Design Variables (design + variable)

Distribution by Scientific Domains


Selected Abstracts


Antecedents of flow in online shopping: a test of alternative models

INFORMATION SYSTEMS JOURNAL, Issue 4 2009
Yi Maggie Guo
Abstract Flow is an optimal state of experience that has been studied in various situations, including online environments. In such environments, it has been found to be positively related to exploratory behaviour, revisit and purchase intention, and positive attitude towards web sites. Based on flow theory, this study tests the complete structure of the flow model as it was originally formulated in an online shopping context. The role of the preconditions of flow is elaborated and the effect of web site complexity, an important interface design variable, on flow is examined. Results show that web site complexity affects flow through the mediating effects of the three preconditions of flow. Theoretical and practical implications of this finding are discussed. [source]


A study of thickness optimization of golf club heads to maximize release velocity of balls

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2004
Kenji Nakai
Abstract In the present study, the shape optimization of a golf club head is investigated. The problem of maximizing the release velocity of the ball after impact is treated under the constraint of a specified weight of club head. The thickness distribution of the clubface is chosen as the design variable for optimization. The basis vector method, which is an approximating method for optimization problems in which the sensitivity cannot be derived analytically, is employed. The basis vector represents a fundamental change of shape, and it is preferable to obtaining effective results that the basis vectors be mutually independent. A simple approach to create the basis vectors using eigenmodes is also presented. The theory of impedance matching is confirmed numerically by a two-dimensional example. A three-dimensional example is given to show that this approach is effective for optimal design of the golf club head. Copyright © 2004 John Wiley & Sons, Ltd. [source]


Reducing dimensionality in topology optimization using adaptive design variable fields

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2010
James K. Guest
Abstract Topology optimization methodologies typically use the same discretization for the design variable and analysis meshes. Analysis accuracy and expense are thus directly tied to design dimensionality and optimization expense. This paper proposes leveraging properties of the Heaviside projection method (HPM) to separate the design variable field from the analysis mesh in continuum topology optimization. HPM projects independent design variables onto element space over a prescribed length scale. A single design variable therefore influences several elements, creating a redundancy within the design that can be exploited to reduce the number of independent design variables without significantly restricting the design space. The algorithm begins with sparse design variable fields and adapts these fields as the optimization progresses. The technique is demonstrated on minimum compliance (maximum stiffness) problems solved using continuous optimization and genetic algorithms. For the former, the proposed algorithm typically identifies solutions having objective functions within 1% of those found using full design variable fields. Computational savings are minor to moderate for the minimum compliance formulation with a single constraint, and are substantial for formulations having many local constraints. When using genetic algorithms, solutions are consistently obtained on mesh resolutions that were previously considered intractable. Copyright © 2009 John Wiley & Sons, Ltd. [source]


Directional and band-gap behavior of periodic auxetic lattices

PHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 3 2005
M. Ruzzene
Abstract The paper investigates the wave propagation characteristics of periodic two dimensional, auxetic lattice structures. Periodic structures in general feature unique wave propagation characteristics, whereby waves are allowed to propagate only within specific frequency bands. Two dimensional periodic structures complement this feature with a low frequency directional behavior. The combination of these unique characteristics makes two dimensional periodic structures ideal candidates for the design of pass-band directional mechanical filters. Focus is here placed on honeycomb lattice configurations. A sensitivity analysis is first presented to investigate the influence of band-gap and directional behaviors with respect to changes in the internal angle. The presented results demonstrate how re-entrant topologies feature enhanced wave attenuation capabilities with respect to hexagonal lay-outs. An optimization problem is then formulated by considering the internal angle as a design variable, and the width of the attenuation frequency ranges and angular range of propagation at low frequencies as objective functions. The identified optimal configurations feature combined properties which demonstrate the effectiveness of the analysis procedure. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]


Spatial and temporal evolution of the photo initiation rate for thick polymer systems illuminated on both sides

POLYMER INTERNATIONAL, Issue 10 2005
Nicole Stephenson
Abstract Photopolymerizations of thick systems are inherently non-uniform and much more complex than polymerizations of films and coatings. This contribution presents a mathematical description of the evolution of the photoinitiation rate profile for a thick photopolymerization system illuminated on two sides. Simulation results revealed that when two lamps of equal intensity are used, the spatial and temporal evolution of the photoinitiation rate profile follows a characteristic progression from a bimodal distribution to a unimodal shape with a maximum in the center of the sample. The addition of a second light source can lead to an initiation profile that is more uniform throughout the sample. System variables such as the initiator concentration, molar absorptivity and monomer absorptivity determine how the photoinitiation rate profile evolves. For example, increasing initiator concentration results in sharper initiation fronts which move through the sample more slowly. A reflective boundary condition, a special case of two-sided illumination using only one lamp, was found to enhance the initiation rate and uniformity for some reaction systems. This model provides the fundamental understanding needed to ensure proper selection of reaction components for effective photoinitiation in thick systems, including the possibility of a second light source as an additional design variable. Copyright © 2005 Society of Chemical Industry [source]


Multiobjective Optimization of Concrete Frames by Simulated Annealing

COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 8 2008
Ignacio Paya
The evaluation of solutions follows the Spanish Code for structural concrete. The methodology was applied to a symmetrical building frame with two bays and four floors. This example has 77 design variables. Pareto results of the MOSA algorithm indicate that more practical, more constructable, more sustainable, and safer solutions than the lowest cost solution are available at a cost increment acceptable in practice. Results Ns -SMOSA1 and Ns -SMOSA2 of the cost versus constructability Pareto front are finally recommended because they are especially good in terms of cost, constructability, and environmental impact. Further, the methodology proposed will help structural engineers to enhance their designs of building frames. [source]


Topology Design of Truss Structures in a Multicriteria Environment

COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 4 2001
Won-Sun Ruy
As an analogy of the general design process, this article presents a novel design approach that could generate structural design alternatives having different topologies and then select the optimal structures from them together with simultaneously determining the optimal design variables related to geometry and member size subjected to a multiple objective design environment. For this purpose, a specialized genetic algorithm, called StrGA_DeAl+MOGA, that can handle the design alternatives and multicriteria problems very effectively is developed for the optimal structural design. To validate the developed method, plain-truss design problems are considered as illustrative examples. To begin with, the promising topologies are generated under the name of "design alternatives" with consideration of the given multiobjective environment. Based on the selected topology of truss structures, the sizing or geometric optimization process starts to determine the optimal design parameters. Three-bar and ten-bar truss problems are treated in the article to test the concept and methodology. [source]


A design-variable-based inelastic hysteretic model for beam,column connections

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 4 2008
Gun Jin Yun
Abstract This paper presents a design-variable-based inelastic hysteretic model for beam,column connections. It has been well known that the load-carrying capacity of connections heavily depends on the types and design variables even in the same connection type. Although many hysteretic connection models have been proposed, most of them are dependent on the specific connection type with presumed failure mechanisms. The proposed model can be responsive to variations both in design choices and in loading conditions. The proposed model consists of two modules: physical-principle-based module and neural network (NN)-based module in which information flow from design space to response space is formulated in one complete model. Moreover, owing to robust learning capability of a new NN-based module, the model can also learn complex dynamic evolutions in response space under earthquake loading conditions, such as yielding, post-buckling and tearing, etc. Performance of the proposed model has been demonstrated with synthetic and experimental data of two connection types: extended-end-plate and top- and seat-angle with double-web-angle connection. Furthermore, the design-variable-based model can be customized to any structural component beyond the application to beam,column connections. Copyright © 2007 John Wiley & Sons, Ltd. [source]


Design of multiple tuned mass dampers by using a numerical optimizer

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 2 2005
Nam Hoang
Abstract A new method to design multiple tuned mass dampers (multiple TMDs) for minimizing excessive vibration of structures has been developed using a numerical optimizer. It is a very powerful method by which a large number of design variables can be effectively handled without imposing any restriction before the analysis. Its framework is highly flexible and can be easily extended to general structures with different combinations of loading conditions and target controlled quantities. The method has been used to design multiple TMDs for SDOF structures subjected to wide-band excitation. Some novel results have been obtained. To reduce displacement response of the structure, the optimally designed multiple TMDs have distributed natural frequencies and distinct damping ratios at low damping level. The obtained optimal configuration of TMDs was different from the earlier analytical solutions and was proved to be the most effective. A robustness design of multiple TMDs has also been presented. Robustness is defined as the ability of TMDs to function properly despite the presence of uncertainties in the parameters of the system. Numerical examples of minimizing acceleration structural response have been given where the system parameters are uncertain and are modeled as independent normal variates. It was found that, in case of uncertainties in the structural properties, increasing the TMD damping ratios along with expanding the TMD frequency range make the system more robust. Meanwhile, if TMD parameters themselves are uncertain, it is necessary to design TMDs for higher damping ratios and a narrower frequency range. Copyright © 2004 John Wiley & Sons, Ltd. [source]


Elastic and inelastic drift performance optimization for reinforced concrete buildings under earthquake loads

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 8 2004
Chun-Man Chan
Abstract This paper presents an effective optimization technique for the elastic and inelastic drift performance design of reinforced concrete buildings under response spectrum loading and pushover loading. Attempts have been made to develop an automatic optimal elastic and inelastic drift design of concrete framework structures. The entire optimization procedure can be divided into elastic design optimization and inelastic design optimization. Using the principle of virtual work, the elastic drift response generated by the response spectrum loading and the inelastic drift response produced by the non-linear pushover loading can be explicitly expressed in terms of element sizing design variables. The optimization methodology for the solution of the explicit design problem of buildings is fundamentally based on the Optimality Criteria approach. One ten-story, two-bay building frame example is presented to illustrate the effectiveness and practicality of the proposed optimal design method. While rapid convergence in a few design cycles is found in the elastic optimization process, relatively slow but steady and smooth convergence of the optimal performance-based design is found in the inelastic optimization process. Copyright © 2004 John Wiley & Sons, Ltd. [source]


Community effects of praying mantids: a meta-analysis of the influences of species identity and experimental design

ECOLOGICAL ENTOMOLOGY, Issue 4 2002
William F. Fagan
Abstract ,1. Generalist arthropod predators are ubiquitous in terrestrial ecosystems but experimental studies have yielded little agreement as to their effects on prey assemblages. Drawing on results from a suite of experimental field studies, a meta-analysis was conducted of the impact of praying mantids (Mantodea: Mantidae) on arthropod assemblages in order to identify predictable and unpredictable effects of these extremely generalised predators. 2. Results across different experiments were synthesised using the log response ratio framework, with a focus on quantifying net mantid impacts on arthropod density across taxonomic orders and trophic levels of arthropods, paying special attention to the contribution of mantid species identity and experimental design variables, such as the use of cages, length of experiment, and manipulated mantid density. 3. Calculated on a per mantid-day basis, the net impacts of Tenodera sinensis on arthropod density were generally weaker but more predictable than the effects of Mantis religiosa. Mantids in general had weak negative effects on density for most taxa but exhibited strong negative and positive effects on some taxa. Tenodera sinensis tended to have negative effects on Homoptera, Diptera, and Hemiptera and herbivores as a group, however M. religiosa exhibited greater variation in response of different taxa that appeared to be affected more strongly by experimental design. The effects of Stagmomantis carolina tended to be negative or non-significant. 4. Experimental cages had little influence on either the sign or magnitude of net community impacts for T. sinensis, however cage experiments reversed the sign of the mean effect for two of six taxonomic orders when the experimental predator was M. religiosa. Cages also increased the variability of effect size greatly for M. religiosa but not for T. sinensis. 5. It was concluded that it is possible to use log response ratios to determine general, predictable trends in a well-studied system. Similar meta-analyses of generalist predator effects in other systems should produce predictions of how these predators influence food webs, an important step towards defining more clearly the influences of generalist predators on community structure and dynamics. [source]


Stochastic Cost Optimization of Multistrategy DNAPL Site Remediation

GROUND WATER MONITORING & REMEDIATION, Issue 3 2010
Jack Parker
This paper investigates numerical optimization of dense nonaqueous phase liquid (DNAPL) site remediation design considering effects of prediction and measurement uncertainty. Results are presented for a hypothetical problem involving remediation using thermal source reduction (TSR) and bioremediation with electron donor (ED) injection. Pump-and-treat is utilized as a backup measure if compliance criteria are not met. Remediation system design variables are optimized to minimize expected net present value (ENPV) cost. Adaptive criteria are assumed for real-time control of TSR and ED duration. Source zone dissolved concentration data enabled more reliable and lower cost operation of TSR than soil concentration data, but using both soil and dissolved data improved results sufficiently to more than offset the additional cost. Decisions to terminate remediation and monitoring or to initiate pump-and-treat are complicated by measurement noise. Simultaneous optimization of monitoring frequency, averaging period, and lookback periods to confirm decisions, in addition to remediation design variables, reduced ENPV cost. Results indicate that remediation design under conditions of uncertainty is affected by subtle interactions and tradeoffs between design variables, compliance rules, site characteristics, and uncertainty in model predictions and monitoring data. Optimized designs yielded cost savings of up to approximately 50% compared with a nonoptimized design based on common engineering practices. Significant improvements in accuracy and reductions in cost were achieved by recalibrating the model to data collected during remediation and re-optimizing design variables. Repeating this process periodically is advisable to minimize total costs and maximize reliability. [source]


A note on hinge-free topology design using the special triangulation of design elements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2005
Jae Eun Kim
Abstract Hinges, the unrepeated checkerboard cells, may appear in the topology optimization using low-order finite elements, especially for compliant mechanism design. Existing hinge-controlling methods are based on the rectangular element discretization, so slant or curved boundary lines may not be represented satisfactorily. To avoid hinge formation and to represent curved boundary lines better, we consider a macro-design element method which subdivides the design element into eight triangular finite elements; the finite element calculation is carried out with triangular elements, but the design variables are defined at the nodes defining rectangular macro-design elements. For hinge-free results, different stiffness interpolations are suggested depending on whether the triangular element belongs to a master group or a slave group. The performance of the proposed method was checked with compliant mechanism design problems from the viewpoint of hinge suppression and the possibility of generating slant boundary lines. Copyright © 2005 John Wiley & Sons, Ltd. [source]


A stabilized pseudo-shell approach for surface parametrization in CFD design problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2002
O. Soto
Abstract A surface representation for computational fluid dynamics (CFD) shape design problems is presented. The surface representation is based on the solution of a simplified pseudo-shell problem on the surface to be optimized. A stabilized finite element formulation is used to perform this step. The methodology has the advantage of being completely independent of the CAD representation. Moreover, the user does not have to predefine any set of shape functions to parameterize the surface. The scheme uses a reasonable discretization of the surface to automatically build the shape deformation modes, by using the pseudo-shell approach and the design parameter positions. Almost every point of the surface grid can be chosen as design parameter, which leads to a very rich design space. Most of the design variables are chosen in an automatic way, which makes the scheme easy to use. Furthermore, the surface grid is not distorted through the design cycles which avoids remeshing procedures. An example is presented to demonstrate the proposed methodology. Copyright © 2002 John Wiley & Sons, Ltd. [source]


Topology optimization for stationary fluid,structure interaction problems using a new monolithic formulation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2010
Gil Ho Yoon
Abstract This paper outlines a new procedure for topology optimization in the steady-state fluid,structure interaction (FSI) problem. A review of current topology optimization methods highlights the difficulties in alternating between the two distinct sets of governing equations for fluid and structure dynamics (hereafter, the fluid and structural equations, respectively) and in imposing coupling boundary conditions between the separated fluid and solid domains. To overcome these difficulties, we propose an alternative monolithic procedure employing a unified domain rather than separated domains, which is not computationally efficient. In the proposed analysis procedure, the spatial differential operator of the fluid and structural equations for a deformed configuration is transformed into that for an undeformed configuration with the help of the deformation gradient tensor. For the coupling boundary conditions, the divergence of the pressure and the Darcy damping force are inserted into the solid and fluid equations, respectively. The proposed method is validated in several benchmark analysis problems. Topology optimization in the FSI problem is then made possible by interpolating Young's modulus, the fluid pressure of the modified solid equation, and the inverse permeability from the damping force with respect to the design variables. Copyright © 2009 John Wiley & Sons, Ltd. [source]


A fictitious energy approach for shape optimization

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2010
M. Scherer
Abstract This paper deals with shape optimization of continuous structures. As in early works on shape optimization, coordinates of boundary nodes of the FE-domain are directly chosen as design variables. Convergence problems and problems with jagged shapes are eliminated by a new regularization technique: an artificial inequality constraint added to the optimization problem limits a fictitious total strain energy that measures the shape change of the design with respect to a reference design. The energy constraint defines a feasible design space whose size can be varied by one parameter, the upper energy limit. By construction, the proposed regularization is applicable to a wide range of problems; although in this paper, the application is restricted to linear elastostatic problems. Copyright © 2009 John Wiley & Sons, Ltd. [source]


Sensitivity analyses of FORM-based and DRM-based performance measure approach (PMA) for reliability-based design optimization (RBDO)

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2010
Ikjin Lee
Abstract In gradient-based design optimization, the sensitivities of the constraint with respect to the design variables are required. In reliability-based design optimization (RBDO), the probabilistic constraint is evaluated at the most probable point (MPP), and thus the sensitivities of the probabilistic constraints at MPP are required. This paper presents the rigorous analytic derivation of the sensitivities of the probabilistic constraint at MPP for both first-order reliability method (FORM)-based performance measure approach (PMA) and dimension reduction method (DRM)-based PMA. Numerical examples are used to demonstrate that the analytic sensitivities agree very well with the sensitivities obtained from the finite difference method (FDM). However, as the sensitivity calculation at the true DRM-based MPP requires the second-order derivatives and additional MPP search, the sensitivity derivation at the approximated DRM-based MPP, which does not require the second-order derivatives and additional MPP search to find the DRM-based MPP, is proposed in this paper. A convergence study illustrates that the sensitivity at the approximated DRM-based MPP converges to the sensitivity at the true DRM-based MPP as the design approaches the optimum design. Hence, the sensitivity at the approximated DRM-based MPP is proposed to be used for the DRM-based RBDO to enhance the efficiency of the optimization. Copyright © 2009 John Wiley & Sons, Ltd. [source]


Reducing dimensionality in topology optimization using adaptive design variable fields

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2010
James K. Guest
Abstract Topology optimization methodologies typically use the same discretization for the design variable and analysis meshes. Analysis accuracy and expense are thus directly tied to design dimensionality and optimization expense. This paper proposes leveraging properties of the Heaviside projection method (HPM) to separate the design variable field from the analysis mesh in continuum topology optimization. HPM projects independent design variables onto element space over a prescribed length scale. A single design variable therefore influences several elements, creating a redundancy within the design that can be exploited to reduce the number of independent design variables without significantly restricting the design space. The algorithm begins with sparse design variable fields and adapts these fields as the optimization progresses. The technique is demonstrated on minimum compliance (maximum stiffness) problems solved using continuous optimization and genetic algorithms. For the former, the proposed algorithm typically identifies solutions having objective functions within 1% of those found using full design variable fields. Computational savings are minor to moderate for the minimum compliance formulation with a single constraint, and are substantial for formulations having many local constraints. When using genetic algorithms, solutions are consistently obtained on mesh resolutions that were previously considered intractable. Copyright © 2009 John Wiley & Sons, Ltd. [source]


Integrated layout design of multi-component system

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2009
Jihong Zhu
Abstract A new integrated layout optimization method is proposed here for the design of multi-component systems. By introducing movable components into the design domain, the components layout and the supporting structural topology are optimized simultaneously. The developed design procedure mainly consists of three parts: (i) Introduction of non-overlap constraints between components. The finite circle method (FCM) is used to avoid the components overlaps and also overlaps between components and the design domain boundaries. (ii) Layout optimization of the components and supporting structure. Locations and orientations of the components are assumed as geometrical design variables for the optimal placement while topology design variables of the supporting structure are defined by the density points. Meanwhile, embedded meshing techniques are developed to take into account the finite element mesh change caused by the component movements. (iii) Consistent material interpolation scheme between element stiffness and inertial load. The commonly used solid isotropic material with penalization model is improved to avoid the singularity of localized deformation in the presence of design dependent loading when the element stiffness and the involved inertial load are weakened by the element material removal. Finally, to validate the proposed design procedure, a variety of multi-component system layout design problems are tested and solved on account of inertia loads and gravity center position constraint. Solutions are compared with traditional topology designs without component. Copyright © 2008 John Wiley & Sons, Ltd. [source]


Multiscale multiresolution genetic algorithm with a golden sectioned population composition

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2008
Dae Seung Kim
Abstract A new genetic algorithm (GA) strategy called the multiscale multiresolution GA is proposed for expediting solution convergence by orders of magnitude. The motivation for this development was to apply GAs to a certain class of large optimization problems, which are otherwise nearly impossible to solve. For the algorithm, standard binary design variables are binary wavelet transformed to multiscale design variables. By working with the multiscale variables, evolution can proceed in multiresolution; converged solutions at a low resolution are reused as a part of individuals of the initial population for the next resolution evolution. It is shown that the best solution convergence can be achieved if three initial population groups having different fitness levels are mixed at the golden section ratio. An analogy between cell division and the proposed multiscale multiresolution strategy is made. The specific applications of the developed method are made in topology optimization problems. Copyright © 2007 John Wiley & Sons, Ltd. [source]


Topology optimization by a neighbourhood search method based on efficient sensitivity calculations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2006
K. Svanberg
Abstract This paper deals with topology optimization of discretized load-carrying continuum structures, where the design of the structure is represented by binary design variables indicating material or void in the various finite elements. Efficient exact methods for discrete sensitivity calculations are developed. They utilize the fact that if just one or two binary variables are changed to their opposite binary values then the new stiffness matrix is essentially just a low-rank modification of the old stiffness matrix, even if some nodes in the structure may disappear or re-enter. As an application of these efficient sensitivity calculations, a new neighbourhood search method is presented, implemented, and applied on some test problems, one of them with 6912 nine-node finite elements where the von Mises stress in each non-void element is considered. Copyright © 2006 John Wiley & Sons, Ltd. [source]


Path-generation of articulated mechanisms by shape and topology variations in non-linear truss representation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2005
A. Kawamoto
Abstract This paper presents studies on an optimization-based method for path-generation of articulated mechanisms. An extended truss ground-structure approach is taken in which both the shape and topology of the truss are designed using cross-sectional areas and nodal positions as design variables. This leads to a technique for simultaneous type and dimensional synthesis of articulated mechanisms. For the analysis part it is essential to control the mechanism configuration so that the mechanism remains within a given configuration space, thus stabilizing the optimization process and resulting in realistic solutions. This can be achieved by using the Levenberg,Marquardt method. The design method is illustrated by a number of design cases for both closed and open input and output paths. Copyright © 2005 John Wiley & Sons, Ltd. [source]


A refined semi-analytic design sensitivity based on mode decomposition and Neumann series

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2005
Maenghyo Cho
Abstract Among various sensitivity evaluation techniques, semi-analytical method (SAM) is quite popular since this method is more advantageous than analytical method (AM) and global finite difference method (GFD). However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified for individual elements. Such errors result from the pseudo load vector calculated by differentiation using the finite difference scheme. In the present study, an iterative refined semi-analytical method (IRSAM) combined with mode decomposition technique is proposed to compute reliable semi-analytical design sensitivities. The improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes and the error of SAM caused by numerical difference scheme is alleviated by using a Von Neumann series approximation considering the higher order terms for the sensitivity derivatives. In eigenvalue problems, the tendency of eigenvalue sensitivity is similar to that of displacement sensitivity in static problems. Eigenvector is decomposed into rigid body mode and pure deformation mode. The present iterative SAM guarantees that the eigenvalue and eigenvector sensitivities converge to the reliable values for the wide range of perturbed size of the design variables. Accuracy and reliability of the shape design sensitivities in static problems and eigenvalue problems by the proposed method are assessed through the various numerical examples. Copyright © 2004 John Wiley & Sons, Ltd. [source]


A continuum sensitivity method for finite thermo-inelastic deformations with applications to the design of hot forming processes

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2002
Shankar Ganapathysubramanian
Abstract A computational framework is presented to evaluate the shape as well as non-shape (parameter) sensitivity of finite thermo-inelastic deformations using the continuum sensitivity method (CSM). Weak sensitivity equations are developed for the large thermo-mechanical deformation of hyperelastic thermo-viscoplastic materials that are consistent with the kinematic, constitutive, contact and thermal analyses used in the solution of the direct deformation problem. The sensitivities are defined in a rigorous sense and the sensitivity analysis is performed in an infinite-dimensional continuum framework. The effects of perturbation in the preform, die surface, or other process parameters are carefully considered in the CSM development for the computation of the die temperature sensitivity fields. The direct deformation and sensitivity deformation problems are solved using the finite element method. The results of the continuum sensitivity analysis are validated extensively by a comparison with those obtained by finite difference approximations (i.e. using the solution of a deformation problem with perturbed design variables). The effectiveness of the method is demonstrated with a number of applications in the design optimization of metal forming processes. Copyright © 2002 John Wiley & Sons, Ltd. [source]


An improved weighting method with multibounds formulation and convex programming for multicriteria structural optimization

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2001
W. H. Zhang
Abstract This paper presents an improved weighting method for multicriteria structural optimization. By introducing artificial design variables, here called as multibounds formulation (MBF), we demonstrate mathematically that the weighting combination of criteria can be transformed into a simplified problem with a linear objective function. This is a unified formulation for one criterion and multicriteria problems. Due to the uncoupling of involved criteria after the transformation, the extension and the adaptation of monotonic approximation-based convex programming methods such as the convex linearization (CONLIN) or the method of moving asymptotes (MMA) are made possible to solve multicriteria problems as efficiently as for one criterion problems. In this work, a multicriteria optimization tool is developed by integrating the multibounds formulation with the CONLIN optimizer and the ABAQUS finite element analysis system. Some numerical examples are taken into account to show the efficiency of this approach. Copyright © 2001 John Wiley & Sons, Ltd. [source]


An evolutionary optimization of diffuser shapes based on CFD simulations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2010
S. Ghosh
Abstract An efficient and robust algorithm is presented for the optimum design of plane symmetric diffusers handling incompressible turbulent flow. The indigenously developed algorithm uses the CFD software: Fluent for the hydrodynamic analysis and employs a genetic algorithm (GA) for optimization. For a prescribed inlet velocity and outlet pressure, pressure recovery coefficient C (the objective function) is estimated computationally for various design options. The CFD software and the GA have been combined in a monolithic platform for a fully automated operation using some special control commands. Based on the developed algorithm, an extensive exercise has been made to optimize the diffuser shape. Different methodologies have been adopted to create a large number of design options. Interestingly, not much difference has been noted in the optimum C values obtained through different approaches. However, in all the approaches, a better design has been obtained through a proper selection of the number of design variables. Finally, the effect of diffuser length on the optimum shape has also been studied. Copyright © 2009 John Wiley & Sons, Ltd. [source]


Optimal airfoil shapes for low Reynolds number flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2009
D. N. Srinath
Abstract Flow over NACA 0012 airfoil is studied at , = 4, and 12, for Re,500. It is seen that the flow is very sensitive to Re. A continuous adjoint based method is formulated and implemented for the design of airfoils at low Reynolds numbers. The airfoil shape is parametrized with a non-uniform rational B-splines (NURBS). Optimization studies are carried out using different objective functions namely: (1) minimize drag, (2) maximize lift, (3) maximize lift to drag ratio, (4) minimize drag and maximize lift and (5) minimize drag at constant lift. The effect of Reynolds number and definition of the objective function on the optimization process is investigated. Very interesting shapes are discovered at low Re. It is found that, for the range of Re studied, none of the objective functions considered show a clear preference with respect to the maximum lift that can be achieved. The five objective functions result in fairly diverse geometries. With the addition of an inverse constraint on the volume of the airfoil the range of optimal shapes, produced by different objective functions, is smaller. The non-monotonic behavior of the objective functions with respect to the design variables is demonstrated. The effect of the number of design parameters on the optimal shapes is studied. As expected, richer design space leads to geometries with better aerodynamic properties. This study demonstrates the need to consider several objective functions to achieve an optimal design when an algorithm that seeks local optima is used. Copyright © 2008 John Wiley & Sons, Ltd. [source]


CFD-based optimization of aerofoils using radial basis functions for domain element parameterization and mesh deformation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2008
A. M. Morris
Abstract A novel domain element shape parameterization method is presented for computational fluid dynamics-based shape optimization. The method is to achieve two aims: (1) provide a generic ,wrap-around' optimization tool that is independent of both flow solver and grid generation package and (2) provide a method that allows high-fidelity aerodynamic optimization of two- and three-dimensional bodies with a low number of design variables. The parameterization technique uses radial basis functions to transfer domain element movements into deformations of the design surface and corresponding aerodynamic mesh, thus allowing total independence from the grid generation package (structured or unstructured). Independence from the flow solver (either inviscid, viscous, aeroelastic) is achieved by obtaining sensitivity information for an advanced gradient-based optimizer (feasible sequential quadratic programming) by finite-differences. Results are presented for two-dimensional aerofoil inverse design and drag optimization problems. Inverse design results demonstrate that a large proportion of the design space is feasible with a relatively low number of design variables using the domain element parameterization. Heavily constrained (in lift, volume, and moment) two-dimensional aerofoil drag optimization has shown that significant improvements over existing designs can be achieved using this method, through the use of various objective functions. Copyright © 2008 John Wiley & Sons, Ltd. [source]


Application of second-order adjoint technique for conduit flow problem

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2007
T. Kurahashi
Abstract This paper presents the way to obtain the Newton gradient by using a traction given by the perturbation for the Lagrange multiplier. Conventionally, the second-order adjoint model using the Hessian/vector products expressed by the product of the Hessian matrix and the perturbation of the design variables has been researched (Comput. Optim. Appl. 1995; 4:241,262). However, in case that the boundary value would like to be obtained, this model cannot be applied directly. Therefore, the conventional second-order adjoint technique is extended to the boundary value determination problem and the second-order adjoint technique is applied to the conduit flow problem in this paper. As the minimization technique, the Newton-based method is employed. The Broyden,Fletcher,Goldfarb,Shanno (BFGS) method is applied to calculate the Hessian matrix which is used in the Newton-based method and a traction given by the perturbation for the Lagrange multiplier is used in the BFGS method. Copyright © 2007 John Wiley & Sons, Ltd. [source]


The harmonic adjoint approach to unsteady turbomachinery design

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3-4 2002
M. C. Duta
Abstract In recent years, there has been rapid progress in aerodynamic optimization methods which use adjoint flow analysis to efficiently calculate the sensitivity of steady-state objective functions to changes in the underlying design variables. This paper shows that the same adjoint approach can be used in turbomachinery applications in which the primary concern is blade vibration due to harmonic flow unsteadiness. The paper introduces the key engineering concepts and discusses the derivation of the adjoint analysis at the algebraic level. The emphasis is on the algorithmic aspects of the analysis, on the iterative solution method and on the role played by the strong solid wall boundary condition, in particular. The novel ideas are exploited to reveal the potential of the approach in the minimization of the unsteady vibration of turbomachinery blades due to incident wakes. Copyright © 2002 John Wiley & Sons, Ltd. [source]