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.     

Optimization of passive vibration isolators mechanical characteristics

The contribution of optimization has been essential to the more recent developments in design of new mechanical structures and materials. The objective of this work is to apply the models of material and structural optimization to the design of passive vibration isolators. A computational tool to identify the optimal viscoelastic characteristics of a nonlinear one-dimensional isolator was developed. The cost functional involves the minimization of a weighted average of the maximum transient and steady state response amplitudes for a set of predefined dynamic loads. The optimal isolator behaviour is obtained by a simulated annealing method. The solutions obtained are analyzed and discussed concerning their dependence on the applied forces and objective function selection. The results obtained can facilitate the design of elastomeric materials with improved behaviour in terms of dynamic stiffness for passive vibration control.     

Shape optimization of structures under earthquake loadings

The optimum design of structures under static loads is well-known in the design world; however, structural optimization under dynamic loading faces many challenges in real applications. Issues such as the time-dependent behavior of constraints, changing the design space in the time domain, and the cost of sensitivities could be mentioned. Therefore, optimum design under dynamic loadings is a challenging task. In order to perform efficient structural shape optimization under earthquake loadings, the finite element-based approximation method for the transformation of earthquake loading into the equivalent static loads (ESLs) is proposed. The loads calculated using this method are more accurate and reliable than those obtained using the building regulations. The shape optimization of the structures is then carried out using the obtained ESLs. The proposed methodologies are transformed into user-friendly computer code, and their capabilities are demonstrated using numerical examples.     

Optimal topology design of structures under dynamic loads

When elastic structures are subjected to dynamic loads, a propagation problem is considered to predict structural transient response. To achieve better dynamic performance, it is important to establish an optimum structural design method. Previous work focused on minimizing the structural weight subject to dynamic constraints on displacement, stress, frequency, and member size. Even though these methods made it possible to obtain the optimal size and shape of a structure, it is necessary to obtain an optimal topology for a truly optimal design. In this paper, the homogenization design method is utilized to generate the optimal topology for structures and an explicit direct integration scheme is employed to solve the linear transient problems. The optimization problem is formulated to find the best configuration of structures that minimizes the dynamic compliance within a specified time interval. Examples demonstrate that the homogenization design method can be extended to the optimal topology design method of structures under impact loads.Presented at WCSMO-2, held in Zakopane, Poland, 1997     

A prestressed tendon based passive control system for bridges

A new concept for passive control of bridges based on prestressed tendon systems is proposed and studied in this paper. It consists of a two-level prestressing cables system whereas permanent (dead) loads are relieved by the first level prestressing cables and moving loads together with excessive displacements are supported by the second level prestressing system. Advantages of using this system instead of classical active and passive control schemes are discussed. The structural analysis problem with the prestressed tendon controllers is formulated as an optimal control problem for structures governed by variational inequalities. Exact and simplified solution methods are considered. An engineering oriented design method is proposed and demonstrated by means of a numerical example.     

Optimal design of elastic plastic frames accounting for seismic protection devices

The optimal design of elastic perfectly plastic steel frames with or without suitable protection devices and subjected to static as well as seismic loadings is studied. Two minimum volume problem formulations are proposed, on the grounds of the so-called statical approach, accounting for three different resistance limits: the purely elastic limit, the (elastic) shakedown limit and the instantaneous collapse limit. The adopted load combinations are characterized by the presence of fixed loads, of quasi-static perfect cyclic loads and dynamic (seismic) loads. The linear elastic effects of the dynamic actions are studied by utilizing a modal technique. The proposed treatment is referred to the most recent Italian code related to the structural analysis and design. The solution of the optimization problem is reached by using an appropriate linearization iterative technique specialized to the proposed formulations. Flexural frames and cross-braced frames are studied, and the related minimum volume structures are reached for assigned features of the base isolation device. The Bree diagrams of the obtained optimal designs are also determined in order to characterize their structural behaviour.     

Optimization of continuous steel plate girder bridges

The minimization method and structural optimization approach used in the SPGBROD program for the optimization of continuous steel plate girder highway bridges are briefly described. The standard optimal design formulation used in the program in discussed. An expression for the maximum deflection of continuous highway bridges is derived in order to form an appropriate deflection constraint equation. The results of some applications of the SPGBROD program are presented.     

Least-weight design of frameworks under multiple dynamic loads

A computer-based structural design methodology is presented for the least-weight design of planar frameworks subjected to multiple dynamic loads. The method makes use of dynamic finite element analysis, sensitivity analysis, first-order Taylor series approximations and the identification of response extrema to convert the time-parametric design problem into an explicit non-parametric form, which is solved iteratively using a dual optimization routine. The focus of the study is not to develop a general-purpose design capability but, rather, to examine the computational aspects of accounting for multiple dynamic loads in the design process. Two example truss designs under multiple regular sinusoidal wave loadings and multiple irregular earthquake loadings are presented.     

Structural design under bounded uncertainty—Optimization with anti-optimization

In many cases precise probabilistic data are not available on uncertainty in loads, but the magnitude of the uncertainty can be bound. This paper proposes a design approach for structural optimization with uncertain but bounded loads. The problem of identifying critical loads is formulated mathematically as an optimization problem in itself (called anti-optimization), so that the design problem is formulated as a two-level optimization. For linear structural analysis it is shown that the antioptimization part is limited to consideration of the vertices of the load-uncertainty domain. An example of a ten-bar truss is used to demonstrate that we cannot replace the anti-optimization process by considering the largest possible loads.     

Optimization of flexible components of multibody systems via equivalent static loads

An optimization methodology that iteratively links the results of multibody dynamics and structural analysis software to an optimization method is presented to design flexible multibody systems under dynamic loading conditions. In particular, rigid multibody dynamic analysis is utilized to calculate dynamic loads of a multibody system and a structural optimization algorithm using equivalent static loads transformed from the dynamic loads are used to design the flexible components in the multibody dynamic system. The equivalent static loads, which are derived from equations of motion, are used as multiple loading conditions of linear structural optimization. A simple example is solved to verify the proposed methodology and the pelvis part of the biped humanoid, a complex multibody system which consists of many bodies and joints, is redesigned using the proposed methodology.     

Optimal earthquake-resistant design: A reliability-based,global cost approach

This paper presents a methodology for incorporating into the decision-making process of design the explicit consideration of possible future performance of the designed structure in the presence of uncertainty in both loading and structural parameters assumed in the design process. Design is viewed as an optimization problem, taking into account as a merit function terms related to building cost as well as possible future damage. Randomness of loads, load-effects, structural resistances and structural parameters affecting response are considered. In this framework a method suited both to linear as well as nonlinear structural behavior is presented. Approximate expressions of the probabilities of the above random variables as functions of the central moment of their distributions are introduced. Together with a firstorder expansion of the input-output response function characterizing the structural model, this procedure gives computational feasibility for actual design applications. An example is included to clarify the methodology proposed and to illustrate typical features of problem formulation and solution.     

Structural optimization under uncertain loads and nodal locations

This paper presents algorithms for solving structural topology optimization problems with uncertainty in the magnitude and location of the applied loads and with small uncertainty in the location of the structural nodes. The second type of uncertainty would typically arise from fabrication errors where the tolerances for the node locations are small in relation to the length scale of the structural elements. We first review the discrete form of the uncertain loads problem, which has been previously solved using a weighted average of multiple load patterns. With minor modifications, we extend this solution to include loads described by continuous joint probability density functions. We then proceed to the main contribution of this paper: structural optimization under uncertainty in the nodal locations. This optimization problem is computationally difficult because it involves variations of the inverse of the structural stiffness matrix. It is shown, however, that for small uncertainties the problem can be recast into a simpler but equivalent structural optimization problem with equivalent uncertain loads. By expressing these equivalent loads in terms of continuous random variables, we are able to make use of the extended form of the uncertain loads problem presented in the first part of this paper. The optimization algorithms are developed in the context of minimum compliance (maximum stiffness) design. Simple examples are presented. The results demonstrate that load and nodal uncertainties can have dramatic impact on optimal design. For structures containing thin substructures under axial loads, it is shown that these uncertainties (a) are of first-order significance, influencing the linear elastic response quantities, and (b) can affect designs by avoiding unrealistically optimistic and potentially unstable structures. The additional computational cost associated with the uncertainties scales linearly with the number of uncertainties and is insignificant compared to the cost associated with solving the deterministic structural optimization problem.     

A design methodology for structural and control systems of a prosthetic leg

A design methodology is proposed to optimize a prosthetic leg considering the structural and control aspects. Previous studies mainly focused on each of a structural design problem or a control problem. The structural design variables of a prosthetic leg are determined in a structural design problem while the trajectory tracking based on the human gait cycle is found to be a control problem. The two problems have been separately solved. However, they should be simultaneously considered to obtain a better design. Then the problem would be nonlinear dynamic response optimization of structural and control systems. An optimization method was recently developed for a linear system of structural and control design problems using the equivalent static loads (ESLs). In this study, a design methodology for the prosthetic leg is presented by expanding the equivalent static loads method (ESLM) to nonlinear dynamic systems. A simple example is solved to validate the proposed methodology, and then a prosthetic leg is optimized to reduce the weight and energy consumption.     

Multi-objective optimization by genetic algorithm of structural systems subject to random vibrations

This paper deals with a multi-objective optimization criterion for linear viscous-elastic device utilised for decreasing vibrations induced in mechanical and structural systems by random loads. The proposed criterion for the optimum design is the minimization of a vector objective function. The multi-objective optimization is carried out by means of a stochastic approach. The design variables are the device frequency and the damping ratio. As cases of study, two different problems are analysed: the base isolation of a rigid mass and the tuned mass damper positioned on a multi degree of freedom structural system subject to a base acceleration. The non-dominated sorting genetic algorithm in its second version (NSGA-II) is adopted to obtain the Pareto sets and the corresponding optima for different characterizations of the system and input.     

Optimal number of hosts in a distributed system based on cost criteria

Redundant or distributed systems are increasingly used in system design so that the required reliability and availability can be easily achieved. However, such an approach requires additional resources that can be very costly. Hence, how to design and test such a system in the most cost-effective way is of concern to the developers. A general cost model and a solution algorithm are presented for the determination of the optimal number of hosts and optimal system debugging time that minimize the total cost while achieving a certain performance objective. During testing, software faults are corrected and the reliability shows an increasing trend, and hence system reliability increases. A general system model is constructed based on a Markov process with software reliability and availability obtained from software reliability growth models. The optimization problem is formulated based on the cost criteria and the solution procedure is described. An application example is presented.     

Synthesis of elastic structures with controlled forces

An analytical model is presented for synthesis of elastic structural systems under external loads and desired “controlled forces”. In the first stage, the optimal force distribution and the final cross sectional dimensions are chosen, solving an optimization problem with elastic compatibility temporarily excluded. In the second stage, the force due to the external loads is determined for the optimal structure by elastic analysis, and the desired controlled force needed for the optimal cross sections and force distribution is obtained by subtracting the above result from the optimal force of the first stage. The final design which has been determined in the first stage, satisfies both conditions of equilibrium and compatibility. It is a lower-bound solution for a similar incontrolled elastic system. In some cases the first-stage optimization problem may be cast in linear programming form. Numerical examples of continuous beam and indeterminate truss demonstrate application of the proposed method.     

Integrated optimization of the material and structure of composites based on the Heaviside penalization of discrete material model

Based on discrete material optimization and topology optimization technologies, this paper discusses the problem of integrated optimization design of the material and structure of fiber-reinforced composites by considering the characteristics of the discrete variable of fiber ply angle because of the manufacture requirements. An optimization model based on the minimum structural compliance with a specified composite volume constraint is established. The ply angle and the distribution of the composite material are introduced as independent variables in two geometric scales (material and structural scales). The void material is added into the optional discrete material set to realize the topology change of the structure. This paper proposes an improved HPDMO (Heaviside Penalization of Discrete Material Optimization) model to obtain a better convergent result, and an explicit sensitivity analysis is performed. The effects of the HPDMO model on the convergence rate of the optimization results, the objective function value and the iteration history are studied and compared with those from the classical Discrete Material Optimization model and the Continuous Discrete Material Optimization model in this paper. Numerical examples in this paper show that the HPDMO model can effectively achieve the integrated optimization of the fiber ply angle and its distribution in the structural domain, and can also considerably improve the convergence rate of the optimal results compared with other DMO models. This model will help to reduce the manufacture cost of the optimal design.     

Parametric modelling and evolutionary optimization for cost-optimal and low-carbon design of high-rise reinforced concrete buildings

Design optimization of reinforced concrete structures helps reducing the global carbon emissions and the construction cost in buildings. Previous studies mainly targeted at the optimization of individual structural elements in low-rise buildings. High-rise reinforced concrete buildings have complicated structural designs and consume tremendous amounts of resources, but the corresponding optimization techniques were not fully explored in literature. Furthermore, the relationship between the optimization of individual structural elements and the topological arrangement of the entire structure is highly interactive, which calls for new optimization methods. Therefore, this study aims to develop a novel optimization approach for cost-optimal and low-carbon design of high-rise reinforced concrete structures, considering both the structural topology and individual element optimizations. Parametric modelling is applied to define the relationship between individual structural members and the behavior of the entire building structure. A novel evolutionary optimization technique using the genetic algorithm is proposed to optimize concrete building structures, by first establishing the optimal structural topology and then optimizing individual member sizes. In an illustrative example, a high-rise reinforced concrete building is used to examine the proposed optimization approach, which can systematically explore alternative structural designs and identify the optimal solution. It is shown that the carbon emissions and material cost are both reduced by 18–24% after performing optimization. The proposed approach can be extended to optimize other types of buildings (such as steel framework) with a similar problem nature, thereby improving the cost efficiency and environmental sustainability of the built environment.     

基于节能瓶颈诊断的循环冷却水系统节能改造

循环冷却水系统是一种常用的工业辅助系统,具有极大的节能潜力,目前对该系统的节能改造往往具有盲目性.鉴于此,基于节能瓶颈诊断对循环冷却水系统进行节能改造分析和研究,以提高改造针对性和节能效果.根据循环冷却水系统特点对能耗分解方法进行改进,提出多工况能效分解法,将该方法与正交试验分析方法相结合设计一种两维度的系统节能瓶颈诊断方法,对系统节能状态进行分析,确定系统各部分的改造优先级,以改造优先级为基础,结合相应的改造措施形成优化问题以实现改造方案的设计.同时结合项目后评价知识,对各最优方案进行评价,从而为决策者提供更多决策信息.最后通过案例应用验证所提出方法的应用效果.