Showing papers on "Shape optimization published in 1984"

Elements of Structural Optimization

Abstract: 1. Introduction.- 1.1 Function Optimization and Parameter Optimization.- 1.2 Elements of Problem Formulation.- Design Variables.- Objective Function.- Constraints.- Standard Formulation.- 1.3 The Solution Process.- 1.4 Analysis and Design Formulations.- 1.5 Specific Versus General Methods.- 1.6 Exercises.- 1.7 References.- 2. Classical Tools in Structural Optimization.- 2.1 Optimization Using Differential Calculus.- 2.2 Optimization Using Variational Calculus.- to the Calculus of Variations.- 2.3 Classical Methods for Constrained Problems.- Method of Lagrange Multipliers.- Function Subjected to an Integral Constraint.- Finite Subsidiary Conditions.- 2.4 Local Constraints and the Minmax Approach.- 2.5 Necessary and Sufficient Conditions for Optimality.- Elastic Structures of Maximum Stiffness.- Optimal Design of Euler-Bernoulli Columns.- Optimum Vibrating Euler-Bernoulli Beams.- 2.6 Use of Series Solutions in Structural Optimization.- 2.7 Exercises.- 2.8 References.- 3. Linear Programming.- 3.1 Limit Analysis and Design of Structures Formulated as LP Problems.- 3.2 Prestressed Concrete Design by Linear Programming.- 3.3 Minimum Weight Design of Statically Determinate Trusses.- 3.4 Graphical Solutions of Simple LP Problems.- 3.5 A Linear Program in a Standard Form.- Basic Solution.- 3.6 The Simplex Method.- Changing the Basis.- Improving the Objective Function.- Generating a Basic Feasible Solution-Use of Artificial Variables.- 3.7 Duality in Linear Programming.- 3.8 An Interior Method-Karmarkar's Algorithm.- Direction of Move.- Transformation of Coordinates.- Move Distance.- 3.9 Integer Linear Programming.- Branch-and-Bound Algorithm.- 3.10 Exercises.- 3.11 References.- 4. Unconstrained Optimization.- 4.1 Minimization of Functions of One Variable.- Zeroth Order Methods.- First Order Methods.- Second Order Method.- Safeguarded Polynomial Interpolation.- 4.2 Minimization of Functions of Several Variables.- Zeroth Order Methods.- First Order Methods.- Second Order Methods.- Applications to Analysis.- 4.3 Specialized Quasi-Newton Methods.- Exploiting Sparsity.- Coercion of Hessians for Suitability with Quasi-Newton Methods.- Making Quasi-Newton Methods Globally Convergent.- 4.4 Probabilistic Search Algorithms.- Simulated Annealing.- Genetic Algorithms.- 4.5 Exercises.- 4.6 References.- 5. Constrained Optimization.- 5.1 The Kuhn-Tucker Conditions.- General Case.- Convex Problems.- 5.2 Quadratic Programming Problems.- 5.3 Computing the Lagrange Multipliers.- 5.4 Sensitivity of Optimum Solution to Problem Parameters.- 5.5 Gradient Projection and Reduced Gradient Methods.- 5.6 The Feasible Directions Method.- 5.7 Penalty Function Methods.- Exterior Penalty Function.- Interior and Extended Interior Penalty Functions.- Unconstrained Minimization with Penalty Functions.- Integer Programming with Penalty Functions.- 5.8 Multiplier Methods.- 5.9 Projected Lagrangian Methods (Sequential Quadratic Prog.).- 5.10 Exercises.- 5.11 References.- 6. Aspects of the Optimization Process in Practice.- 6.1 Generic Approximations.- Local Approximations.- Global and Midrange Approximations.- 6.2 Fast Reanalysis Techniques.- Linear Static Response.- Eigenvalue Problems.- 6.3 Sequential Linear Programming.- 6.4 Sequential Nonlinear Approximate Optimization.- 6.5 Special Problems Associated with Shape Optimization.- 6.6 Optimization Packages.- 6.7 Test Problems.- Ten-Bar Truss.- Twenty-Five-Bar Truss.- Seventy-Two-Bar Truss.- 6.8 Exercises.- 6.9 References.- 7. Sensitivity of Discrete Systems.- 7.1 Finite Difference Approximations.- Accuracy and Step Size Selection.- Iterative Methods.- Effect of Derivative Magnitude on Accuracy.- 7.2 Sensitivity Derivatives of Static Displacement and Stress Constraints.- Analytical First Derivatives.- Second Derivatives.- The Semi-Analytical Method.- Nonlinear Analysis.- Sensitivity of Limit Loads.- 7.3 Sensitivity Calculations for Eigenvalue Problems.- Sensitivity Derivatives of Vibration and Buckling Constraints.- Sensitivity Derivatives for Non-Hermitian Eigenvalue Problems.- Sensitivity Derivatives for Nonlinear Eigenvalue Problems.- 7.4 Sensitivity of Constraints on Transient Response.- Equivalent Constraints.- Derivatives of Constraints.- Linear Structural Dynamics.- 7.5 Exercises.- 7.6 References.- 8. Introduction to Variational Sensitivity Analysis.- 8.1 Linear Static Analysis.- The Direct Method.- The Adjoint Method.- Implementation Notes.- 8.2 Nonlinear Static Analysis and Limit Loads.- Static Analysis.- Limit Loads.- Implementation Notes.- 8.3 Vibration and Buckling.- The Direct Method.- The Adjoint Method.- 8.4 Static Shape Sensitivity.- The Material Derivative.- Domain Parametrization.- The Direct Method.- The Adjoint Method.- 8.5 Exercise.- 8.6 References.- 9. Dual and Optimality Criteria Methods.- 9.1 Intuitive Optimality Criteria Methods.- Fully Stressed Design.- Other Intuitive Methods.- 9.2 Dual Methods.- General Formulation.- Application to Separable Problems.- Discrete Design Variables.- Application with First Order Approximations.- 9.3 Optimality Criteria Methods for a Single Constraint.- The Reciprocal Approximation for a Displacement Constraint.- A Single Displacement Constraint.- Generalization for Other Constraints.- Scaling-based Resizing.- 9.4 Several Constraints.- Reciprocal-Approximation Based Approach.- Scaling-based Approach.- Other Formulations.- 9.5 Exercises.- 9.6 References.- 10. Decomposition and Multilevel Optimization.- 10.1 The Relation between Decomposition and Multilevel Formulation.- 10.2 Decomposition.- 10.3 Coordination and Multilevel Optimization.- 10.4 Penalty and Envelope Function Approaches.- 10.5 Narrow-Tree Multilevel Problems.- Simultaneous Analysis and Design.- Other Applications.- 10.6 Decomposition in Response and Sensitivity Calculations.- 10.7 Exercises.- 10.8 References.- 11.Optimum Design of Laminated Composite Materials.- 11.1 Mechanical Response of a Laminate.- Orthotropic Lamina.- Classical Laminated Plate Theory.- Bending, Extension, and Shear Coupling.- 11.2 Laminate Design.- Design of Laminates for In-plane Response.- Design of Laminates for Flexural Response.- 11.3 Stacking Sequence Design.- Graphical Stacking Sequence Design.- Penalty Function Formulation.- Integer Linear Programming Formulation.- Probabilistic Search Methods.- 11.4 Design Applications.- Stiffened Plate Design.- Aeroelastic Tailoring.- 11.5 Design Uncertainties.- 11.6 Exercises.- 11.7 References.- Name Index.

Shape optimization of elastic bars in torsion

Abstract: The problem of shape optimal design for multiply-connected elastic bars in torsion is formulated and solved numerically. A variational formulation for the equation is presented in a Sobolev space setting and the material derivative idea of Continuum Mechanics is used for the shape design sensitivity analysis. The finite element method is used for a numerical solution of the variational state equation and is integrated into an iterative optimization algorithm. Numerical results are presented for both simply- and doubly-connected bars, with prescribed bounds on admissible location of both inner and outer boundaries.

Shape optimization of elastic hollow bars.

Abstract: In this paper a unified shape optimum design scheme, combining the material derivative and boundary parametrization is presented to find the optimal cross-sectional shapes of elastic hollow bars. Performance criteria can be the bending stiffness, the torsional rigidity, or the weight of the bar. The existence of a keyway (an example of geometric irregularity) can be considered as well. Material property can be either isotropic or anisotropic. Various numerical examples have been provided to show the validity of the presented approach.

Shape optimization approach to numerical solution of the obstacle problem

Abstract: We discuss an algorithm for the numerical solution of the Obstacle Problem in which the coincidence set is considered as the prime unknown. Domain functionals are defined for which the coincidence set serves as the minimizing element. Their gradients are computed (in the sense of the material derivative), and the gradient descent method employed to minimize these functionals. Numerical example is given.

System modelling and optimization : proceedings of the 11th IFIP conference, Copenhagen, Denmark, July 25-29, 1983

Abstract: Modelling and optimization in system planning in China.- Uncertainty algebra. A linear algebraic submodel of probability theory.- Energy models and energy policy problems.- The essentials of hierarchical control.- New developments in econometric commodity market modeling: A model of the world copper market.- The great recession: A crisis in parameters?.- Analysis and modelling of the development economy in the least developed countries.- Macroeconomic equilibrium with rationing and variable working time.- Continuous-time asset-pricing models: Selected results.- The national investment model - "N.I.M.".- A nonlinear econometric model with bounded controls and an entropy objective.- A model of coal transport management in a rail network.- Decomposition of optimal control in energy minimisation in railway traffic.- Optimal urban bus routing with scheduling flexibilities.- Development of demand-responsive strategies for urban traffic control.- An algorithm for Multiple Choice Knapsack Problem.- Aggregation of equalities in integer programming.- On job-shop sheduling with resources constraints.- Space covering technique for multicriterion optimization.- Lexicographical order, inequality systems and optimization.- Stability of generalized equations and Kuhn-Tucker points of perturbed convex programs.- Duality and stability theorems for convex multifunctional programs.- Parametrizing the value functions in dynamic programming.- A smooth sequential penalty function method for solving nonlinear programming problems.- A class of continuously differentiable exact penalty function algorithms for nonlinear programming problems.- On the effectiveness of the Bayesian nonparametric approach to global optimization.- Convergent cutting planes for linear programs with additional reverse convex constraints.- A fast Voronoi-diagram algorithm with applications to geographical optimization problems.- Nonlinear optimization by a curvilinear path strategy.- A unified nonlinear programming theory for penalty, multiplier, SQP and GRG methods.- A linearization algorithm for constrained nonsmooth minimization.- Better than linear convergence and safeguarding in nonsmooth minimization.- On three approaches to the construction of nondifferentiable optimization algorithms.- An algorithm for minimizing nondifferentiable convex functions under linear constraints.- On singular and bang-bang processes in optimal control.- Shape controlability for free boundaries.- Approximation of boundary control problems for evolution variational inequalities arising from free boundary problems.- Optimal control of generalized flow networks.- Hoelder condition for the minimum time function of linear systems.- The quadratic cost problem for L2[0,T L2(?)] boundary input hyperbolic equations.- Modelling and control of water quality in a river section.- A Galerkin approximation for the Zakai equation.- Some singular control problem with long term average criterion.- On Ergodic control problems associated with optimal maintenance and inspection.- Convergence of a stochastic variable metric method with application in adaptive prediction.- Modelization and filtering of discrete systems and discrete approximation of continuous systems.- Extremals in stochastic control theory.- Design wave determination by fast integration technique.- A method to evaluate the consequences of member failure in jacket-type offshore platform structures.- On selecting a target reliability for deep water tension leg platforms.- Frequency versus time domain identification of complex structures modal shapes under natural excitation.- Fatigue of offshore platforms: A method of analysis.- Stochastic design of rubble mound breakwaters.- Probabilistically optimum design of frame structure.- Reliability analysis of elasto-plastic structures.- Threshold crossings in nonlinear systems and ship capsize prevention.- Asymptotic approximations for multinormal domain and surface integrals.- Model uncertainty for bilinear hysteretic systems.- A stochastic algorithm for the optimization of simulation parameters.- Approximations and bounds in discrete stage markov decision processes.- Overall control of an electricity supply and demand system: A global feedback for the french system.- Optimal maintenance policies for modular standby systems.- Probabilistic analysis of some travelling salesman heuristics.- An optimal method for the mixed postman problem.- Modeling and analysis of computer and communications systems with queueing networks: An analytical study.- A hierarchical algorithm for large-scale system optimization problems with duality gaps.- Aggregation bounds in stochastic production problems.- An allocation problem in the design of a class of large-scale systems: Model and algorithm.- An immune lymphocyte circulation model.- Mathematical modeling of infectious diseases: Present state, problems and prospects.- Hyperthermia cancer therapy: Modelling, parameter estimation and control of temperature distribution in human tissue.- Optimal control of the heel-off to lift-off phase of two maximum height jumps.- Theoretical analysis of the sliding filament model for the evaluation of muscle macroscopic performance.- Or is what or does.- On the development of large-scale personnel planning models.- Modeling dynamic systems of variable structure.- Optimal structural design for maximum distance between adjacent eigenfrequencies.- Existence proofs for a class of plate optimization problems.- Short term production scheduling of the pulp mill - A decentralized optimization approach.- Shape optimization for contact problems.- Variational approach to optimal design and sensitivity analysis of elastic structures.- Shape optimal design of a radiating fin.- Application of optimization procedures on the design of various shell structures.- On nondifferentiable plate optimal design problems.- Optimum geometry modeling for minimizing weight of plate bending structure with substructures.- Optimal management of an almost purely hydro system : The ivory coast case.- Discretization of Bellman's equation.- Real-time optimal energy management by mathematical programming in industrial plants.- A computerized-optimized study on film cooling technique (part III).- Optimization of resource allocation for large scale projects.- Experience running optimisation algorithms on parallel processing systems.

Computer aided design of timber space frames

Abstract: This paper illustrates how the sequential linear programming technique has been used to design three-dimensional rigidly jointed timber framed structures in accordance with the British Code of Practice. The objective was to obtain a minimum weight design by varying the member cross-sectional dimensions and the coordinate positions of the joints of the structure employing stress constraints formulated using the Code. To arrive at a design algorithm that yielded practical designs, several features were introduced into the algorithm which included provision for uniformly distributed loading and the grouping of member cross-sectional properties or joint coordinates as single design variables. Example structures are given and the design reviewed with respect to the shape optimization of the structure and the resulting saving in weight.

Shape optimization of three-dimensional folded plate structures

Abstract: The basic features of a previously described shape optimization capability included a general geometric problem description format and adaptive finite element analysis. The finite element mesh for each design step was created from the boundary information only and refined using finite element solution results. At that time, only structures in a single plane could be treated. This work has now been extended to handle structures created from an assembly of segments that may be rotated into any plane as well as to contain the nonplanar surface curvature within any segment. In order to handle these more general problems, it was necessary to introduce a more efficient mesh generation scheme. Several design examples are presented to demonstrate each of the features.

Gradient-projection and policy-iteration methods for solving optimization problems in STEOR networks

Abstract: The problem of optimal time-cost trade-offs in STEOR networks is considered. An optimal control approach is presented where the control variables are the time-dependent execution probabilities of the activities of the underlying project. An optimal controller can be determined by means of a gradient-projection method or a policy-improvement routine.

Chapter 14 Numerical & Biological Shape Optimization

Abstract: This paper describes a shape optimization code which moves the Joints of the structure toward optimal positions and handles the possibility of degeneracy in the underlying linear program. The code is applied to a design problem arising in biology, attempting to analyze the framework of internal fibers in the patella and eventually to predict their pattern of remodeling after fracture. The underlying problems also appear in engineering design applications, involving optimal bounds on the effective properties of composite materials and nonconvex functionals in the calculus of variations.

A numerical method of shape optimization and the coarse line search strategy

Abstract: The present paper analyses some special features of structural shape optimization and the sizing of elements, such as cross-sectional areas of bars and thicknesses of membranes, and points out that the introduction of a coarse line search strategy is necessary in order to maintain the rigour of mathematical programming and preserve the high efficiency of modern structural size optimization algorithms. Making use of the idea of a coarse line search strategy, we supplement sequential linear programming with the adaptive move limit approach and apply it to minimax problems in shape optimization, i.e. problems of minimizing the maximum stress of a plane stress (plane strain) continuum. Encouraging numerical results are obtained.