Topology Optimization

Topology optimization plays a key role in the production of strong, lightweight functional parts. It uses mathematical algorithms to create optimized geometries under given constraints while at the same time improving performance. The conventional design process is time consuming and requires high technical expertise. The raisons d'etre for using algorithms is to reduce part development time and to keep the computational cost low. Further reduction in cost through weight savings can be realized though monolithic (one piece) design. In this method, weight reduction is achieved through the elimination of bolts, nuts and other joining material. Combining topology optimization with monolithic design also blends the benefit of weight reduction with the simplification of the assembly process. To reach optimum weight, an effective part development process requires a methodology which takes into account the objective function and all the constraints. The methodology can be used from the early stages, throughout the design process. This provides a step-by-step approach to the design process and keeps iterations to a minimum, thereby reducing the product development time. This research therefore focuses on the trends in the development of a methodology for the topology optimization of monolithic vehicle components. It also highlights the challenges and opportunities, placing emphasis on the vehicle aftermarket industry components.

The paper proposes a mixed strain-and stress-based topology optimization method for designing the ideal geometry of carbon fibers in composite laminates subjected to either applied tractions or prescribed displacements. On the basis of standard micromechanical approaches, analytical elastic solutions for a single cell, assumed to be a Representative Volume Element (RVE), are ad hoc constructed by involving anisotropy induced by fiber orientation and volume fraction, also taking into account inter-laminar stresses and strains. The analytical solutions are then implemented in a Finite Element (FE) custom-made topology optimization-based procedure rewritten to have as output the best curves the reinforcing fibers have to draw in any composite laminate layer to maximize the overall panel stiffness or to minimize the elastic energy. To verify the effectiveness of the proposed strategy, different structures undergoing either in-plane or out-plane boundary conditions have been selected and theoretically investigated, determining the optimal fibers' maps and showing the related results in comparison to standard sequences of alternate fibers disposition for the same composites. Two optimized panels were at the end actually produced using an innovative Automated Fiber Placement (AFP) machine and consolidating the materials by means of autoclave curing processes, in this way replicating the fiber paths obtained from theoretical outcomes. As a control, two corresponding composite structures were also realized without employing the fiber optimization strategy. The panels have been tested in laboratory and the theoretical results have been compared with the experimental findings, showing a very good agreement with our predictions and confirming the capability of the proposed algorithm to suggest how to arrange the fibers to obtain enhanced mechanical performances. It is felt that the hybrid analytical-FE topology optimization strategy, in conjunction with the possibilities offered by AFP devices, could pave the way for a new generation of ultra-lightweight composites for aerospace, automotive and many industrial applications.

In this paper, the advantages of using cognition when solving the impairment-aware virtual topology design problem are demonstrated. To this end, an algorithm to design the virtual topology, GAPDELT, previously proposed by the University of Valladolid, has been extended to ensure that all the lightpaths of the virtual topology comply with quality of transmission constraints. The new version, called IA-GAPDELT, is a multiobjective genetic algorithm which uses Pareto optimality to reduce both the network congestion and the number of transmitters in operation, and so the energy consumption. By means of simulation, we show that when the algorithm is enhanced with a simple cognitive technique, it obtains a higher number of feasible solutions (virtual topologies) and, moreover, they are generally better in terms of the optimization parameters, than those obtained without cognition.

An efficient and explicit topology optimization approach is initially proposed for eigenfrequencies of a rotating thin plate in this study. First of all, an accurate dynamic model of the rotating thin plate is established via the thin plate elements of the absolute nodal coordinate formulation (ANCF). When performing the modal characteristic analysis of the rotating thin plate at a prescribed angular velocity, the linear perturbation analysis is employed, during which the coupling between the membrane and bending deformations is considered. The coupling term makes the dynamic model established in the study more accurate than conventional models, especially in the case of large deformations. Then, the moving morphable components (MMC) are used to describe the topology of the plate. In the frame of MMC-based topology optimization, explicit geometrical parameters, positions, and orientations of the components are taken as the design variables so that the total number of the design variables can be greatly reduced. For the topology optimization, the sensitivities of a simple eigenfrequency and multiply repeated eigenfrequencies with respect to a design variable are analytically derived. During the optimization, in order to remove the localized modes in the low-density areas, the mass and stiffness matrices of the thin plate elements of ANCF are carefully penalized. Finally, four numerical examples are presented to validate the proposed topology optimization approach and to demonstrate its effectiveness for two objectives, i.e., maximizing either the first eigenfrequency or the gap between two consecutive eigenfrequencies of a rotating thin plate.

Topology optimization techniques are applied in most cases for static applications. However, recently topology optimization procedures for structures under dynamic loads have been the focus of several studies. In this work, a topology optimization scheme for flexible multibody systems using equivalent static loads and displacement fields is investigated. The optimization problem is formulated using a homogenization method, more precisely, the solid isotropic material with penalization (SIMP) approach. The objective function in the optimization problem is the compliance and the method of moving asymptotes is used as optimizer. The objective function and the sensitivities are computed directly from the displacement field computed in the dynamic simulation. The examples of a 2‐arm manipulator and a slider‐crank mechanism are presented and the results are discussed to verify the improved dynamical behavior through this optimization method. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinh...

Multiscale structures require excellent multiphysical properties to withstand the loads in various complex engineering fields. In this study, a concurrent isogeometric topology optimization method is proposed to design multiscale structures with high thermal conductivity and low mechanical compliance. First, the mathematical description model of multi-objective topology optimization for multiscale structures is constructed, and a single-objective concurrent isogeometric topology optimization formulation for mechanical and thermal compliance is proposed. Then, by combining the isogeometric analysis method, the material interpolation model and decoupled sensitivity analysis scheme of the objective function are established on macro and micro scales. The solid isotropic material with penalization method is employed to update iteratively the macro and microstructure topologies simultaneously. Finally, the feasibility and advantages of the proposed approach are illustrated by several 2D and 3D numerical examples with different volume fractions, while the effects of volume fraction and different boundary conditions on the final configuration and multiobjective performance of the multiscale structure are explored. Results show that the isogeometric concurrent design of multiscale structures through multi-objective optimization can produce better multi-objective performance compared with a single-scale one.

We consider the problem of data aggregation using two aggregators. We assume that the source racks can split the data they need to send to the aggregators across multiple paths. We show that obtaining a topology that minimizes aggregation time is NP-hard for k = 2, 3, 4, where k the degree of ToR (topof-rack) switches. We also show that an optimal topology can be computed in polynomial time for k = 5 and 6 and conjecture this to be the case when k > 6 as well. Experimental results show that, when k = 6, our topology optimization algorithm reduces the aggregation time by as much as 83.3% and reduces total network traffic by as much as 99.5% relative to the torus heuristic, proposed by .

Algorithms ba8ed on Semi -De員nite Programming ( SDP ) are proposed f( )r the truss topology optimization problems for sp i丘ed fUndamental eigenvalue of free vibratlon and 髄near budding load factor ， and optimal topologies of trusses are compu 七ed by using the Semi -De 且nite Programming Algor孟 thm ( SDPA ) ， it is wen known that optimizing structures for speci 丘ed minimum eigenvalue is di冊 cult because of nondifferentiability of th6 minimum eigenvalue 長 )r the cases of multimodal sQlutions ． It is shown ， in the exampLes ， 丗 at the

The last few decades, the application of 3D Printing (3DP) techniques in construction scale has shown an increased trend, with advantages as well as limitations, mainly related to overhanging angle restrictions during printing of complex geometries including free-form shell structures. This work suggests a five steps methodology as an alternative approach for their design and then their 3DP. In particular, in the first stage, parametric design based on the catenary concept is used for the overall geometrical configuration of free-form shells, aiming at minimization of exercised tension and compression forces. Then, Topology Optimization (TO) principles are applied, in order to reduce total material volume and at the same time to achieve structural stability of the selected shell system. This is followed by an approach for alternating individual unit members based on the functionally graded cellular structures concept, which aims at material distribution and customization in different areas. In the fourth stage, a reconfigurable formwork system is developed and used as a supporting structure for on-site 3DP in different angles and for different design configurations. Finally, the 3DP process of toolpath development and simulation are demonstrated, accompanied by real scale physical experimentation. The work is assessed in providing initial information regarding the effectiveness of the process to be used in the construction of shell structures through multi-axis 3DP assisted by reconfigurable supporting systems.

The engine is the most important component of a vehicle. It attaches to the main frame via the engine mounting bracket which supports weight and operating loads. The engine mount therefore plays a crucial role in the durability and comfort of the vehicle. This article contributes to the search for the most optimal model from the point of view of resistance, environmental impact, and manufacturing cost. This involves, on the one hand, optimizing the support by reducing its initial mass by 30%, and on the other hand, seeking suitable material and manufacturing process with the least environmental impact. To this end, topology optimization will be combined with an environmental assessment and a manufacturing cost analysis. Four materials will be tested and evaluated. Finally, a cost analysis will present a comparison between a conventional process and 3D printing.

Communication infrastructure for multi-core Systems-on-Chip (SoCs) is provided by Network-on-Chip (NoC). Point-to-Point (P2P) and bus-based communication systems are NoCs and are two communication channels of NoC that can probably overcome the scalability and performance restrictions of NoC. Latency and throughput are two of the essential characteristic metrics measured for a routing algorithm that affect the performance of a given NoC. This study evaluated and compared static and dynamic routing algorithms Dijkstra and distance vector on the scale of increasing flit length and network traffic. In a network, considering the effects of topology, traffic, buffer, and packet size, the dynamic algorithm performs better than a static algorithm on the network's performance. Moreover, the effect of increased network traffic on throughput and average packet delay with the increase in network size in a fixed MS topology and distance vector routing protocol has been evaluated. The results show that while using the Dijkstra algorithm, the average packet delay reached 50-60 packets/cycle in comparison to the Distance Vector where it reached a maximum of 40 packets/cycle in 4 different topologies. Throughput is achieved up to 100% in both algorithms using various topologies. In only MS topology, throughput reached 100% but packet delay increased to 400 pkts/cycle with an increase in network size.

This paper proposes an algorithm for the synthesis/optimization of microstructures based on an exact formula for the topological derivative of the macroscopic elasticity tensor and a level-set domain representation. The macroscopic elasticity tensor is estimated by a standard multi-scale constitutive theory where the strain and stress tensors are volume averages of their microscopic counterparts over a Representative Volume Element (RVE). The algorithm is of simple computational implementation. In particular, it does not require artificial algorithmic parameters or strategies. This is in sharp contrast with existing microstructural optimization procedures and follows as a natural consequence of the use of the topological derivative concept. This concept provides the correct mathematical framework to treat topology changes such as those characterizing microstuctural optimization problems. The effectivenes of the proposed methodology is illustrated in a set of finite element-based numerical examples.

The main aim of this study was to decrease the weight of mobile transportation robots and to check the optimized shape using topology optimization and structural analysis. The analyses were applied using CAE Software with the methods of topology optimization and structural analysis. In the topology optimization process, the preserved areas were defined for connection and fixing areas. The aim was to decrease the weight of the robot structure and lower the energy consumption of the robotic system. After topology optimization, the structural strength analysis was applied to the new optimized structure to check the strength. The weight of the structure was decreased with a ratio of 20%. In addition to this, the structural strength of the robot was observed similar to the original body with the factor of safety value as three.

In structural engineering systems, shear walls are two-dimensional vertical elements designed to endure lateral forces acting in-plane, most frequently seismic and wind loads. Shear walls come in a variety of materials and are typically found in high-rise structures. Because steel shear walls are lighter, more ductile, and stronger than other concrete shear walls, they are advised for usage in steel constructions. It is important to remember that the steel shear wall has an infill plate, which can be produced in a variety of forms. The critical zones in flat steel shear walls are the joints and corners where the infill plate and frame meet. The flat infill plate can be modified to improve the strength and weight performance of the steel shear walls. One of these procedures is Topology Optimization (TO) and this method can reduce the weight and also, increase the strength against the cyclic loading sequences. In the current research paper, the TO of the infill steel plate was considered based on the two methods of volume constraint and maximization of strain energy. Four different volumes (i.e., 60%, 70%, 80%, and 90%) were assumed for the mentioned element in the steel shear wall. The obtained results revealed that the topology configuration of CCSSW with 90% volume constraint presented the highest seismic loading performance. The cumulated energy for this type of SSW was around 700 kJ while it was around 600 kJ for other topology optimization configurations. Keywords Steel shear wall, Infill plate, Topology optimization, Finite element analysis, Cyclic load conditions Cyclic loading is the process of applying repeated or variable strains, stresses, or stress intensities to various locations on structural components 1 . The term "fatigue degradation" refers to potential degradation and localized damage 2 . Shear walls are one of the responsibilities that are taken into consideration throughout the design and manufacturing process of structures in order to reduce damages 3 . A shear wall is a structural support element that can withstand shear stresses, including those caused by severe winds and seismic activity 4 . In the field of civil engineering, shear force refers to the forces that apply perpendicularly against the structural components of a building, causing the structure to twist and bend 5 . Shear walls make structures stable and prevent them from tilting or collapsing by transferring lateral loads to the base 6 . Shear walls all serve the same purpose, but they must follow specific construction guidelines and can vary based on several building-related factors, such as the material they are made of (such as concrete 7 , steel 8 , or wood 9 ), their thickness 10 , length 11 , and placement 12 . The purpose of load-bearing and shear walls is to transfer the pressure and tension associated with a load from its source to the ground foundation. Load-bearing walls, on the other hand, absorb vertical loads and hold a building up, whereas shear walls resist horizontal forces and prevent a building from tumbling sideways 13 . Shear walls can

Topology optimization (TO) is a computational method of determining material distribution in a given design area to create the optimal shape of a part under given boundary conditions. The increased interest in the development of effective methods of designing parts of the optimal topology testifies to the relevance of these theoretical studies and the important applied value of the obtained results. In the classic formulation of maintenance, the minimization of the flexibility of the part under restrictions on the volume (mass) of the optimization result is chosen as a criterion for finding the specified distribution. Closer to practical application is the formulation of the maintenance problem, which involves minimizing the volume of the part, taking into account the condition of its strength. The inclusion of aggregate functions for the calculation of integral measures of the stress state has a number of advantages over the traditional check of the maximum value of mechanical stre...

A phase field approach for structural topology optimization with application to additive manufacturing is analyzed. The main novelty is the penalization of overhangs (regions of the design that require underlying support structures during construction) with anisotropic energy functionals. Convex and non-convex examples are provided, with the latter showcasing oscillatory behavior along the object boundary termed the dripping effect in the literature. We provide a rigorous mathematical analysis for the structural topology optimization problem with convex and non-continuouslydifferentiable anisotropies, deriving the first order necessary optimality condition using subdifferential calculus. Via formally matched asymptotic expansions we connect our approach with previous works in the literature based on a sharp interface shape optimization description. Finally, we present several numerical results to demonstrate the advantages of our proposed approach in penalizing overhang developments.

This work concerns a structural topology optimisation problem for 4D printing based on the phase field approach. The concept of 4D printing as a targeted evolution of 3D printed structures can be realised in a two-step process. One first fabricates a 3D object with multi-material active composites and apply external loads in the programming stage. Then, a change in an environmental stimulus and the removal of loads cause the object deform in the programmed stage. The dynamic transition between the original and deformed shapes is achieved with appropriate applications of the stimulus. The mathematical interest is to find an optimal distribution for the materials such that the 3D printed object achieves a targeted configuration in the programmed stage as best as possible. Casting the problem as a PDE-constrained minimisation problem, we consider a vector-valued order parameter representing the volume fractions of the different materials in the composite as a control variable. We prove the existence of optimal designs and formulate first order necessary conditions for minimisers. Moreover, by suitable asymptotic techniques, we relate our approach to a sharp interface description. Finally, the theoretical results are validated by several numerical simulations both in two and three space dimensions.

We consider the shape optimization of an object in Navier-Stokes flow by employing a combined phase field and porous medium approach, along with additional perimeter regularization. By considering integral control and state constraints, we extend the results of earlier works concerning the existence of optimal shapes and the derivation of first order optimality conditions. The control variable is a phase field function that prescribes the shape and topology of the object, while the state variables are the velocity and the pressure of the fluid. In our analysis, we cover a multitude of constraints which include constraints on the center of mass, the volume of the fluid region, and the drag of the object. Finally, we present numerical results of the optimization problem that is solved using the variable metric projection type (VMPT) method proposed by Blank and Rupprecht, where we consider one example of topology optimization without constraints and one example of maximizing the lift of the object with a state constraint, as well as a comparison with earlier results for the drag minimization.

A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement.

This paper assesses the feasibility of performing topology optimization of laminar incompressible flows governed by the steady-state Navier-Stokes equations using anisotropic mesh adaptation to achieve a high-fidelity description of all fluid-solid interfaces. The present implementation combines an immersed volume method solving stabilized finite element formulations cast in the variational multiscale (VMS) framework and level-set representations of the fluid-solid interfaces, which are used as an a posteriori anisotropic error estimator to minimize interpolation errors under the constraint of a prescribed number of nodes in the mesh. Numerical results obtained for several two-dimensional problems of power dissipation minimization show that the optimal designs are mesh-independent (although the convergence rate does decreases as the number of nodes increases), agree well with reference results from the literature, and provide superior accuracy over prior studies solved on isotropic meshes (fixed or adaptively refined).

Under the concept of "Industry 4.0", production processes will be pushed to be increasingly interconnected, information based on a real time basis and, necessarily, much more efficient. In this context, capacity optimization goes beyond the traditional aim of capacity maximization, contributing also for organization's profitability and value. Indeed, lean management and continuous improvement approaches suggest capacity optimization instead of maximization. The study of capacity optimization and costing models is an important research topic that deserves contributions from both the practical and theoretical perspectives. This paper presents and discusses a mathematical model for capacity management based on different costing models (ABC and TDABC). A generic model has been developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization's value. The trade-off capacity maximization vs operational efficiency is highlighted and it is shown that capacity optimization might hide operational inefficiency.

Topology optimisation defines a set of tools associated to the modelling of an effective material domain within structural optimisation. Based on this type of optimisation, it is possible to obtain an optimal material distribution for several applications and requirements. Cellular materials are part of the most prominent materials today, both in terms of applications, and in terms of research and development. However, their potentially complex and heterogeneous structures carry some complexities, associated to the prediction of effective constitutive properties and to its design. Homogenisation procedures can provide answers for both cases. On the one hand, the asymptotic expansion homogenisation can be used to determine thermomechanical effective properties for these materials through the detailed modelling of representative unit-cells, in a flexible and accurate fashion, regardless of the type of constituent distribution. On the other hand, this homogenisation technique integrates a localisation procedure, able to obtain detailed information on the behaviour of the material within the unit-cell, giving way to local sensitivities that can be used to control optimisation procedures. This leads to a material topology optimisation approach, perfectly suited for the design of this type of material. Within this scope, this work focuses on the analysis of effective thermomechanical material properties of cellular materials designed with topology optimisation procedures.

Composite materials are among the most prominent materials today, both in terms of applications and development. Nevertheless, their complex structure and heterogeneous nature lead to difficulties, both in the prediction of its properties and on the achievement of the ideal constituent distributions. The main focus of this work is to show the importance of computational procedures in this sense, namely in terms of the different applications of Asymptotic Expansion Homogenisation (AEH) and its integration in multiscale topology optimisation procedures.

This paper presents a level set topology optimization method in combination with the reproducing kernel particle method (RKPM) for the design of structures subjected to design-dependent pressure loads. RKPM allows for arbitrary particle placement in discretization and approximation of unknowns. This attractive property in combination with the implicit boundary representation given by the level set method provides an effective framework to handle the design-dependent loads by moving the particles on the pressure boundary without the need of remeshing or special numerical treatments. Moreover, the reproducing kernel (RK) smooth approximation allows for the Young's modulus to be interpolated using the RK shape functions. This is another advantage of the proposed method as it leads to a smooth Young's modulus distribution for smooth boundary sensitivity calculation which yields a better convergence. Numerical results show good agreement with those in the literature.

This paper presents a level set topology optimization method in combination with the reproducing kernel particle method (RKPM) for the design of structures subjected to design-dependent pressure loads. RKPM allows for arbitrary particle placement in discretization and approximation of unknowns. This attractive property in combination with the implicit boundary representation given by the level set method provides an effective framework to handle the design-dependent loads by moving the particles on the pressure boundary without the need of remeshing or special numerical treatments. Moreover, the reproducing kernel (RK) smooth approximation allows for the Young's modulus to be interpolated using the RK shape functions. This is another advantage of the proposed method as it leads to a smooth Young's modulus distribution for smooth boundary sensitivity calculation which yields a better convergence. Numerical results show good agreement with those in the literature.

The paper presents an optimization-based method for topology error detection in power systems. The method utilizes the residual analysis in state estimation and minimization of normalized measurement residual, with the application of matrix inverse lemma. The work considers a hybrid measurement configuration, i.e., both SCADA and PMU measurements, for the test systems studied. The proposed method is implemented on the TOMLAB optimization platform under the mixed integer nonlinear programming category. The proposed method has been applied and tested on standard IEEE 14-bus and IEEE 118-bus test systems. The method is designed to be computationally efficient and produces accurate results for single topology error detection. The results from the IEEE 14-bus and IEEE 118-bus test systems have shown that the proposed method produces 100% and 94% accurate results for single topology error detection, respectively. The proposed method performs robustly with the increased measurement uncertainties and inclusion of bad data or gross errors in the measurements. The method has superiority in practical implementation over the meta-heuristics-based optimization methods. The proposed method can be easily implemented and could have potential application in the energy management systems of the power system control center.

We study the rate of convergence of some nonlocal functionals recently considered by Bourgain, Brezis, and Mironescu, and, after a suitable rescaling, we establish the Γ-convergence of the corresponding rate functionals to a limit functional of second order. Contents 1. Introduction 1 2. Finite difference functionals in the 1-dimensional case 3 2.1. Pointwise limit and upper bound 4 2.2. Lower bound in the strongly convex case 6 3. Γ-limit in arbitrary dimension 12 3.1. Slicing 14 3.2. Lower bound, compactness, and proof of the main result 16 References 25

In this article, a Python-programmed advanced design paradigm is firstly introduced to topology and size optimization of the X-bracing system of nonlinear inelastic space steel frames. For that purpose, an advanced analysis method considering both geometric and material nonlinearities is utilized as an effective finite element analysis (FEA) solver. In which, X-bracing members are modeled by truss elements, while the beam and column members are simulated by beam-column ones. The bracing members’ cross-sectional area and their position are respectively treated as discrete size and topology design variables. The problem aims to minimize the weight of X-bracing system so that the constraints on the strength, inter-story drift and maximum displacement are satisfied. An adaptive hybrid evolutionary firefly algorithm (AHEFA) is employed as an optimizer. Numerical examples are exhibited to illustrate the powerful ability of the present methodology.

The determination of the optimal architecture of a supervised neural network is an important and a difficult task. The classical neural network topology optimization methods select weight(s) or unit(s) from the architecture in order to give a high performance of a learning algorithm. However, all existing topology optimization methods do not guarantee to obtain the optimal solution. In this work, we propose a hybrid approach which combines variable selection method and classical optimization method in order to improve optimization topology solution. The proposed approach suggests to identify the relevant subset of variables which gives a good classification performance in the first step and then to apply a classical topology optimization method to eliminate unnecessary hidden units or weights. A comparison of our approach to classical techniques for architecture optimization is given.

This paper presents a structural application of a shape optimization method based on a Genetic Algorithm (GA). The method produces a sequence of fixeddistance step-wise movements of the boundary nodes of a finite element model to derive optimal shapes from an arbitrary initial design space. The GA is used to find the optimal or near-optimal combination of boundary nodes to be moved for a given step movement. The GA uses both basic and advanced operators. For illustrative purposes, the method has been applied to structural shapeoptimization. The shape-optimization methodology presented allows local optimization, where only crucial parts of a structure are optimized as well as global shapeoptimization which involves finding the optimal shape of the structure as a whole for a given environment as described by its loading and freedom conditions. Material can be removed or added to reach the optimal shape. Two examples of structural shape optimization are included showing local and global optimization through material removal and addition.

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.

In this article, a two-step structural damage identification method for structural damage detection under variable ambient temperature conditions presented. First, to extract the environmental temperature effects from the obtained structural responses, the principal components method has been used.
In the first stage, three damage indices, namely the modal strain energy damage index, the strain energy loss ratio as a frequency response function, and the strain energy damage rate flexibility, have been calculated. Then the Bayesian data integration method has been applied to find the location of damage to these three damage indices.It is observed that the number of suspected damaged elements is reduced significance.
In the second step, using natural frequencies and mode shapes of the
function.The objective of the optimization problem has been formed and optimization has been done with the help of the gray wolf algorithm. Two examples include a plate truss and a space truss are considered and the performance of the proposed method in damage detection is evaluated. The results demonstrate the efficiency of the proposed method.

This paper presents a novel approach for analyzing plane frame systems by using Finite Element Method. The topology matrices are used to analyze the system. The releases may be easily assigned to elements and any boundary conditions may be applied to the system. In analysis process, all frame elements are assumed as having rigid connections, even though elements have releases or not. Additional freedoms are added to the nodes to consider releases. The coordinate system of nodes can be changed and supports can be assigned with any angle. Additional freedoms and the coordinate system rotations of nodes are taken into account by using topology matrices. An educational program was developed to analyze frame systems by using proposed approach. A numerical example is taken into account to explain the analysis process. The results of numerical example have compared with SAP2000 structural analysis program and suitable results are obtained. Keywords: Finite element method, topology matrix, ...

Isogeometric analysis is a popular method for the analysis of problems involving complex geometry and governed by differential equations. Meta-heuristics are widely used to determine the optimum distribution of material within the given design domain. The focus of this study is to perform isogeometric topology optimization of continuum structures using meta-heuristics nature inspired firefly algorithm. NURBS basis functions are used to construct the geometric model and to calculate the displacements as well. In this paper, a two dimensional plate structure is modeled using NURBS basis functions and analyzed for the given loading and boundary conditions. ESO technique is used to identify the elements which carry the material and penalize the remaining elements which do not carry any stress. Few examples have been solved and the results are presented. The results clearly show that the distribution of material using isogeometric analysis is similar to the distribution of material using FEA.

A brief review of different strategies for designing simultaneously the global structural topology and the local material properties is presented. Different treatments have been developed in the last decade to design the stiffest continuum structure using the concept of material distribution introduced in 1988 by Bends0e and Kikuchi. The comparison of such treatments shows a trend towards simplification, as expected, and also towards unification of metrics that allows the expression of design variables, objective functions, and constraints in a single basis. Numerical examples are presented to show the capabilities of the 'natural basis' treatment introduced by Taylor in 1998.

La présence de porosités dans les lingots métalliques représente un problème majeur dans l’industrie des matériaux. En effet, ces porosités altèrent significativement les caractéristiques mécaniques du matériau (ductilité notamment), et sont des sources d’apparition de défauts en mise en forme ou en tenue en service. Pour éliminer ces porosités, les industriels utilisent souvent des procédés de mise forme à chaud tels que le forgeage ou le laminage, mais il est souvent difficile de définir le taux de déformation à appliquer pour refermer entièrement ces porosités. La modélisation numérique s’avère donc être un outil particulièrement intéressant afin d’étudier l’impact des paramètres procédé sur le taux de refermeture de porosités. Dans ce travail, nous avons développé une méthodologie de calibration basée sur des algorithmes d’optimisation et une base de données de 800 simulations à champ complet sur VER, où les paramètres influents sur la refermeture des porosités sont variés (méca...

Recommended Citation Brandt, Kathleen; Lonsway, Brian; Brown, Lori; Chun, Junho; Cooke, Sekou; Corso, Gregory; Czerniak, Julia; Davis, Lawrence; Dixit, Mitesh; Louie, Jonathan; McIntosh, Nicole; Parga, Marcos; Park, Daekwon; Wang, Fei; Bartosh, Amber; Bedard, Jean-Francois; Chua, Lawrence; Hunker, Molly; Hubeli, Roger; Larsen, Julie; Krietemeyer, Elizabeth; Linder, Mark; Namara, Sinead Mac; Sho, Yutaka; Brown, Ted; Godlewski, Joseph; Miller, Kyle; and Shanks, David, "Faculty Publications for Academic Year 2018-19" (2019). Full list of publications from School of Architecture. 230. https://surface.syr.edu/arc/230

Most real-world engineering problems deal with multiple conflicting objectives simultaneously. In order to address this issue in truss optimization, this paper presents a multi-objective genetic programming approach for sizing and topology optimization of trusses. It aims to find the optimal cross-sectional areas and connectivities between the nodes to achieve a set of trade-off solutions to satisfy all the optimization objective functions subjected to some constraints such as kinematic stability, maximum allowable stress in members and nodal deflections. It also uses the variable-length representation of potential solutions in the shape of computer programs and evolves to the potential final set of solutions. This approach also employs an adaptive mutant factor besides the classical genetic operators to improve the exploring capabilities of Genetic Programming in structural optimization. The intrinsic features of genetic programming help to identify redundant truss members and nodes in the design space, while no violation of constraints occurs. Our approach applied to some numerical examples and found a better non-dominated solution set in the most cases in comparison with the competent methods available in the literature.

We propose an efficient probabilistic method to solve a deterministic problem -we present a randomized optimization approach that drastically reduces the enormous computational cost of optimizing designs under many load cases for both continuum and truss topology optimization. Practical structural designs by topology optimization typically involve many load cases, possibly hundreds or more. The optimal design minimizes a, possibly weighted, average of the compliance under each load case (or some other objective). This means that in each optimization step a large finite element problem must be solved for each load case, leading to an enormous computational effort. On the contrary, the proposed randomized optimization method with stochastic sampling requires the solution of only a few (e.g., 5 or 6) finite element problems (large linear systems) per optimization step. Based on simulated annealing, we introduce a damping scheme for the randomized approach. Through numerical examples in two and three dimensions, we demonstrate that the stochastic algorithm drastically reduces computational cost to obtain similar final topologies and results (e.g., compliance) compared with the standard algorithms. The results indicate that the damping scheme is effective and leads to rapid convergence of the proposed algorithm.

We outline a robust method for topology optimization with adaptive mesh refinement and derefinement (AMR). Since the total volume fraction in topology optimization is usually modest, after a few initial iterations the domain of computation is largely void. It is inefficient to have many small elements in such regions, as these contribute significantly to the overall computational cost but little to the accuracy of computation and design. At the same time, we want high spatial resolution for accurate three-dimensional designs to avoid significant postprocessing or interpretation. AMR offers the possibility to balance these two requirements, but it has received little attention in the context of topology optimization. We will discus approaches by Costas and Alves [2] and Stainko [3]. Unfortunately, both approaches may lead to suboptimal designs that are mesh dependent. We extend these approaches to obtain a method that yields optimal designs, and we show experimentally that our improvements lead to designs that are equivalent to designs computed on uniform meshes at the finest level of refinement. Furthermore, we demonstrate significant reductions of run time by using AMR and efficient methods for the solution of the resulting large, linear systems, following Wang et al. [4]. 6th International Conference on Computation of Shell and Spatial Structures IASS-IACM 2008, Ithaca not satisfy these properties. We propose simple but essential changes to these methodologies that lead to AMR based designs that are equivalent (up to some small tolerance) to designs on uniform fine meshes. In topology optimization we solve for the material distribution in a given design domain . Here, we minimize the compliance of a structure under given loads as a function of the material distribution. To solve this problem numerically, we discretize the computational domain using finite elements, where we use a lower order interpolation for the density field (material distribution) than for the displacement field. We take the most common approach using trilinear interpolation for the displacement field and constant density in each element. The compliance minimization problem after finite element discretization is defined as Ω [ ] ( ) 0 ,1

We outline a robust method for topology optimization with adaptive mesh refinement and derefinement (AMR). Since the total volume fraction in topology optimization is usually modest, after a few initial iterations the domain of computation is largely void. It is inefficient to have many small elements in such regions, as these contribute significantly to the overall computational cost but little to the accuracy of computation and design. At the same time, we want high spatial resolution for accurate three-dimensional designs to avoid significant postprocessing or interpretation. AMR offers the possibility to balance these two requirements, but it has received little attention in the context of topology optimization. We will discus approaches by Costas and Alves [2] and Stainko . Unfortunately, both approaches may lead to suboptimal designs that are mesh dependent. We extend these approaches to obtain a method that yields optimal designs, and we show experimentally that our improvements lead to designs that are equivalent to designs computed on uniform meshes at the finest level of refinement. Furthermore, we demonstrate significant reductions of run time by using AMR and efficient methods for the solution of the resulting large, linear systems, following Wang et al. [4].

We outline a robust method for topology optimization with adaptive mesh refinement and derefinement (AMR). Since the total volume fraction in topology optimization is usually modest, after a few initial iterations the domain of computation is largely void. It is inefficient to have many small elements in such regions, as these contribute significantly to the overall computational cost but little to the accuracy of computation and design. At the same time, we want high spatial resolution for accurate three-dimensional designs to avoid significant postprocessing or interpretation. AMR offers the possibility to balance these two requirements, but it has received little attention in the context of topology optimization. We will discus approaches by Costas and Alves [2] and Stainko . Unfortunately, both approaches may lead to suboptimal designs that are mesh dependent. We extend these approaches to obtain a method that yields optimal designs, and we show experimentally that our improvements lead to designs that are equivalent to designs computed on uniform meshes at the finest level of refinement. Furthermore, we demonstrate significant reductions of run time by using AMR and efficient methods for the solution of the resulting large, linear systems, following Wang et al. [4].

We propose a new technique for minimization of convex functions not necessarily smooth. Our approach employs an equivalent constrained optimization problem and approximated linear programs obtained with cutting planes. At each iteration a search direction and a step length are computed. If the step length is considered "non serious", a cutting plane is added and a new search direction is computed. This procedure is repeated until a "serious" step is obtained. When this happens, the search direction is a feasible descent direction of the constrained equivalent problem. The search directions are computed with FDIPA, the Feasible Directions Interior Point Algorithm. We prove global convergence and solve several test problems very efficiently.

This article demonstrates the interest of topology optimization in designing the ferrite plate used in an inductive power transfer system for electric vehicles. The solid isotropic material with the penalization (SIMP) method is used to optimize the ferrite plate, and it modifies the topology of the ferrite shape iteratively. This SIMP method can lead to novel structures compared with usual existing shapes. In this article, it is found that a part of the ferrite from the center and the edges of the predefined ferrite plate can be removed to save the ferrite volume while achieving a minimal reduction of transmission efficiency. Moreover, the results from topology optimization are influenced by the aluminum shielding plate near the ferrite plate. Hence, the ferrite on the receiver side has to be larger than the one on the transmitter side. These results give some design guidelines on arranging the ferrite placement for the system, and the approach could be generalized for shielding sheets/walls.

A high-performance density-based topology optimization tool is presented for laminar flows with focus on 2D and 3D aerodynamic problems via OpenFOAM software. Density-based methods are generally robust in terms of initial design, making them suitable for designing purposes. However, these methods require relatively fine resolutions for external flow problems to accurately capture the solid-fluid interfaces on Cartesian meshes, which makes them computationally very expensive, particularly for 3D problems. To address such high computational costs, two techniques are developed here. Firstly, an operator-based analytical differentiation (OAD) is proposed, which efficiently computes the exact partial derivatives of the flow solver (simpleFOAM). OAD also facilitates a convenient development process by minimizing hand-coding and utilizing the chain-rule technique, in contrast to full hand-differentiation, which is very complex and prone to implementation errors. Secondly, a multi-stage design process is proposed to further reduce the computational costs. In this technique, instead of using a fixed refined mesh, the optimization processes are initiated with a coarse mesh, and the converged solutions are projected to a locally refined mesh (as an initial guess) for a secondary optimization stage, which can be repeated to obtain a sufficient accuracy. A set of 2D and 3D laminar aerodynamic problems were studied, which promisingly confirmed the utility of the present approach, which can be adopted as a starting point for developing a design tool for large-scale aerodynamic engineering applications. In addition, the 3D problems indicated that less than 3% of total optimization CPU-time is devoted to OAD, and multi-staging up to 45% has reduced the overall costs.

Forced convective pin-fin heat exchangers, due to the high wet surface area per volume and the hindered thermal boundary layers, feature low thermal resistances. However, the considerable coolant pressure drop, particularly for densely packed fin arrays, imposes operational costs for pumping power supply. This paper develops a multi-objective topology optimization approach to optimize sink geometries in order to minimize thermal resistance and pressure loss, concurrently. In accordance to the pin-fin geometrical characteristics, a dedicated pseudo-3D conjugate heat transfer model is utilized, by assuming periodic flow and fin design pattern, to reasonably reduce the high cost of full-3D model optimization. For the solution of flow part, a pseudo-spectral scheme is used, which is intrinsically periodic and features a high spectral accuracy, and the finite element method for the non-periodic conjugate heat transfer model. Exact partial derivatives of the discrete solutions are obtained analytically by hand-differentiation. This task is rather convenient for the flow part, due to the simplicity of the pseudo-spectral implementation; however, the MATLAB symbolic toolbox is selectively utilized for the finite element code to ensure an error-free implementation. Finally, the sensitivities are computed directly or via a discrete adjoint method, for the flow and heat models, respectively. To examine the present approach, two approaches are used for optimization of a practical cooling task: constrained and unconstrained multi-objective formulations, where in all cases more emphasis is placed on thermal resistance minimization. A series of optimized heat sink geometries via constrained or unconstrained multi-objective optimizations are obtained to examine practical utility of the present approach. The optimized topologies demonstrated superior cooling performances at lower costs of pressure losses compared to conventional (circular) in-line and staggered fins, and confirmed the supremacy of topology over pure sizing optimization.

A high-performance density-based topology optimization tool is presented for laminar flows with focus on 2D and 3D aerodynamic problems via OpenFOAM software. Density-based methods are generally robust in terms of initial design, making them suitable for designing purposes. However, these methods require relatively fine resolutions for external flow problems to accurately capture the solid-fluid interfaces on Cartesian meshes, which makes them computationally very expensive, particularly for 3D problems. To address such high computational costs, two techniques are developed here. Firstly, an operator-based analytical differentiation (OAD) is proposed, which efficiently computes the exact partial derivatives of the flow solver (simpleFOAM). OAD also facilitates a convenient development process by minimizing hand-coding and utilizing the chain-rule technique, in contrast to full hand-differentiation, which is very complex and prone to implementation errors. Secondly, a multi-stage des...

The focus of this paper is topology optimization of fluid flow systems, particularly 2D laminar flows, widely found in microfluidic devices. The flow equations are solved numerically using a pseudo-spectral scheme and accurate derivatives are directly derived to facilitate gradient-based optimization. The proposed tool is utilized to enhance the performance of micro heat exchangers, in terms of minimizing the total pressure drop required to be supplied by micro pumps. It is well known that the geometry and arrangement of pinned fins play a pivotal role in total pressure drop of the system. Hence, in this work we aim to find the optimum topologies for various test cases by minimization of drag force on pined fins with a constraint on volume.

Forced convective pin-fin heat exchangers, due to the high wet surface area per volume and the hindered thermal boundary layers, feature low thermal resistances. However, the considerable coolant pressure drop, particularly for densely packed fin arrays, imposes operational costs for pumping power supply. This paper develops a multi-objective topology optimization approach to optimize sink geometries in order to minimize thermal resistance and pressure loss, concurrently. In accordance to the pin-fin geometrical characteristics, a dedicated pseudo-3D conjugate heat transfer model is utilized, by assuming periodic flow and fin design pattern, to reasonably reduce the high cost of full-3D model optimization. For the solution of flow part, a pseudo-spectral scheme is used, which is intrinsically periodic and features a high spectral accuracy, and the finite element method for the non-periodic conjugate heat transfer model. Exact partial derivatives of the discrete solutions are obtaine...