Additional Design Variables Research Articles

Velocity field level‐set method for topological shape optimization using freely distributed design variables

SummaryThe velocity field level‐set topological shape optimization method combines the implicit representation in the standard level‐set method and the capabilities of general mathematical programming algorithms in handling multiple constraints and additional design variables. The key concept is to construct the normal velocity field using basis functions and the velocity design variables at specified points (referred to as velocity knots) in the entire design domain. In this study, the velocity design variables are decoupled from the level‐set grid points. Making use of this property, we can adaptively change the arrangement of the velocity knots as the structural boundary evolves. This provides more design freedom in the optimization and allows for a significant reduction in the number of design variables. Several numerical examples in two‐ and three‐dimensional design domains are presented to demonstrate the robustness and efficiency of the proposed method. We also show that changing the number of velocity knots may implicitly exert certain control on topological complexity and length scale.

Topology optimization of self-sensing nanocomposite structures with designed boundary conditions

Controlling volume fractions of nanoparticles in a matrix can have a substantial influence on composite performance. This paper presents a topology optimization algorithm that designs nanocomposite structures for objectives pertaining to stiffness and strain sensing. Local effective properties are obtained by controlling local volume fractions of carbon nanotubes (CNTs) in an epoxy matrix, which are assumed to be well dispersed and randomly oriented. The method is applied to the optimization of a plate with a hole structure. Several different allowable CNT volume fraction constraints are examined, and the results show a tradeoff in preferred CNT distributions for the two objectives. It is hypothesized that the electrode location plays an important role in the strain sensing performance, and a surrogate model is developed to incorporate the electrode boundary as a set of additional design variables. It is shown that optimizing the topology and boundary electrode location together leads to further improvements in resistance change.

A velocity field level set method for shape and topology optimization

SummaryIn this paper, we propose a new implementation of the level set shape and topology optimization, the velocity field level set method. Therein, the normal velocity field is constructed with specified basis functions and velocity design variables defined on a given set of points that are independent of the finite element mesh. A general mathematical programming algorithm can be employed to find the optimal normal velocities on the basis of the sensitivity analysis. As compared with conventional level set methods, mapping the variational boundary shape optimization problem into a finite‐dimensional design space and the use of a general optimizer makes it more efficient and straightforward to handle multiple constraints and additional design variables. Moreover, the level set function is updated by the Hamilton‐Jacobi equation using the normal velocity field; thus, the inherent merits of the implicit representation is retained. Therefore, this method combines the merits of both the general mathematical programming and conventional level set methods. Integrated topology optimization of structures with embedded components of designable geometries is considered to show the capability of this method to deal with general design variables. Several numerical examples in 2D or 3D design domains illustrate the robustness and efficiency of the method using different basis functions.

A Study of Shrink-Fitting for Optimal Design of Multi-Layer Composite Tubes Subjected to Internal and External Pressure

This paper addresses the effect of shrink-fitting on the optimal design of pressurized multi-layer composite tubes. Analytical solutions for structural response calculations are provided for axially constrained two- and three-layer shrink-fitted tubes under both internal and external pressure. A recently developed numerical evolutionary optimization algorithm is employed for weight and cost minimization of these assemblies. In order to investigate the effect of shrink-fitting, first, optimal material selection and thickness optimization of tightly fitted tubes, under either internal or both internal and external pressure, are accomplished without shrink-fitting. Next, under the same loading and boundary conditions the assemblies are optimized where shrink-fitting parameters are taken into account for weight and cost minimization. The numerical results obtained for multi-layer composite tubes with and without shrink-fitting indicate that more economical or lightweight assemblies can be obtained if shrink-fitting parameters are treated as additional design variables of the optimization problem. Furthermore, it is observed that considering the shrink-fitting parameters for optimal design becomes more advantageous in the test cases with a higher ratio of internal pressure to external pressure.

Unified topology and joint types optimization of general planar linkage mechanisms

We propose a gradient-based topology optimization method to synthesize a planar linkage mechanism consisting of links and revolute/prismatic joints, which converts an input motion to a desired output motion at its end effector. Earlier gradient-based topology optimization methods were mainly applicable to the synthesis of linkage mechanisms connected by revolute joints only. The proposed method simultaneously determines not only the topology of planar linkage mechanisms but also the required revolute and/or prismatic joint types. For the synthesis, the design domain is discretized into rectangular rigid blocks that are connected to each other by the newly proposed revolute and prismatic joint elements, the joint states of which vary depending on the corresponding design variables. The new concept of joint elements is materialized thorough an elaborately configured set of zero-length springs whose stiffnesses vary as the functions of the design variables. Therefore, any connectivity state among unconnected, rigidly connected, revolute joint, and prismatic joint states can be represented by properly adjusting the stiffnesses. After presenting our modeling, formulation, and sensitivity analysis, the developed method is tested with verification examples. Then the developed method is extended to be able include additional shape design variables and applied to solve a realistic problem of synthesizing a finger rehabilitation robotic device. We expect the developed method to play a critical role in synthesizing a wide class of general linkage mechanisms.

Topology and material orientation optimization based on evolution equations

AbstractMany modern high‐performance materials have inherent anisotropic elastic properties and its local material orientation can be considered to be an additional design variable for the topology optimization [1–3]. We extend our previous model for topology optimization with variational controlled growth [4–6] for linear elastic anisotropic materials, for which the material orientation is introduced as an additional design variable. We solve the optimization problem purely with the principles of thermodynamics by minimizing the Gibbs energy. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling of water quality downgradient of a mulch biowall

AbstractGroundwater treatment biowalls may be located close to a surface water body to prevent contaminant discharge from a groundwater plume into the surface water. Groundwater contaminants passing through the biowall are treated within the biowall or immediately downgradient of the biowall. Biowalls designed and constructed for the treatment of chlorinated solvents typically contain either a solid and/or liquid source of organic carbon to promote contaminant degradation by enhanced anaerobic reductive dechlorination. Common solid organic materials in biowalls include wood mulch or similar waste plant material, and common liquid organic materials are vegetable oil (possibly emulsified) or other long‐chain fatty acids. Such biowalls then develop anaerobic conditions in the constructed biowall volume, and potentially downgradient, as dissolved oxygen originally present in the aquifer is consumed. This groundwater condition can lead to the appearance of sulfide if groundwater influent to the biowall contains moderate to high sulfate concentrations. Other researchers have presented evidence for groundwater conditions downgradient of a biowall or a permeable reactive barrier (PRB) that are altered in relation to groundwater quality, besides the desired effect of contaminant degradation or removal by precipitation. The objective of this work was to investigate with modeling the changes in downgradient groundwater species chemistry as a result of a constructed biowall. This was accomplished with a chemical species model to predict levels of sulfate and sulfide present in groundwater in close downgradient proximity to the biowall. The results indicate that downgradient chemical changes could impact a surface water body to which groundwater discharges. The model described could be enhanced by incorporating additional design variables that should be considered in biowall feasibility assessments.

Optimized growth and reorientation of anisotropic material based on evolution equations

Modern high-performance materials have inherent anisotropic elastic properties. The local material orientation can thus be considered to be an additional design variable for the topology optimization of structures containing such materials. In our previous work, we introduced a variational growth approach to topology optimization for isotropic, linear-elastic materials. We solved the optimization problem purely by application of Hamilton’s principle. In this way, we were able to determine an evolution equation for the spatial distribution of density mass, which can be evaluated in an iterative process within a solitary finite element environment. We now add the local material orientation described by a set of three Euler angles as additional design variables into the three-dimensional model. This leads to three additional evolution equations that can be separately evaluated for each (material) point. Thus, no additional field unknown within the finite element approach is needed, and the evolution of the spatial distribution of density mass and the evolution of the Euler angles can be evaluated simultaneously.

Effect of tacticity-derived topological constraints in bactericidal peptides

Topology is a key element in structure-activity relationship estimation while designing physiologically-active molecular constructs. Peptides may be a preferred choice for therapeutics, principally due to their biocompatibility, low toxicity and predictable metabolism. Peptide design only guarantees functional group constitution by opting specific amino acid sequence, and not their spatial orientation to bind and incite physiological response on chosen targets. This is principally because peptide conformation is subject to external flux, due to the isotactic stereochemistry of the peptide chain. Stereochemical engineering of the peptide main chain offers the possibility of multiplying the structural space of a typical sequence to many orders of magnitude, and limiting the otherwise fluxional non-specific functional group dispensation in space by offering greater conformational rigidity. We put to test, this conceptual possibility already established in theoretical models, by designing amphipathic peptide systems and experimenting with them on Gram-positive, Gram-negative and antibiotic-resistant bacteria. The unusual conformational rigidity and stability of syndiotactic peptides enable them to retain the designed electrostatic environment, while they encounter the membrane surface. All the six designed systems exhibited bactericidal activity, pointing to the utility and specificity of stereo-engineered peptide systems for therapeutic applications. Overall, we hope that this work provides important insights and useful directives in designing novel peptide systems with antimicrobial activity, by expanding the design space, incorporating D-amino acid as an additional design variable.

Reentry Trajectory Optimization for Hypersonic Glide Vehicle with Flexible Initial Conditions

In the reentry trajectory optimization for unpowered hypersonic glide vehicles (HGVs), the initial reentry conditions (IRCs), which are crucial for flight performance, are partly flexible instead of being specified. Aiming at simultaneously determining the optimal IRCs and optimal control policy, a hybrid optimization strategy with an evaluate-during-optimize framework is proposed in this paper. The IRCs are considered as additional independent design variables, and an evaluation process with multiple performance indicators is established to determine the best IRCs. With the analytic hierarchy process (AHP)-based multicriteria decision-making (MCDM) method, a synthesized scalar objective function is set up. Adopting this objective function, feedback information from the evaluation process can be fully included in the optimization process, resulting in a unified optimization framework. The Chebyshev pseudospectral method (CPM) is then introduced as a direct method for solving the resulting trajectory optimization problem. Numerical simulation results for a generic HGV show that the proposed technique is efficient and straightforward. Moreover, this strategy has strong universality for solving optimal control problems with flexible initial conditions.

Multi-objective optimal design of braced frames using hybrid genetic and ant colony optimization

In this article, multi-objective optimization of braced frames is investigated using a novel hybrid algorithm. Initially, the applied evolutionary algorithms, ant colony optimization (ACO) and genetic algorithm (GA) are reviewed, followed by developing the hybrid method. A dynamic hybridization of GA and ACO is proposed as a novel hybrid method which does not appear in the literature for optimal design of steel braced frames. Not only the cross section of the beams, columns and braces are considered to be the design variables, but also the topologies of the braces are taken into account as additional design variables. The hybrid algorithm explores the whole design space for optimum solutions. Weight and maximum displacement of the structure are employed as the objective functions for multi-objective optimal design. Subsequently, using the weighted sum method (WSM), the two objective problem are converted to a single objective optimization problem and the proposed hybrid genetic ant colony algorithm (HGAC) is developed for optimal design. Assuming different combination for weight coefficients, a trade-off between the two objectives are obtained in the numerical example section. To make the final decision easier for designers, related constraint is applied to obtain practical topologies. The achieved results show the capability of HGAC to find optimal topologies and sections for the elements.

Optimal strengthening of concrete plates with unidirectional fiber-reinforcing layers

The problem of the optimal strengthening of concrete plates subjected to transverse loads by unidirectional FRP layers is dealt with. A topology optimization (TO) procedure is proposed to define the layout of the layers that maximizes the elastic stiffness of the reinforced plate for a given maximum amount of reinforcing material. The anisotropy of the layers is taken into account, and local orientations of the fibers are included in the set of design variables. According to the SIMP model for TO problems, the mechanical properties of the reinforcing layers are assumed to depend locally on the densities of the material in the layers, which are additional design variables. Compressive stresses along the fibers are avoided by a suitable penalization technique. The possibility of cracking in the concrete core is also indirectly taken into account. The discretized version of the constrained minimization problem that gives the optimal solution is solved by mathematical programming, using the Method of Moving Asymptotes and the finite element method in its displacement-based formulation. Numerical investigations are presented to discuss the features of the computed optimal layouts, along with the possible application as preliminary design for the structural retrofitting of concrete plates. The reliability of the achieved layouts is also investigated comparing the distribution and orientation of the reinforcing fibers with the yield lines that characterize the collapse mechanisms of the analyzed concrete plates suggested by limit analysis theory. The good performances of the adopted numerical procedure are also pointed out. It follows that the proposed procedure is a robust and computationally effective tool for the preliminary design of the optimal reinforcement of concrete plates in bending.

Robust optimal design of a magnetizer to reduce the harmonic components of cogging torque in a HDD spindle motor

This research proposes a robust optimal design methodology to reduce the cogging torque of a hard disk drive (HDD) spindle motor due to the coil-positioning error of the magnetizer. The design optimization problem of the magnetizer is formulated with an objective function of the cogging torque and the constraints of the torque constant. The coil-positioning errors measured by computerized tomography are considered as the random variables of the robust optimal design problem. Additional design variables of the magnetizer are chosen in the optimization problem, such as back-yoke thickness, notch depth, etc. Magnetic finite element analysis of the HDD spindle motor is also performed to calculate the cogging torque and torque constant. The cogging torque and torque constant of the optimal design are compared with those of the conventional design, demonstrating that the proposed method effectively reduces the cogging toque of the HDD spindle motor.

Size and configuration syntheses of rigid-link mechanisms with multiple rotary actuators using the constraint force design method

This study presents a new synthetic approach for path-generating or function-generating rigid-body mechanisms in the framework of a new hybrid genetic algorithm. In spite of some advantages of synthesis methods in designing rigid-body mechanisms, some inherent issues remain in determining optimal sizes and configurations of rigid links with multiple rotary actuators. To alleviate these difficulties and limitations, we improve our previous contribution, called the constraint force design method, by parameterizing and optimizing the existence of links, the x–y locations of joints modeled by unit masses (particles), and the kind of selection between rigid and string links, using binary, integer, and binary design variables, respectively. This new genotype coding system for GA for the integer and binary phenotypes makes it possible to use a smaller number of unit masses to synthesize manifold configurations of rigid-body mechanisms. In addition, the locations and types of rotary actuators are parameterized with additional integer design variables for the synthesis of realistic rigid-body mechanisms. Furthermore, for efficient optimization of GA, a new h-GA integrated with the Sequential Quadratic Programming (SQP) optimization algorithm is also developed to optimize the locations of joints. To demonstrate the validity of the present constraint force design method, several mechanism synthesis problems are solved.

Passivity-Preserving Parametric Macromodeling for Highly Dynamic Tabulated Data Based on Lur'e Equations

We present a new method for the construction of parametric macromodels for admittance and impedance input- output representations starting from multivariate data samples that depend on frequency and additional design variables such as geometric and material parameters. Poles and residues are parameterized indirectly, while stability and passivity of the parametric macromodel are guaranteed over a user defined range of design parameter values. Pertinent numerical examples validate the proposed parametric macromodeling approach.

Optimization of a composite scarf repair patch under tensile loading

Mechanics of the composite repair under tensile loading with and without overlay plies was examined for nontraditional patch ply orientations. Three-dimensional nonlinear analysis was performed for repair failure prediction and good baseline comparison for open hole scarfed panels and panels repaired by using standard ply-by-ply replacement patch composition was achieved. Multidimensional optimization was performed to calculate the repair patch ply orientations which minimize the von Mises stresses in the adhesive. These optimal stacking sequences achieved significant reduction of the stress levels and resulted in predicted up to 85% and 90% strength restoration for flush and single ply thickness over-ply repair. These results are intended to illustrate additional design variables available for efficient composite repair design, namely the composition of the repair patch.

Flooding Probability-Based Optimal Design of Trapezoidal Open Channel Using Freeboard as a Design Variable

A flooding probability based cost effective design of open channel section has been proposed using freeboard as an additional design variable. The freeboard of the channel is calculated based on the flooding probability value. The proposed model is solved using classical optimization techniques as well as a nondominated sorting genetic algorithm. The results of the model are compared with an earlier reported model to demonstrate its superiority and field applicability.

A Review of an Optimal Design Problem for a Plate of Variable Thickness

We revisit a classic design problem for a plate of variable thickness under the model of Kirchhoff. Our main contribution has two goals. One is to provide a rather general existence result under a main assumption on the structure of the tensor of material constants. The other focuses on providing a minimal number of additional design variables for a relaxation of the problem when that assumption on the tensor of elastic constants does not hold. In both situations, the cost functional can be pretty general.

등제한조건을 이용한 목적함수에 대한 최적민감도

Optimum sensitivity analysis (OSA) is the process to find the sensitivity of optimum solution with respect to the parameter in the optimization problem. The prevalent OSA methods calculate the optimum sensitivity as a post-processing. In this research, a simple technique is proposed to obtain optimum sensitivity as a result of the original optimization problem, provided that the optimum sensitivity of objective function is required. The parameters are considered as additional design variables in the original optimization problem. And then, it is endowed with equality constraints to penalize the additional variables. When the optimization problem is solved, the optimum sensitivity of objective function is simultaneously obtained as Lagrange multiplier. Several mathematical and engineering examples are solved to show the applicability and efficiency of the method compared to other OSA ones.

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

AbstractPhotopolymerizations 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