Optimality Criteria Method Research Articles

인력선 프레임의 병렬화 위상 최적설계

Topology design optimization is a method to determine the optimal distribution of material that yields the minimal compliance of structures, satisfying the constraint of allowable material volume. The method is easy to implement and widely used so that it becomes a powerful design tool in various disciplines. In this paper, a large-scale topology design optimization method is developed using the efficient adjoint sensitivity and optimality criteria methods. Parallel computing technique is required for the efficient topology optimization as well as the precise analysis of large-scale problems. Parallelized finite element analysis consists of the domain decomposition and the boundary communication. The preconditioned conjugate gradient method is employed for the analysis of decomposed sub-domains. The developed parallel computing method in topology optimization is utilized to determine the optimal structural layout of human powered vessel.

Optimization of fiber geometry for fiber reinforced composites considering damage

The present contribution deals with an optimization strategy of fiber reinforced composites. Although the methodical concept is very general we concentrate on Fiber Reinforced Concrete with a complex failure mechanism resulting from material brittleness of both constituents matrix and fibers. Because of these unfavorable characteristics the interface between fiber and matrix plays a particularly important role in the structural response. A prominent objective for this kind of composite is the improvement of ductility. The influential factors on the entire structural response of this composite are (i) material parameters involved in the interface, (ii) the material layout at the small scale level, and (iii) the fiber geometry on the macroscopic structural level. The purpose of the present paper is to improve the structural ductility of the fiber reinforced composites applying an optimization method with respect to the geometrical layout of continuous long textile fibers. The method proposed is achieved by applying a so-called embedded reinforcement formulation. This methodology is extended to a damage formulation in order to represent a realistic structural behavior. For the optimization problem a gradient-based optimization scheme is assumed. An optimality criteria method is applied because of its numerically high efficiency and robustness. The performance of the method is demonstrated by a series of numerical examples; it is verified that the ductility can be substantially improved.

Megapixel Topology Optimization on a Graphics Processing Unit

We show how the computational power and programmability of modern graphics processing units (GPUs) can be used to efficiently solve large-scale pixel-based material distribution problems using a gradient-based optimality criterion method. To illustrate the principle, a so-called topology optimization problem that results in a constrained nonlinear programming problem with over 4 million decision variables is solved on a commodity GPU.

Optimal Material Distribution of a Micro-Gripper Manipulator with Straight-Line Path and Parallel Movements

Abstract Micro electro-mechanical systems (MEMS) are miniaturized devices that consist of both mechanical and electrical parts. Compliant mechanisms have made an enormous contribution in the design process of various fields such as adaptive structures, hand-held tools, components in transportations, electronics and medical tools. The use of compliant mechanisms will help in reducing the number of components, as a result decreasing manufacturing cost and increasing the performance. The topology optimization methods search for an ideal material distribution of a structure. In this investigation, a new two-dimensional micro-grippers compliant mechanism, which can realize a straight-line path and parallel movement arms, are developed. Material models, which parameterize stiffness and density properties, are implemented based on the well-known solid isotropic materials with penalization model. Optimality criteria method is applied as the optimization algorithm using the ANSYS package. The micro-grippers with compliant mechanism can be applied to targets with a diameter of up to 400 μm.

Using artificial reaction force to design compliant mechanism with multiple equality displacement constraints

Monolithic compliant mechanisms are elastic workpieces which transmit force and displacement from an input position to an output position. Continuum topology optimization is suitable to generate the optimized topology, shape and size of such compliant mechanisms. The optimization strategy for a single input single output compliant mechanism under volume constraint is known to be best implemented using an optimality criteria or similar mathematical programming method. In this standard form, the method appears unsuitable for the design of compliant mechanisms which are subject to multiple outputs and multiple constraints. Therefore an optimization model that is subject to multiple design constraints is required. With regard to the design problem of compliant mechanisms subject to multiple equality displacement constraints and an area constraint, we here present a unified sensitivity analysis procedure based on artificial reaction forces, in which the key idea is built upon the Lagrange multiplier method. Because the resultant sensitivity expression obtained by this procedure already compromises the effects of all the equality displacement constraints, a simple optimization method, such as the optimality criteria method, can then be used to implement an area constraint. Mesh adaptation and anisotropic filtering method are used to obtain clearly defined monolithic compliant mechanisms without obvious hinges. Numerical examples in 2D and 3D based on linear small deformation analysis are presented to illustrate the success of the method.

Stiffness Optimization for Wind-Induced Dynamic Serviceability Design of Tall Buildings

Contemporary tall buildings with increasing height and slenderness are highly sensitive to the actions of wind. The structural design of modern tall buildings is generally governed by the need to provide adequate strength and stiffness against dynamic movement induced by strong wind. In addition to the strength-based safety design considerations, the major design effort of a tall building is related to the assessment of the wind-induced serviceability design requirements in terms of lateral drift and motion perception criteria. With tall buildings of today continuing to increase in height, the mitigation of wind-induced vibrations in tall buildings becomes a more critical challenge in the design synthesis process. This paper presents an integrated dynamic analysis and computer-based design optimization method for minimizing the structural cost of tall buildings subject to wind-induced serviceability acceleration design criteria. Once the optimal dynamic serviceability design problem is explicitly formulated, a rigorously derived optimality criteria method is developed for seeking the optimal distribution of element stiffness for a tall building system, satisfying the peak acceleration design constraints. Two full-scale 60-story building examples of mixed steel and concrete construction, with and without complex three-dimensional (3D) mode shapes, are used to illustrate the effectiveness and practical application of the optimal design technique. The results showed that the computer-based optimal design technique provides a powerful tool for wind-induced dynamic serviceability design of tall general buildings with complex 3D mode shapes.

A hybrid genetic algorithm and optimality criteria method for optimum design of RC tall buildings under multi‐load cases

AbstractThis paper proposes a hybrid heuristic and criteria‐based method of optimum design that combines the advantages of both the genetic algorithm (GA) and the rigorously derived optimality criteria (OC) for structural optimum design of reinforced concrete tall buildings under multi‐load cases based on the current Chinese design codes. The entire optimum design procedure is divided into two parts: strength optimum design and stiffness optimum design, which are performed by the GA and the OC method, respectively. The optimum reinforcement detailing, which satisfies the strength, serviceability, ductility and other constraints related to the user‐specified rules and regulations in design codes, is achieved by constructing the data sets containing different available reinforcement bar diameter in a pre‐specified pattern. An adaptive feasible region technique is developed to improve the efficiency of GA. Finally, a practical frame‐shear‐wall structure (30‐storey) is optimized to illustrate the effectiveness and practicality of the proposed optimum design method. Copyright © 2009 John Wiley & Sons, Ltd.

On Hashin–Shtrikman bounds for mixtures of two isotropic materials

In the context of stationary diffusion equation we calculate explicitly the optimal microstructure for the Hashin–Shtrikman energy bound in the case of two isotropic phases with prescribed ratio, in three dimensions. A similar, but more general problem arises in the study of optimal design in conductivity with multiple state equations. Here, the necessary condition of optimality leads to a finite-dimensional optimisation problem which extends the problem of Hashin–Shtrikman bounds, which can be solved explicitly, as well. These calculations have important applications to the optimality criteria method for numerical solution of optimal design problems with multiple state equations. In this iterative algorithm, the presented results enable one to calculate explicitly the update of design variables, similar to the problems with one state equation. Therefore, its implementation is simple, showing nice convergence results on a number of examples, two of them being demonstrated here.

Analysis of Neighborhood Behavior in Lead Optimization and Array Design

Neighborhood behavior describes the extent to which small structural changes defined by a molecular descriptor are likely to lead to small property changes. This study evaluates two methods for the quantification of neighborhood behavior: the optimal diagonal method of Patterson et al. and the optimality criterion method of Horvath and Jeandenans. The methods are evaluated using twelve different types of fingerprint (both 2D and 3D) with screening data derived from several lead optimization projects at GlaxoSmithKline. The principal focus of the work is the design of chemical arrays during lead optimization, and the study hence considers not only biological activity but also important drug properties such as metabolic stability, permeability, and lipophilicity. Evidence is provided to suggest that the optimality criterion method may provide a better quantitative description of neighborhood behavior than the optimal diagonal method.

Comparative Study of Topology Optimization Techniques

This paper presents a comparison between three continuum-based topology optimization methods: the hybrid cellular automaton method, the optimality criteria method, and the method of moving asymptotes. The purpose of the study is to highlight the differences between the three. The optimality criteria method and the method of moving asymptotes are well established in topology optimization. The hybrid cellular automaton method is a recently developed gradient-free technique that combines both local design rules based on the cellular automaton paradigm and the finite element analysis. The closed-loop controllers used in the hybrid cellular automaton method are used to modify the mass distribution in the design domain to find an optimum material layout. The hybrid cellular automaton and optimality criteria methods and the method of moving asymptotes are described and applied in a comparative study to three sample problems. The influence of different algorithm control parameters is shown in this work. The paper demonstrates that, for the sample problems presented, the hybrid cellular automaton method generally required the fewest number of iterations to converge to a solution compared with the optimality criteria method and the method of moving asymptotes. The final topologies generated using the hybrid cellular automaton method typically had the lowest compliance and exhibited the fewest number of intermediate densities at the solution.

Two-material optimal design for nonlinear elastica

The work considers an optimal design problem in the context of nonlinear elastica. More specifically, we deal with finding the best way of mixing fixed amounts of two different elastic materials, so as to minimize the tip deflection of a cantilever beam loaded on its free extreme under the assumption of large deflections. Applying an optimality criteria method to the relaxed problem, simulations give us numerical evidence that the original design problem admits classical solutions (i.e. there is no microstructure) and those are the same as the respective ones for the case of small deflections.

Integrated design optimization of base-isolated concrete buildings under spectrum loading

Base isolation has become a practical control strategy for protecting structures against seismic hazards. Most previous studies on the optimum design of base-isolated structures have been focused on the design optimization of either the base isolation or the superstructure. It is necessary to simultaneously optimize both the base isolation and the superstructure as a whole to seek the most cost-efficient design for such structures. This paper presents an effective numerical optimization technique for the seismic design of base-isolated concrete building structures under spectrum loading. Attempts have been made to automate the integrated spectrum analysis and design optimization procedure and to minimize the total cost of the base-isolated building subject to design performance criteria in terms of the interstory drifts of the superstructure and the lateral displacement of the isolation system. In the optimal design problem formulation, the cost of the superstructure can be expressed in terms of concrete member sizes while assuming all these members to be linearly elastic under earthquake actions. However, the isolation system is assumed to behave nonlinearly, and its cost can be related to the effective horizontal stiffness of each isolator. Using the principle of virtual work, the lateral drift responses of concrete base-isolated buildings can be explicitly formulated and the integrated optimization problem can be solved by the optimality criteria method. The technique is capable of achieving the optimal balance between the costs of the superstructure and the isolation system while the design performance criteria can be simultaneously satisfied. One practical building example with and without base isolation is used to illustrate the effectiveness of the optimal design technique.

538 最適性規準法は最適形状解をもたらすか?(OS17.計算力学と最適化(6),オーガナイズドセッション)

There have been observed unstable numerical processes in some cases of the optimization of the statically indeterminate beams. On the other hand, it is known in the area of optimal structural design that the optimality criteria method can derive the optimum solution efficiently. In this paper, it is examined whether the optimality criterion method can lead us to the optimum solution in some examples.

SIMP-Based Dynamic Topological Optimum depending on Maximum Eigenfrequency for Reinforcement of Concrete Beams

Computer aided topology optimization design is a relatively new but rapidly expanding area of structural mechanics. Topology optimization design is used in an increasing rate by for example building and bridge engineering as well as the car, machine and aerospace industries. The reason for this is that it often achieves great savings and design improvements by solving the basic engineering problem of distributing a limited amount of material in a design space, in which a certain objective function has to be optimized. In static problems a common objective is to minimize the compliance such as strain energy and in dynamic problems the first natural eigenfrequency is often maximized in order to evaluate the stiffest structures. The goal of this study is to get a wide use for structural designs in the topology optimization. Therefore with respect to SIMP dynamic topology optimization problems are treated in comparisons with static problems in this research. For the topology optimization problems implemented algorithms can be the optimality criteria method and the method of moving asymptotes (MMA). Numerical applications topologically maximizing the first natural eigenfrequency or minimizing strain energy of plates verify the generality and wide use of topology optimization with respect to structural designs.

Design of distributed compliant micromechanisms with an implicit free boundary representation

In this paper, a parameterization approach is presented for structural shape and topology optimization of compliant mechanisms using a moving boundary representation. A level set model is developed to implicitly describe the structural boundary by embedding into a scalar function of higher dimension as zero level set. The compactly supported radial basis function of favorable smoothness and accuracy is used to interpolate the level set function. Thus, the temporal and spatial initial value problem is now converted into a time-separable parameterization problem. Accordingly, the more difficult shape and topology optimization of the Hamilton–Jacobi equation is then transferred into a relatively easy size optimization with the expansion coefficients as design variables. The design boundary is therefore advanced by applying the optimality criteria method to iteratively evaluate the size optimization so as to update the level set function in accordance with expansion coefficients of the interpolation. The optimization problem of the compliant mechanism is established by including both the mechanical efficiency as the objective function and the prescribed material usage as the constraint. The design sensitivity analysis is performed by utilizing the shape derivative. It is noted that the present method is not only capable of simultaneously addressing shape fidelity and topology changes with a smooth structural boundary but also able to avoid some of the unfavorable numerical issues such as the Courant–Friedrich–Levy condition, the velocity extension algorithm, and the reinitialization procedure in the conventional level set method. In particular, the present method can generate new holes inside the material domain, which makes the final design less insensitive to the initial guess. The compliant inverter is applied to demonstrate the availability of the present method in the framework of the implicit free boundary representation.

Parameter Identification and Damage Detection Using Structural Optimization and Static Response Data

A new parameter identification method and algorithm will be presented that utilizes structural optimization concepts to correctly identify the stiffness in linear elastic models of civil structures. Displacement measurements resulting from applied static point loads are used as constraints in an optimization algorithm that employs optimality criterion methods to extract the cross sectional properties of elements within a mathematical model of a structure. Through simulated examples the algorithm will correctly identify stiffness parameters in a 10-bar truss structure and a two bay, two story moment frame. Once the parameter identification process has been illustrated in each example, the same algorithm and procedure is used to detect areas of simulated damage. Changes in the cross sectional properties of elements in the mathematical model of the structure are used to locate and quantify damage. Changes in cross section are used to simulate damage such as brittle fracture of steel members, spalling of concrete structures, and decay of wood structures. Lastly, the effects of measurement error on the damage detection results will be explored.

Gradient methods for multiple state optimal design problems

We optimise a distribution of two isotropic materials α I and β I (α < β) occupying the given body in R d . The optimality is described by an integral functional (cost) depending on temperatures u 1, . . . , u m of the body obtained for different source terms f 1, . . . ,f m with homogeneous Dirichlet boundary conditions. The relaxation of this optimal design problem with multiple state equations is needed, introducing the notion of composite materials as fine mixtures of different phases, mathematically described by the homogenisation theory. The necessary conditions of optimality are derived via the Gâteaux derivative of the cost functional. Unfortunately, there could exist points in which necessary conditions of optimality do not give any information on the optimal design. In the case m < d we show that there exists an optimal design which is a rank-m sequential laminate with matrix material α I almost everywhere on Ω. Contrary to the optimality criteria method, which is commonly used for the numerical solution of optimal design problems (although it does not rely on a firm theory of convergence), this result enables us to effectively use classical gradient methods for minimising the cost functional.

New Approaches to Phylogenetic Tree Search and Their Application to Large Numbers of Protein Alignments

Phylogenetic tree estimation plays a critical role in a wide variety of molecular studies, including molecular systematics, phylogenetics, and comparative genomics. Finding the optimal tree relating a set of sequences using score-based (optimality criterion) methods, such as maximum likelihood and maximum parsimony, may require all possible trees to be considered, which is not feasible even for modest numbers of sequences. In practice, trees are estimated using heuristics that represent a trade-off between topological accuracy and speed. I present a series of novel algorithms suitable for score-based phylogenetic tree reconstruction that demonstrably improve the accuracy of tree estimates while maintaining high computational speeds. The heuristics function by allowing the efficient exploration of large numbers of trees through novel hill-climbing and resampling strategies. These heuristics, and other computational approximations, are implemented for maximum likelihood estimation of trees in the program Leaphy, and its performance is compared to other popular phylogenetic programs. Trees are estimated from 4059 different protein alignments using a selection of phylogenetic programs and the likelihoods of the tree estimates are compared. Trees estimated using Leaphy are found to have equal to or better likelihoods than trees estimated using other phylogenetic programs in 4004 (98.6%) families and provide a unique best tree that no other program found in 1102 (27.1%) families. The improvement is particularly marked for larger families (80 to 100 sequences), where Leaphy finds a unique best tree in 81.7% of families.

A level set‐based parameterization method for structural shape and topology optimization

AbstractThis paper presents an effective parametric approach by extending the conventional level set method to structural shape and topology optimization using the compactly supported radial basis functions (RBFs) and the optimality criteria (OC) method. The structural design boundary is first represented implicitly by embedding into a higher‐dimensional level set function as its zero level set, and the RBFs of a favorable smoothness are then applied to interpolate the level set function. The original initial value problem is thus converted to a parametric optimization, with the expansion coefficients of the interplant posed as the design variables.The OC method is then applied to advance the structure boundary in terms of the velocity field derived from the parametric optimization. Hence, the structural shape and topology optimization is now transformed into a process of iteratively finding coefficients to update the level set function to achieve an optimal configuration. The numerical considerations of the conventional level set method, including upwind schemes, velocity extension, and reinitialization, are eliminated. The proposed scheme is capable of addressing structural shape fidelity and topology change simultaneously and of keeping the boundary smooth during the optimization process. Furthermore, numerical convergence is expected to be improved. A widely investigated example, in the framework of structural stiffness designs, is applied to demonstrate the efficiency and accuracy of the proposed approach. Copyright © 2007 John Wiley &amp; Sons, Ltd.

On the equivalence of optimality criterion and sequential approximate optimization methods in the classical topology layout problem

AbstractWe study the ‘classical’ topology optimization problem, in which minimum compliance is sought, subject to linear constraints. Using a dual statement, we propose two separable and strictly convex subproblems for use in sequential approximate optimization (SAO) algorithms.Respectively, the subproblems use reciprocal and exponential intermediate variables in approximating the non‐linear compliance objective function. Any number of linear constraints (or linearly approximated constraints) are provided for. The relationships between the primal variables and the dual variables are found in analytical form.For the special case when only a single linear constraint on volume is present, we note that application of the ever‐popular optimality criterion (OC) method to the topology optimization problem, combined with arbitrary values for the heuristic numerical damping factor η proposed by Bendsøe, results in an updating scheme for the design variables that is identical to the application of a rudimentary dual SAO algorithm, in which the subproblems are based on exponential intermediate variables. What is more, we show that the popular choice for the damping factor η=0.5 is identical to the use of SAO with reciprocal intervening variables.Finally, computational experiments reveal that subproblems based on exponential intervening variables result in improved efficiency and accuracy, when compared to SAO subproblems based on reciprocal intermediate variables (and hence, the heuristic topology OC method hitherto used). This is attributed to the fact that a different exponent is computed for each design variable in the two‐point exponential approximation we have used, using gradient information at the previously visited point. Copyright © 2007 John Wiley &amp; Sons, Ltd.