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Structural and Multidisciplinary Optimization

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ISSN (Print) 1615-1488 - ISSN (Online) 1615-147X
Published by Springer-Verlag

[2216 journals]

Exploring or reducing noise?
- Abstract: Abstract We consider the problem of the global minimization of a function observed with noise. This problem occurs for example when the objective function is estimated through stochastic simulations. We propose an original method for iteratively partitioning the search domain when this area is a finite union of simplexes. On each subdomain of the partition, we compute an indicator measuring if the subdomain is likely or not to contain a global minimizer. Next areas to be explored are chosen in accordance with this indicator. Confidence sets for minimizers are given. Numerical applications show empirical convergence results, and illustrate the compromise to be made between the global exploration of the search domain and the focalization around potential minimizers of the problem.
  PubDate: 2013-06-01
Shape optimization of structures under earthquake loadings
- Abstract: Abstract 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.
  PubDate: 2013-06-01
Application of gradient-based optimization methods for a rotor system with static stress, natural frequency,and harmonic response constraints
- Abstract: Abstract This paper demonstrates the application of gradient-based optimization methods to the minimal weight design optimization of rotor systems. A nonlinear constrained optimization problem is considered. Design variables are inner radii and wall thicknesses of shaft sections. Constraints are imposed on torsional and equivalent stresses, natural frequencies, and unbalance response amplitudes. The sizing optimization problem is solved using a gradient projection method and a sequential quadratic programming technique. A typical turbine rotor system is considered. An in-house beam-based finite element method code is used for the prediction of static and dynamic characteristics of the rotor system. Analytical sensitivity analysis is performed for the static and harmonic equations using the adjoint method. Sensitivity coefficients for the natural frequencies are obtained directly from the quadratic eigenvalue problem. Results of several optimization runs with different constraint sets show a significant shaft weight reduction in comparison with the baseline configuration with all constraints being satisfied. The two optimization methods are compared and discussed in regard to their performance.
  PubDate: 2013-06-01
Performance of an ensemble of ordinary, universal, non-stationary and limit Kriging predictors
- Abstract: Abstract The selection of stationary or non-stationary Kriging to create a surrogate model of a black box function requires apriori knowledge of the nature of response of the function as these techniques are better at representing some types of responses than others. While an adaptive technique has been previously proposed to adjust the level of stationarity within the surrogate model such a model can be prohibitively expensive to construct for high dimensional problems. An alternative approach is to employ a surrogate model constructed from an ensemble of stationary and non-stationary Kriging models. The following paper assesses the accuracy and optimization performance of such a modelling strategy using a number of analytical functions and engineering design problems.
  PubDate: 2013-06-01
An optimal shifting vector approach for efficient probabilistic design
- Abstract: Abstract The application of reliability-based design optimization (RBDO) is hindered by the unbearable computational cost in the structure reliability evaluating process. This study proposes an optimal shifting vector (OSV) approach to enhance the efficiency of RBDO. In OSV, the idea of using an optimal shifting vector in the decoupled method and the notation of conducting reliability analysis in the super-sphere design space are proposed. The shifted limit state function, instead of the specific performance function, is used to identify the inverse most probable point (IMPP) and derive the optimal shifting vector for accelerating the optimization process. The super-sphere design space is applied to reduce the number of constraints and design variables for the novel reliability analysis model. OSV is very efficient for highly nonlinear problems, especially when the contour lines of the performance functions vary widely. The computation capability of the proposed method is demonstrated and compared to existing RBDO methods using four mathematical and engineering examples. The comparison results show that the proposed OSV approach is very efficient.
  PubDate: 2013-06-01
Artificial Bee Colony (ABC) algorithm in the design optimization of RC continuous beams
- Abstract: Abstract The objective of this study is to obtain the optimum design for reinforced concrete continuous beams in terms of cross section dimensions and reinforcement details using a fine tuned Artificial Bee Colony (ABC) Algorithm while still satisfying the constraints of the ACI Code (2008). The ABC algorithm used in this paper has been slightly modified to include a Variable Changing Percentage (VCP) that further improves its performance when dealing with members consisted of multiple variables. The objective function is the total cost of the continuous beam which includes the cost of concrete, formwork and reinforcing steel bars. The design variables used are beam width, beam height, number and diameter of: bottom continuous reinforcing bars, bottom cutoff reinforcing bars, top continuous reinforcing bars and top cutoff reinforcing bars as well as the diameter of stirrups. Four RC beams of varying complexity are presented and optimized. The first three beams are used to fine tune the control parameters of the ABC algorithm, whereas the fourth beam was previously optimized by Arafa et al. (J Artif Intell 76–88, 2011) and is presented here to prove the superiority of this relatively new optimization algorithm.
  PubDate: 2013-06-01
A Sequential Element Rejection and Admission (SERA) method for compliant mechanisms design
- Abstract: Abstract A Sequential Element Rejection and Admission (SERA) method to design compliant mechanisms with topology optimization techniques is presented in this work. This procedure allows material to flow between two different material models: ‘real’ and ‘virtual’. The method works with two separate criteria for the rejection and admission of elements to efficiently achieve the optimum design. The SERA method overcomes the problems encountered by the ESO method when used to design compliant mechanisms. Three benchmark problems are presented to show the validity and robustness of the SERA method to design complaint mechanisms, regardless of the design parameters chosen.
  PubDate: 2013-06-01
Numerical optimization of pacing strategy in cross-country skiing
- Abstract: Abstract When studying events involving locomotive exercise, such as cross-country skiing, one generally assumes that pacing strategies (i.e. power distributions) have a significant impact on performance. In order to better understand the importance of pacing strategies, a program is developed for numerical simulation and optimization of the pacing strategy in cross-country ski racing. This program computes the optimal pacing strategy for an arbitrary athlete skiing on a delineated course. The locomotion of the skier is described by introducing the equations of motion for cross-country skiing. A transformation of the motion equations is carried out in order to improve the simulation. Furthermore, a nonlinear optimization routine is connected to the simulation program. Simulation and optimization are performed on a fictional male skier. Results show that it is possible to attain an optimal pacing strategy by simulating cross-country skiing while connecting nonlinear optimization routines to the simulation. It is also shown that an optimal pacing strategy is characterized by minor variations in speed. In our opinion, this kind of optimization could serve as essential preparations before important competitions.
  PubDate: 2013-06-01
Geometry optimization of a slender cantilever beam subjected to lateral buckling
- Abstract: Abstract The paper deals with the geometry optimization of a slender cantilever beam subjected to a concentrated force acting at the free end. The two-parametric mathematical model of lateral torsional buckling is based on the Bernoulli–Euler beam theory and is given in dimensionless form. The optimization procedure is performed using the optimal control theory and the relation between state and adjoint variables is presented. The boundary value problem derived from the optimization procedure is solved numerically and compared to solutions obtained via an alternative optimization approach called sequential approximate optimization.
  PubDate: 2013-06-01
Exact analytical solutions for some popular benchmark problems in topology optimization III: L-shaped domains revisited
- Abstract: Abstract The paper provides the corrections and extensions of the paper of the same title, published in vol. 35, 2008, pp. 165–174 of the current journal. The analytical solutions of Michell trusses constructed within the L-shaped domains are confirmed by the ground structure method of the truss optimization, thus giving the upper bounds of the exact solutions.
  PubDate: 2013-06-01
Efficient surrogate construction by combining response surface methodology and reduced order modeling
- Abstract: Abstract Response surface methodology is an efficient method for approximating the output of complex, computationally expensive codes. Challenges remain however in decreasing their construction cost as well as in approximating high dimensional output instead of scalar values. We propose a novel approach addressing both these challenges simultaneously for cases where the expensive code solves partial differential equations involving the resolution of a large system of equations, such as by finite element. Our method is based on the combination of response surface methodology and reduced order modeling by projection, also known as reduced basis modeling. The novel idea is to carry out the full resolution of the system only at a small, appropriately chosen, number of points. At the other points only the inexpensive reduced basis solution is computed while controlling the quality of the approximation being sought. A first application of the proposed surrogate modeling approach is presented for the problem of identification of orthotropic elastic constants from full field displacement measurements based on a tensile test on a plate with a hole. A surrogate of the entire displacement field was constructed using the proposed method. A second application involves the construction of a surrogate for the temperature field in a rocket engine combustion chamber wall. Compared to traditional response surface methodology a reduction by about an order of magnitude in the total system resolution time was achieved using the proposed sequential surrogate construction strategy.
  PubDate: 2013-06-01
Continuum-based sensitivity analysis for coupled atomistic and continuum simulations for 2-D applications using bridging scale decomposition
- Abstract: Abstract The concept of linking simulations at multiple length and time scales is found useful for studying local physical phenomena such as crack propagation. Many multi-scale methods, which couple molecular dynamics models with continuum models, have been proposed over the last decade. One of the most advanced methods developed recently is the bridging scale method, in which the total displacement is decomposed into orthogonal coarse and fine scales. This paper presents the continuum-based sensitivity analysis for two-dimensional coupled atomistic and continuum problems using the bridging scale method. A variational formulation for the bridging scale decomposition is developed based on the Hamilton’s principle. The continuum-based variational formulation provides a uniform and generalized system of equations from which the differential equations can be obtained naturally. The sensitivity expressions for both direct differentiation method (DDM) and adjoint variable method (AVM) are derived in a continuum setting. Due to its efficiency for crack problems, the direct differentiation method is chosen to be implemented numerically and applied to two examples, including a crack propagation problem. Both material and sizing design variables are included to reveal the impact of design changes at the macroscopic level to the responses at the atomistic level. Also demonstrated is the feasibility of achieving the variation of the time history kernel computed using numerical procedures. The sensitivity coefficients calculated are shown to be accurate compared with overall finite difference method. The physical implications of the sensitivity results are also discussed, which accurately predict the behavior of the structural responses.
  PubDate: 2013-06-01
Symmetry properties in structural optimization: some extensions
- Abstract: Abstract In the present paper, some extensions of the previous theoretical results about the symmetry properties of structural optimization problems are reported. It is found that generally the condition of convexity can be relaxed to quasi-convexity in order to guarantee the existence of symmetry global optima. Furthermore, some new results about the symmetry properties of robust and discrete structural optimization problems are also presented. Numerous concrete examples illustrate the claims made in the present work explicitly.
  PubDate: 2013-06-01
Graph and heuristic based topology optimization of crash loaded structures
- Abstract: Abstract For the efficient development of new structural concepts, it is necessary to perform an optimization of the mechanical properties of profile cross-sections taking into account all relevant load cases. Especially for crash load cases, there currently exists no established method for the conceptual design and topology optimization. The main problems are the complicated deformation conditions in the crash, the huge number of design variables, the existence of simulative and physical bifurcation points and the costly determination of sensitivity information. For the application area of developing profile cross-sections, the method presented in this paper attempts to overcome these shortfalls. It has been developed for the combined topology, shape and sizing optimization taking into account all relevant crash load cases. For this a flexible description of the structure’s profile cross-section via mathematical graphs is used. Modifications of the structure’s topology are performed with heuristics (rules), which are based on expert knowledge, whereas the automatically generated shape und sizing parameters of the structure are optimized with mathematic optimization algorithms.
  PubDate: 2013-06-01
Design optimization of balloon-expandable coronary stent
- Abstract: Abstract To prevent the dogboning effect of stent implantation (i.e. the ends of a stent opening first during expansion), an adaptive optimization method based on the kriging surrogate model is proposed to reduce the absolute value of the dogboning rate. Integrating design of experiment (DOE) methods with the kriging surrogate model can approximate the functional relationship between the dogboning rate and the geometrical design parameters of the stent, replacing the expensive reanalysis of the stent dogboning rate during the optimization process. In this adaptive process, an infilling sampling criterion termed expected improvement (EI) is used to balance local and global search and tends to find the global optimal design. Finite element method is used to analyze stent expansion. As an example, a typical diamond-shaped coronary stent is investigated, where four key geometries are selected to be the design variables. Numerical results demonstrate that the proposed adaptive optimization method can effectively decrease the absolute value of the dogboning rate of stent dilation.
  PubDate: 2013-05-10
Process for design optimization of honeycomb core sandwich panels for blast load mitigation
- Abstract: Abstract A general process for optimization of a sandwich panel to minimize the effects of air blast loading is presented here. The panel geometry consists of two metal face plates with a crushable honeycomb or other type of core. Optimization is necessary as there is strong coupling between the several variables and the physics, which makes parametric studies relatively ineffective. Virtual testing is used to develop a homogenized model for the stress–strain curve of the honeycomb core, which can be readily applied to other types of cellular core. The homogenized model has been validated by comparison to existing results as well as to results from detailed finite element (FE) models. A design of experiments (DOE) based response surface optimization method in combination with LS-DYNA is used to minimize dynamic deflection or acceleration of the back face plate. Constraints on total mass and on plastic strain in the face plates are imposed. The mechanism of lowering the backface deflection is by increasing front face plate thickness which effectively distributes the blast load to a larger area of the core and avoids local concave deformation of the front face plate. Further, core depth is increased which increases panel stiffness. For acceleration minimization, results again produce a stiffer front face plate, but accompanied by a sufficiently soft core. The mechanism of lowering the backface acceleration is by absorbing energy with low transmitted stress. A clear cut comparison between monolithic metal plates and sandwich plates, for the same loading and failure criteria, is presented here.
  PubDate: 2013-05-01
Simulation-based time-dependent reliability analysis for composite hydrokinetic turbine blades
- Abstract: Abstract The reliability of blades is vital to the system reliability of a hydrokinetic turbine. A time-dependent reliability analysis methodology is developed for river-based composite hydrokinetic turbine blades. Coupled with the blade element momentum theory, finite element analysis is used to establish the responses (limit-state functions) for the failure indicator of the Tsai–Hill failure criterion and blade deflections. The stochastic polynomial chaos expansion method is adopted to approximate the limit-state functions. The uncertainties considered include those in river flow velocity and composite material properties. The probabilities of failure for the two failure modes are calculated by means of time-dependent reliability analysis with joint upcrossing rates. A design example for the Missouri river is studied, and the probabilities of failure are obtained for a given period of operation time.
  PubDate: 2013-05-01
Structural design for desired eigenfrequencies and mode shapes using topology optimization
- Abstract: Abstract A technique is proposed for determining the material distribution of a structure to obtain desired eigenmode shapes for problems of maximizing the fundamental eigenfrequency. The design objective is achieved using the solid isotropic method with penalization (SIMP) for topology optimization. Weighted constraints added in bound formulation are proposed to maximize the fundamental natural frequency, which provides an easy and straightforward way to prevent mode switching in the optimization process. Aside from maximizing the fundamental frequency, a method to modify existing eigenmodes to continuously evolve and assume the same shapes as the desired modes within the optimization process is proposed. The topology layout of a structure with desired eigenmodes is obtained by adding the modal assurance criterion (MAC) as additional constraints in the bound formulation optimization. Examples are presented to illustrate the proposed method, and a potential application of the proposed technique in decoupling a mechanical system is demonstrated.
  PubDate: 2013-05-01
A gradient-based transformation method in multidisciplinary design optimization
- Abstract: Abstract Multidisciplinary design optimization (MDO) has become essential for solving the complex engineering design problems. The most common approach is to “divide and conquer” the MDO problem, that is, to decompose the complex problem into several sub-problems and to collect the local solutions to give a new design point for the original problem. In 1990s, researchers have developed some decomposition strategies to find or synthesize the optimal model of the optimization structure in order to evenly distribute the computational workloads to multiple processors. Several MDO methods, such as Collaborative Optimization (CO) and Analytical Target Cascading (ATC), were then developed to solve the decomposed sub-problems and coordinate the coupling variables among them to find the optimal solution. However, both the synthesis of the decomposition structure and the coordination of the coupling variables require additional function evaluations, in terms of evaluating the functional dependency between each sub-problem and determining the proper weighting coefficients between each coupling functions respectively. In this paper, a new divide-and-conquer strategy, Gradient-based Transformation Method (GTM), is proposed to overcome the challenges in structure synthesis and variable coordination. The proposed method first decomposes the MDO problem into several sub-systems and distributes one constraint from the original problem to each sub-system without evaluating the dependency between each sub-system. Each sub-system is then transformed to the single-variate coordinate along the gradient direction of the constraint. The total function evaluations equal the number of constraints times the number of variables plus one in every iteration. Due to the monotonicity characteristics of the transformed sub-problems, they are efficiently solved by Monotonicity Analyses without any additional function evaluations. Two coordination principles are proposed to determine the significances of the responses based on the feasibility and activity conditions of every sub-problem and to find the new design point at the average point of the most significant responses. The coordination principles are capable of finding the optimal solution in the convex feasible space bounded by the linearized sub-system constraints without additional function evaluations. The optimization processes continue until the convergence criterion is satisfied. The numerical examples show that the proposed methodology is capable of effectively and efficiently finding the optimal solutions of MDO problems.
  PubDate: 2013-05-01
On robust design optimization of truss structures with bounded uncertainties
- Abstract: Abstract This paper investigates robust design optimization of truss structures with uncertain-but-bounded parameters and loads. The variations of the cross-sectional areas, Young’s moduli and applied loads are treated with non-probabilistic ellipsoid convex models. A robustness index for quantitatively measuring the maximal allowable magnitude of system variations is presented, and the design problem is then formulated as to maximize the minimum of the robustness indices for all the concerned design requirements under a given material volume constraint. For circumventing the difficulty associated with the max-min type problem, an aggregate function technique is employed to construct a smooth objective function. The computational scheme for the sensitivity of the robustness index is derived on the basis of optimum sensitivity analysis. The optimization problem is then solved by using the GCMMA optimizer. Numerical examples illustrate the validity and effectiveness of the present formulation and solution techniques.
  PubDate: 2013-05-01