A practical fractional numerical optimization method for designing economically and environmentally friendly super-tall buildings

Due to the complexity of super tall buildings, many well-known optimization algorithms are not well applicable. Using structural lateral system of super tall buildings as engineering background, the paper developed a practical fractional numerical optimization method (FNOM), which applies fractional strategy and quasi-constant assumption, to reduce material cost and embodied carbon cost by searching the optimal structural dimensions. Firstly, two kinds of relationships among optimization variables (structural dimensions), driven design constraints (the interstory drift and the natural period) and optimization objective (cost including material cost and embodied carbon cost) are mathematically modelled. Genetic algorithm (GA) is then introduced to search the optimal structural dimensions based on the quasi-constant assumption of virtual work and internal work of the inactive components. Thirdly, fractional strategy is applied to create assemblies composed of different structural component sets, and the assemblies are then to be optimized in proper sequences. Fourthly, FNOM is implemented as a user-friendly software called C-FNO to practically support the preliminary design of super-tall buildings. Finally, a 700 m high super-tall building is employed to illustrate FNOM by using C-FNO, and the results show that only three design constraints of the interstory drift, the natural period and the stress ratio need to be solved during each optimization step. Belt truss, mega column, outrigger truss and shear wall of the super tall building should be optimized in sequence to save more cost. A great amount of cost can be still saved for the super tall building with the normal traditional design.     

Integrated process for structural–topological configuration design of weight-reduced vehicle components

Due to the speedy development trends of design stages, the material distributions and geometric configurations in view of the weight-reduction design of structures are the details taken into account from the stage of conceptual design with low cost, high performance and quality. In this point, a structural–topological configuration with a feasible design of structure is important. This paper presents the integrated process using three optimization techniques, in which the geometric boundaries and physical dimensions of the structure and material distribution of structure-configured elements are hierarchically optimized in the specifications of the maximum rigidity, plastic strain, residual deformations and lightweight.     

Increasing the scanning range of Lamb wave based SHM systems by optimizing the sensor design and excitation frequency

The objective of the paper is to investigate and to optimize parameters which effect the excitation of Lamb waves generated by adhesively bonded piezoceramic actuators. Particularly, the influence of the adhesive layer and the resonances of the actuator are examined both numerically and experimentally. Understanding these properties helps to develop energy efficient structural health monitoring (SHM) systems, meaning that less energy is needed to excite waves with the same scanning range. Knowing the main influence parameters a numerical optimization is proposed, which is aimed at increasing the range of the excited waves by optimizing the sensor geometry and the excitation frequency. Various tests with different test specimens have been performed. An evolutionary based algorithm is used to find the optimal configuration. It has been found that small changes in the geometry and an optimized excitation frequency elevate the amplitudes of the signal measured with a piezoelectric transducer significantly. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Coherence of Structural Optimization and Configurational Mechanics

This contribution is concerned with the similarities of structural optimization and configurational mechanics. In structural optimization sensitivity analysis is used to obtain the sensitivity of continuum mechanical functions with respect to variations of the material body, i.e. the reference configuration. In the same manner in configurational mechanics we are interested in changes of the material body, e.g. crack propagation or phase transition problems. Consequently, variational design sensitivity analysis and the numerical techniques from structural optimization are applicable to problems fromconfigurational mechanics. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variational sensitivity analysis and changes in the material configuration

This contribution is concerned with some aspects of variational design sensitivity analysis in the physical and material configuration. Sensitivity analysis is a branch of structural optimization, e.g. shape or topology optimization. In these disciplines we consider variations of the material configuration and we are interested in the change of the state variables and the objective functional due to these variations. In the context of structural optimization this is termed as design sensitivity analysis. The sensitivities are required in order to solve the corresponding Lagrangian equation within standard nonlinear programming algorithms. In many engineering applications, the energy functional of the problem is used as the objective functional. In this paper, we consider variations of the energy with respect to the state and the design and we investigate sensitivity relations for the physical and material problem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multipoint Aerodynamical Shape Optimization of Flying Configurations with Spanwise Movable Leading Edge Flaps,in Supersonic Flow

The multipoint aerodynamical shape optimization of a flying configuration (FC) is realized by morphing. Spanwise movable leading edge flaps are used. It leads to two enlarged variational problems, with free boundaries. The own developed iterative optimum-optimorum theory, which searches the global optimized shape inside an elitary class of flying configurations (FCs) and new hybrid solutions for the compressible full Navier-Stokes PDEs, are used. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On two different inverse form finding methods for hyperelastic and elastoplastic materials

This contribution focuses on two different developments of mechanical-computational methods for the optimal determination of the initial shape of formed functional components knowing the deformed configuration, the applied loads and the boundary conditions. The first method uses an inverse mechanical formulation and can be applied to materials with hyperelastic behaviors. For materials with elastoplastic properties this method is not advocated, without knowing the final plastic strains, due to the non uniqueness of the solution. The second method uses a shape optimization formulation in the sense of an inverse problem via successive iterations of the direct problem. For hyperelastic materials the inverse mechanical formulation is preferred for its velocity and the non exhibition of possible mesh distortions. In the shape optimization formulation mesh distortions can be avoided by an update of the reference configuration of the functional part. Both methods are using a formulation in the logarithmic strain space. A numerical example for materials with isotropic elastoplastic behaviors illustrates the shape optimization formulation. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Incorporation of delivery times in stereotactic radiosurgery treatment optimization

Although the use of mathematical optimization techniques can greatly improve the quality of treatment plans in various radiation therapy treatment settings, one complication is the potentially clinically unrealistic nature of optimized treatments. The difficulty arises from two factors: (1) machine limitations that govern the minimum amount of radiation delivery time, and (2) long treatment times due to the complexity of optimized treatments. In the first scenario, if a particular configuration of the radiation delivery device is used, then it typically must deliver radiation for a minimum length of time. Incorporation of such requirements in a mathematical model generally requires additional constraints and binary variables, increasing the difficulty of the optimization. In the second scenario, mathematically optimized treatments commonly assign (small amounts of) radiation to be delivered from many configurations, drastically increasing the time needed to deliver the treatment (beam-on time). We examine these two issues within the penalty-based sector duration optimization model for Leksell Gamma Knife\(^{\textregistered }\) Perfexion\(^{\mathrm{TM}}\) (Elekta, Stockholm, Sweden) and the combined sector duration and isocentre optimization model to reduce beam-on time and to ensure that machine limitations regarding delivery times are met.     

On the multi-component layout design with inertial force

The purpose of this paper is to introduce inertial forces into the proposed integrated layout optimization method designing the multi-component systems. Considering a complex packing system for which several components will be placed in a container of specific shape, the aim of the design procedure is to find the optimal location and orientation of each component, as well as the configuration of the structure that supports and interconnects the components. On the one hand, the Finite-circle Method (FCM) is used to avoid the components overlaps, and also overlaps between components and the design domain boundaries. One the other hand, the optimal material layout of the supporting structure in the design domain is designed by topology optimization. A consistent material interpolation scheme between element stiffness and inertial load is presented to avoid the singularity of localized deformation due to the presence of design dependent inertial loading when the element stiffness and the involved inertial load are weakened with the element material removal. The tested numerical example shows the proposed methods extend the actual concept of topology optimization and are efficient to generate reasonable design patterns.     

Minimizing the Mean Damage for Parallel-Series Systems with Two Failure Modes

We address a non-convex optimization problem involving the minimization of the difference between two symmetric functions which are log convex. Specifically we are interested in minimizing the mean system damage of a parallel-series system composed of a maximal number of identical units, each capable of failing in one of two ways.We characterize the solution of the problem, and develop an algorithm to solve large scale versions of it.Numerical results are presented. It is shown that an optimal configuration with n available components may not use all n components.     

Topology optimization of space vehicle structures considering attitude control effort

The topology optimization of load-bearing structural components for reducing attitude control efforts of miniature space vehicles is investigated. Based on the derivation of the cold gas consumption rate of three-axis stabilization actuators, it is pointed out that the attitude control efforts associated with cold gas micro thrusters are closely related to the mass moment inertia of the system. Therefore, the need to restrict the mass moments of inertia of the structural components is highlighted in the design of the load-bearing structural components when the attitude control performance is concerned. The optimal layout design of the space vehicle structure considering attitude control effort is, thus, reformulated as a topology optimization problem for minimum compliance under constraints on mass moments of inertia. Numerical techniques for the optimization problem are discussed. For the case of a single constraint on the mass moment of inertia about a given axis, a design variable updating scheme based on the Karush–Kuhn–Tucker optimality criteria is used to solve the minimization problem. For the problem with multiple constraints, mathematical programming approach is employed to seek the optimum. Numerical examples will be given to demonstrate the validity and applicability of the present problem statement.     

Joint optimization of product family configuration and scaling design by Stackelberg game

Product family design is generally characterized by two types of approaches: module-based and scale-based. While the former aims to enable product variety based on module configuration, the latter is to variegate product design by scaling up or down certain design parameters. The prevailing practice is to treat module configuration and scaling design as separate decisions or aggregate two design problems as a single-level, all-in-one optimization problem. In practice, optimization of scaling variables is always enacted within a specific modular platform; and meanwhile an optimal module configuration depends on how design parameters are to be scaled. The key challenge is how to deal with explicitly the coupling of these two design optimization problems.     

Optimization of the static and dynamic characteristics of plates with isogrid stiffeners

In this paper, the orientation angles of stiffeners arranged in the form of isogrid configuration over a flat plate are selected to optimize the static and dynamic characteristics of these plates/stiffeners assemblies. The static characteristics are optimized by maximizing the critical buckling loads of the isogrid plate, while the dynamic characteristics are optimized by maximizing multiple natural frequencies of the stiffened plate.

A finite element model is developed to describe the statics and dynamics of Mindlin plates which are stiffened with arbitrarily oriented stiffeners. The model is used as a basis for optimizing separately or simultaneously the critical buckling loads and natural frequencies of the plates per unit volume of the plates/stiffeners assemblies.

Numerical examples are presented to demonstrate the utility of the developed model and optimization procedures. The presented approach can be invaluable in the design of plates with isogrid stiffeners for various vibration and noise control applications.     

Sobre la necesidad de controlar el error de discretización de elementos finitos en optimización de forma estructural con algoritmos evolutivos

This work analyzes the influence of the discretization error contained in the Finite Element (FE) analyses of each design configuration proposed by the structural shape optimization algorithms over the behavior of the algorithm. The paper clearly shows that if FE analyses are not accurate enough, the final solution provided by the optimization algorithm will neither be optimal nor satisfy the constraints. The need for the use of adaptive FE analysis techniques in shape optimum design will be shown. The paper proposes the combination of two strategies to reduce the computational cost related to the use of mesh adaptivity in evolutionary optimization algorithms: (a) the use of the algorithm described by Bugeda et al. [1] which reduces the computational cost associated to the adaptive FE analysis of each geometrical configuration and, (b) the successive increase of the required accuracy of the FE analyses in order to obtain a considerable reduction of the computational cost in the early stages of the optimization process.     

Mathematical modelling for optimized control of Moscow's sewer network

An algorithm for the optimized control of a branching urban head-and-gravity sewer network is proposed. The control consists in redistribution of the sewage flows between the network structural components. The algorithm is based on a mathematical model and presupposes the use of a computer. The mathematical model consists of a set of algebraic equations with the structure transporting capacities captured as constraints. The mathematical task of control is stated and solved as an optimization problem. The objective function is the minimization of total electric energy consumption over all the network pumping stations. The assumptions substantiated by practice would reduce the problem to the known problem of linear programming. The discharge through each pumping station of the considered subnetwork of Moscow's sewer network was computed using a mathematical model and was compared to the value observed under the same actual conditions. From this comparison, it was concluded that the proposed algorithm was more successful in controlling the network than was the traditional operation. The correction of the working conditions of some pumping stations of the Moscow sewer subnetwork in accordance with the precalculated time schedule, has allowed a significant decrease in the electric energy consumption for conveyance of the sewage through the network.     

Structural macroscopic theory of stiff and soft composites. Invariant description

A structural macroscopic theory of stiff and soft composites, which generalizes the theory in [1] constructed with application of a model of one-dimensional stressed state of reinforcing fibers in the current configuration of a composite is presented. The theory combines the micro- and macromechanics of composite materials. The two trends in the mechanics of composites are based on the idea of a field of macroscopic displacements and the concept of macroscopic stresses of the composite material when changes in the metrics of the matrix and reinforcing fibers in the current state of a composite medium are taken into consideration. The fibers of the reinforcing systems and matrix are analyzed on the basis of a general 3D model of deformation. No limits on the stiffness of the materials of the structural components are imposed. The analysis of the composite medium, on the macromechanical level, includes a definition of macrodisplacement and macrodeformation fields, as well as parametric structural fields in the current configuration. On the micromechanical level, the fields of macroscopic stresses in the medium, together with the fields of microscopic strains and stresses in the structural components, are defined on the basis of information obtained from the analysis of the field of the macroscopic displacements. With the corresponding interpretation of the field of macroscopic displacements, the structural macroscopic theory is applied to composite media with fibrous, laminated, and matrix structures.     

Manufacturing constraints in parameter–free shape optimization

Structural shape optimization has become an important tool for engineers when it comes to improving components with respect to a given goal function. During this process the designer has to ensure that the optimized part stays manufacturable. Depending on the manufacturing process several requirements could be relevant such as demolding or different kinds of symmetry. This work introduces two approaches on how to handle manufacturing constraints in parameter-free shape optimization. In the so–called explicit approach equality and inequality equations are formulated using the coordinates of the FE-nodes. These equations can be used to extend the optimization problem. Since the number of the additional constraint equations may be very large we apply aggregation formulations, e.g. the Kreisselmeier-Steinhauser function, if necessary. In the second approach, the so–called implicit method, the set of design nodes is split in two groups called optimization nodes and dependent nodes. The optimization nodes are now handled as design nodes but the dependent nodes are coupled to the optimization nodes in such a way that the manufacturing constraint is fulfilled. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bat algorithm for optimization of reinforced concrete columns

In structural mechanics, when the design contains two different materials with opposite mechanical behaviours and costs, the optimum design cannot exactly found. In that case, numerical optimization algorithms are a good source. Reinforced concrete design shows that behaviour since concrete is a cheap material comparing to steel while the tensile strength of concrete is very low to use. The cross sections are effective on the stresses and balance of tensile and compressive forces. This situation shows the importance of the dimension optimization of reinforced concrete members. Also, the number and size of the reinforcements need an optimization. The place of the reinforcements is effective on the place of tensile forces in the calculation of axial force and flexural moment capacity. In this paper, reinforced concrete columns are optimized for the cost minimization by employing a bio-inspired metaheuristic algorithm called bat algorithm. The idealization of the echolocation behaviour of bats is the inspiration of the bat algorithm. Differently from the algorithms, the bat algorithm uses global and local optimization with a changeable probability. The optimization process considers the security measures and slenderness of the according to the design regulation called ACI 318. The slenderness is taken into consideration by using a magnified design flexural moment, which is factored by a value defined according to the buckling load and axial load of columns. The proposed approach is applied for different numerical cases and the results are compared with the approach using harmony search algorithm. The present approach is effective for the optimization problem. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Extremum theorems for large displacement analysis of discrete elastoplastic structures with piecewise linear yield surfaces

Discrete or discretized structures are considered in the range of large displacements. Elastic plastic behavior is assumed, under the hypothesis that both yield functions and hardening rules are piecewise linear. The structural response to a single finite loading step is assumed to involve regularly progressive yielding (no local unloading). An extremum property of this structural response is established, by recognizing that the relations governing the configuration change coincide with the Kuhn-Tucker conditions of a particular nonlinear constrained optimization problem, subject to sign constraints alone. This extremum property can be regarded as an extension of the theorem of minimum potential energy. Other properties, even if computationally less attractive, broaden the theory developed, so that some results previously obtained are derived as special cases.     

Systematic occurrence of repeated eigenvalues in structural optimization

Examples of finite-dimensional structural design problems with constraints on natural frequency and buckling are used to demonstrate that repeated eigenvalues may be expected to occur when a structure is optimized. It is shown that a repeated eigenvalue is not generally differentiable with respect to design variables. Directional derivatives are shown to exist, and a method of calculating directional derivatives is given. Necessary conditions of optimality are derived and applied to a vibration optimization problem. Extensions of the theory to distributed-parameter structures and numerical methods are outlined.This research was supported by NSF Grant No. CMS-80-05677