.6 Optimization Techniques. 1.7 Engineering Optimization Literature. 1.8 Solution of Optimization Problems Using MATLAB. References and Bibliography. Review Questions. Problems. 2 Classical Optimization Techniques. 2.1 Introduction. 2.2 Single-Variable Optimization. 2.3 Multivariable Optimization with No Constraints. 2.4 Multivariable Optimization with Equality Constraints. 2.5 Multivariable Optimization with Inequality Constraints. 2.6 Convex Programming Problem. References and Bibliography. Review Questions. Problems. 3 Linear Programming I: Simplex Method. 3.1 Introduction. 3.2 Applications of Linear Programming. 3.3 Standard Form of a Linear Programming Problem. 3.4 Geometry of Linear Programming Problems. 3.5 Definitions and Theorems. 3.6 Solution of a System of Linear Simultaneous Equations. 3.7 Pivotal Reduction of a General System of Equations. 3.8 Motivation of the Simplex Method. 3.9 Simplex Algorithm. 3.10 Two Phases of the Simplex Method. 3.11 MATLAB Solution of LP Problems. References and Bibliography. Review Questions. Problems. 4 Linear Programming II: Additional Topics and Extensions. 4.1 Introduction. 4.2 Revised Simplex Method. 4.3 Duality in Linear Programming. 4.4 Decomposition Principle. 4.5 Sensitivity or Postoptimality Analysis. 4.6 Transportation Problem. 4.7 Karmarkar's Interior Method. 4.8 Quadratic Programming. 4.9 MATLAB Solutions. References and Bibliography. Review Questions. Problems. 5 Nonlinear Programming I: One-Dimensional Minimization Methods. 5.1 Introduction. 5.2 Unimodal Function. ELIMINATION METHODS. 5.3 Unrestricted Search. 5.4 Exhaustive Search. 5.5 Dichotomous Search. 5.6 Interval Halving Method. 5.7 Fibonacci Method. 5.8 Golden Section Method. 5.9 Comparison of Elimination Methods. INTERPOLATION METHODS. 5.10 Quadratic Interpolation Method. 5.11 Cubic Interpolation Method. 5.12 Direct Root Methods. 5.13 Practical Considerations. 5.14 MATLAB Solution of One-Dimensional Minimization Problems. References and Bibliography. Review Questions. Problems. 6 Nonlinear Programming II: Unconstrained Optimization Techniques. 6.1 Introduction. DIRECT SEARCH METHODS. 6.2 Random Search Methods. 6.3 Grid Search Method. 6.4 Univariate Method. 6.5 Pattern Directions. 6.6 Powell's Method. 6.7 Simplex Method. INDIRECT SEARCH (DESCENT) METHODS. 6.8 Gradient of a Function. 6.9 Steepest Descent (Cauchy) Method. 6.10 Conjugate Gradient (Fletcher-Reeves) Method. 6.11 Newton's Method. 6.12 Marquardt Method. 6.13 Quasi-Newton Methods. 6.14 Davidon-Fletcher-Powell Method. 6.15 Broyden-Fletcher-Goldfarb-Shanno Method. 6.16 Test Functions. 6.17 MATLAB Solution of Unconstrained Optimization Problems. References and Bibliography. Review Questions. Problems. 7 Nonlinear Programming III: Constrained Optimization Techniques. 7.1 Introduction. 7.2 Characteristics of a Constrained Problem. DIRECT METHODS. 7.3 Random Search Methods. 7.4 Complex Method. 7.5 Sequential Linear Programming. 7.6 Basic Approach in the Methods of Feasible Directions. 7.7 Zoutendijk's Method of Feasible Directions. 7.8 Rosen's Gradient Projection Method. 7.9 Generalized Reduced Gradient Method. 7.10 Sequential Quadratic Programming. INDIRECT METHODS. 7.11 Transformation Techniques. 7.12 Basic Approach of the Penalty Function Method. 7.13 Interior Penalty Function Method. 7.14 Convex Programming Problem. 7.15 Exterior Penalty Function Method. 7.16 Extrapolation Techniques in the Interior Penalty Function Method. 7.17 Extended Interior Penalty Function Methods. 7.18 Penalty Function Method for Problems with Mixed Equality and Inequality Constraints. 7.19 Penalty Function Method for Parametric Constraints. 7.20 Augmented Lagrange Multiplier Method. 7.21 Checking the Convergence of Constrained Optimization Problems. 7.22 Test Problems. 7.23 MATLAB Solution of Constrained Optimization Problems. References and Bibliography. Review Questions. Problems. 8 Geometric Programming. 8.1 Introduction. 8.2 Posynomial. 8.3 Unconstrained Minimization Problem. 8.4 Solution of an Unconstrained Geometric Programming Program Using Differential Calculus. 8.5 Solution of an Unconstrained Geometric Programming Problem Using Arithmetic-Geometric Inequality. 8.6 Primal-Dual Relationship and Sufficiency Conditions in the Unconstrained Case. 8.7 Constrained Minimization. 8.8 Solution of a Constrained Geometric Programming Problem. 8.9 Primal and Dual Programs in the Case of Less-Than Inequalities. 8.10 Geometric Programming with Mixed Inequality Constraints. 8.11 Complementary Geometric Programming. 8.12 Applications of Geometric Programming. References and Bibliography. Review Questions. Problems. 9 Dynamic Programming. 9.1 Introduction. 9.2 Multistage Decision Processes. 9.3 Concept of Suboptimization and Principle of Optimality. 9.4 Computational Procedure in Dynamic Programming. 9.5 Example Illustrating the Calculus Method of Solution. 9.6 Example Illustrating the Tabular Method of Solution. 9.7 Conversion of a Final Value Problem into an Initial Value Problem. 9.8 Linear Programming as a Case of Dynamic Programming. 9.9 Continuous Dynamic Programming. 9.10 Additional Applications. References and Bibliography. Review Questions. Problems. 10 Integer Programming. 10.1 Introduction 588. INTEGER LINEAR PROGRAMMING. 10.2 Graphical Representation. 10.3 Gomory's Cutting Plane Method. 10.4 Balas' Algorithm for Zero-One Programming Problems. INTEGER NONLINEAR PROGRAMMING. 10.5 Integer Polynomial Programming. 10.6 Branch-and-Bound Method. 10.7 Sequential Linear Discrete Programming. 10.8 Generalized Penalty Function Method. 10.9 Solution of Binary Programming Problems Using MATLAB. References and Bibliography. Review Questions. Problems. 11 Stochastic Programming. 11.1 Introduction. 11.2 Basic Concepts of Probability Theory. 11.3 Stochastic Linear Programming. 11.4 Stochastic Nonlinear Programming. 11.5 Stochastic Geometric Programming. References and Bibliography. Review Questions. Problems. 12 Optimal Control and Optimality Criteria Methods. 12.1 Introduction. 12.2 Calculus of Variations. 12.3 Optimal Control Theory. 12.4 Optimality Criteria Methods. References and Bibliography. Review Questions. Problems. 13 Modern Methods of Optimization. 13.1 Introduction. 13.2 Genetic Algorithms. 13.3 Simulated Annealing. 13.4 Particle Swarm Optimization. 13.5 Ant Colony Optimization. 13.6 Optimization of Fuzzy Systems. 13.7 Neural-Network-Based Optimization. References and Bibliography. Review Questions. Problems. 14 Practical Aspects of Optimization. 14.1 Introduction. 14.2 Reduction of Size of an Optimization Problem. 14.3 Fast Reanalysis Techniques. 14.4 Derivatives of Static Displacements and Stresses. 14.5 Derivatives of Eigenvalues and Eigenvectors. 14.6 Derivatives of Transient Response. 14.7 Sensitivity of Optimum Solution to Problem Parameters. 14.8 Multilevel Optimization. 14.9 Parallel Processing. 14.10 Multiobjective Optimization. 14.11 Solution of Multiobjective Problems Using MATLAB. References and Bibliography. Review Questions. Problems. A Convex and Concave Functions. B Some Computational Aspects of Optimization. B.1 Choice of Method. B.2 Comparison of Unconstrained Methods. B.3 Comparison of Constrained Methods. B.4 Availability of Computer Programs. B.5 Scaling of Design Variables and Constraints. B.6 Computer Programs for Modern Methods of Optimization. References and Bibliography. C Introduction to MATLAB(R) . C.1 Features and Special Characters. C.2 Defining Matrices in MATLAB. C.3 CREATING m-FILES. C.4 Optimization Toolbox. Answers to Selected Problems. Index .

Engineering Optimization : Theory and Practice

Carbon nanotubes subject to large deformations reversibly switch into different morphological patterns. Each shape change corresponds to an abrupt release of energy and a singularity in the stress-strain curve. These transformations, simulated using a realistic many-body potential, are explained by a continuum shell model. With properly chosen parameters, the model provides a remarkably accurate ``roadmap'' of nanotube behavior beyond Hooke's law.

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Nanomechanics of carbon tubes: Instabilities beyond linear response.

This is a study of the formulation, some basic solutions, and applications of the Biot linearized quasistatic elasticity theory of fluid-infiltrated porous materials. Whereas most previously solved problems are based on idealizing the fluid and solid constituents as separately incompressible, full account is taken here of constituent compressibility. Previous studies are reviewed and the Biot constitutive equations relating strain and fluid mass content to stress and pore pressure are recast in terms of new material parameters, more directly open to physical interpretation as the Poisson ratio and induced pore pressure coefficient in undrained deformation. Different formulations of the coupled deformation/diffusion field equations and their analogues in coupled thermoelasticity are discussed, and a new formulation with stress and pore pressure as basic variables is presented that leads, for plane problems, to a convenient complex variable representation of solutions. The problems solved include those of the suddenly introduced edge dislocation and concentrated line force and of the suddenly pressurized cylindrical and spherical cavity. The dislocation solution is employed to represent that for quasi-static motions along a shear fault, and a discussion is given, based on fracture mechanics models for fault propagation, of phenomena involving coupled behavior between the rupturing solid and its pore fluid, which could serve to stabilize a fault against rapid spreading. Also, the solution for a pressurized cylindrical cavity leads to a time-dependent stress field near the cavity wall, and its relevance to time effects in the inception of hydraulic fractures from boreholes, or from drilled holes in laboratory specimens, is discussed. Various limiting cases are identified, and numerical values of the controlling porous media elastic parameters are given for several rocks.

Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents

Review of natural gas hydrates as an energy resource: Prospects and challenges ☆

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The localization of plastic deformation

In heavily over-consolidated clays there is a marked peak in the observed relation between shear stress and shear strain. As the strain increases, the stress falls from a peak to a much smaller residual stress. Slopes made from such a clay often fail progressively many years after construction. Sliding occurs on a concentrated slip surface, and it is found that the mean resolved shear stress on that surface is markedly less than the peak shear strength. Concepts from fracture mechanics, and in particular the J -integral, are used to derive conditions for the propagation of a concentrated shear band of this kind. The results indicate the presence of a strong size effect, which has important implications for the use of models in soil mechanics. An elastic analysis makes it possible to determine the size of the end zone in which the shear stress on the shear band falls to its residual value. An attempt is made to assess the possible sources of the time-dependence governing propagation speed of the shear band. They include pore-water diffusion to the dilating tip of the band (which governs the rate at which local strength reductions can occur), viscoelastic deformation of the clay (which allows a gradual build-up of strain concentration at the tip of the band), and the weathering break-down of diagenetic bonds.

The Growth of Slip Surfaces in the Progressive Failure of Over-Consolidated Clay

A study is made of the problem of interpreting the results of Menard pressuremeter tests on soil in situ. In the test a cylindrical cavity is expanded by internal pressure, and the relation between applied pressure and cavity volume change is measured. It is shown that the results of a single test are enough to determine a complete stress-strain relation in plane strain, and a simple graphical procedure for doing this is derived. The only restrictive assumption necessary is that the deformation is under undrained conditions; there is no restriction to infinitesimal strain or to elastic perfectly-plastic soils. On a etudie le probleme pose par l'interpretation des resultats fournis par le pressiometre Menard in situ. Dans ce type d'essais, une cavite cylindrique verticale est dilatee par pression interne. On mesure la relation entre la pression appliquee et le changement de volume de la cavite. On montre que les resultats obtenus avec un seul essai sont suffisants pour determiner une relation complete ‘con...

Undrained plane-strain expansion of a cylindrical cavity in clay: a simple interpretation of the pressuremeter test

Subsea Pipeline Engineering

DURING its construction a submarine pipeline is at the same time bent and loaded by the external pressure of the sea. If it is bent too far, it buckles. If the local external pressure is small, the buckle is limited to a short kink on the compressed side of the pipe. But if the external pressure is large enough, the local bending buckle can transform itself into a buckle of a different form, which once initiated can propagate along the pipe, driven by external pressure alone, even into regions free of bending. Figure 1 shows a pipe along which a buckle has propagated in this way. The mode can be observed by grasping a tube of toothpaste firmly between thumb and forefinger, and then moving the fingers along the tube. In a short transition region, between the fingers, the pipe bends from a circular into a dumb-bell cross section.

Buckle propagation in submarine pipelines

Experiments at 8.0 MPa and 277.15 K were carried out in different porous media, such as silica sand and activated carbon, to observe the formation and dissociation of methane hydrate in a specially designed crystallizer for mophology observation. In silica sand bed, we observed a clear hydrate front moving across the bed in the crystallizer at the experimental conditions with 50 and 100% water saturation. The hydrate crystals were observed to form in the interstitial pore space available between the silica sand particles. Whereas in activated carbon bed experiments, hydrates were observed to nucleate on the surface of the activated carbon grain and then dissociate within the stable hydrate formation region. For the first time, we were able to observe this behavior of transient hydrate crystal formation/dissociation in the stable hydrate region in porous media. We postulated that the particle size, pore space, and water saturation level may play a role in the above phenomenon. A clear hydrate front movemen...

Andrew Palmer

Papers

The Growth of Slip Surfaces in the Progressive Failure of Over-Consolidated Clay

Undrained plane-strain expansion of a cylindrical cavity in clay: a simple interpretation of the pressuremeter test

Subsea Pipeline Engineering

Buckle propagation in submarine pipelines

Morphology of Methane Hydrate Formation in Porous Media