Topology Optimization Scheme Research Articles

Aerodynamic-driven topology optimization of compliant airfoils

A strategy for density-based topology optimization of fluid-structure interaction problems is proposed that deals with some shortcomings associated to non stiffness-based design. The goal is to improve the passive aerodynamic shape adaptation of highly compliant airfoils at multiple operating points. A two-step solution process is proposed that decouples global aeroelastic performance goals from the search of a solid-void topology on the structure. In the first step, a reference fully coupled fluid-structure problem is solved without explicitly penalizing non-discreteness in the resulting topology. A regularization step is then performed that solves an inverse design problem, akin to those in compliant mechanism design, which produces a discrete-topology structure with the same response to the fluid loads. Simulations are carried out with the multi-physics suite SU2, which includes Reynolds-averaged Navier-Stokes modeling of the fluid and hyper-elastic material behavior of the geometrically nonlinear structure. Gradient-based optimization is used with the exterior penalty method and a large-scale quasi-Newton unconstrained optimizer. Coupled aerostructural sensitivities are obtained via an algorithmic differentiation based coupled discrete adjoint solver. Numerical examples on a compliant aerofoil with performance objectives at two Mach numbers are presented.

On Performance Improvement of Centroid Topology Optimization Schemes in LTE Networks

On Performance Improvement of Centroid Topology Optimization Schemes in LTE Networks

An optimization method based on the evolutionary and topology approaches to reduce the mass of composite wind turbine blades

The design of large and lightweight wind turbines is a current challenge in the wind energy industry. In this context, this work aims to present a novel methodology to reduce the mass of composite wind turbine blades by combining evolutionary and topology optimization schemes in a staggered mode. First, the optimal laminate layout in the outer shell skin of the blade is determined by using genetic algorithms and by assuming that the shear webs are fully dense. Considering this optimized shell skin, the material is removed from the shear webs by using topology optimization. In both cases, the blade is assumed to be subjected to an extreme load scenario, with constraints on the tip displacement, the stresses, the natural vibration frequencies, and buckling phenomena. As an extra feature, the methodology integrates the inverse finite element method to recover the aerodynamically efficient shape of the blade when it is working in normal load scenario as well as to increase the tower clearance safety margin under the extreme load scenario. To illustrate the performance of the methodology, the design of a 28.5-m composite blade is presented. Results show mass savings of up to 23% and a significant increase of the tower clearance safety margin. Furthermore, it is observed that after the classical genetic optimization of the shell skin, there is still margin to achieve additional mass savings via topology optimization of the shear webs without compromising the structural response of the blade.

Eliminating occluded voids in additive manufacturing design via a projection-based topology optimization scheme

Design for additive manufacturing (AM) requires knowledge of the constraints associated with your targeted AM process. One important design concern is the unintentional trapping of parasitic mass in occluded void geometries with either uncured or non-solidified material, or in some cases, sacrificial support material. These occluded features create the need to physically alter the optimal topology to remove the material. In this work, a projection-based topology optimization design formulation is proposed to eliminate occluded void topological features in optimal AM designs. The algorithm is based on the combination and enhancement of two existing algorithms: a projection-based, overhang-constrained algorithm to design self-supporting structures in AM, and a void projection algorithm to design topologies through control of the void phase. The combined algorithm results in topologies with void regions that always possess an exit path to predefined outer surfaces – i.e. drainage pathways. Solutions are first demonstrated in two dimensions, with increasing design freedom allowed through algorithm enhancements. The algorithm is then adapted to 3D, adopting a multi-phase TO approach to not only regain control of the solid phase length scale, but also to drive toward superior performing topologies with minimal impact on the part performance.

Linear and nonlinear topology optimization design with projection‐based ground structure method (P‐GSM)

SummaryA new topology optimization scheme called the projection‐based ground structure method (P‐GSM) is proposed for linear and nonlinear topology optimization designs. For linear design, compared to traditional GSM which are limited to designing slender members, the P‐GSM can effectively resolve this limitation and generate functionally graded lattice structures. For additive manufacturing‐oriented design, the manufacturing abilities are the key factors to constrain the feasible design space, for example, minimum length and geometry complexity. Conventional density‐based method, where each element works as a variable, always results in complex geometry with large number of small intricate features, while these small features are often not manufacturable even by 3D printing and lose its geometric accuracy after postprocessing. The proposed P‐GSM is an effective method for controlling geometric complexity and minimum length for optimal design, while it is capable of designing self‐supporting structures naturally. In optimization progress, some bars may be disconnected from each other (floating in the air). For buckling‐induced design, this issue becomes critical due to severe mesh distortion in the void space caused by disconnection between members, while P‐GSM has ability to overcome this issue. To demonstrate the effectiveness of proposed method, three different design problems ranging from compliance optimization to buckling‐induced mechanism design are presented and discussed in details.

Level-set topology optimization considering nonlinear thermoelasticity

At elevated temperature environments, elastic structures experience a change of the stress-free state of the body that can strongly influence the optimal topology of the structure. This work presents level-set based topology optimization of structures undergoing large deformations due to thermal and mechanical loads. The nonlinear analysis model is constructed by multiplicatively decomposing thermal and mechanical effects and introducing an intermediate stress-free state between the undeformed and deformed coordinates. By incorporating the thermoelastic nonlinearity into the level-set topology optimization scheme, wider design spaces can be explored with the consideration of both mechanical and thermal loads. Four numerical examples are presented that demonstrate how temperature changes affect the optimal design of large-deforming structures. In particular, we show how optimization can manipulate the material layout in order to create a counteracting effect between thermal and mechanical loads, even up to a degree that buckling and snap-through are suppressed. Hence the consideration of large deformations in conjunction with thermoelasticity opens many new possibilities for controlling and manipulating the thermo-mechanical response via topology optimization.

A discrete-continuous parameterization (DCP) for concurrent optimization of structural topologies and continuous material orientations

Combining topology optimization and continuous orientation design of fiber-reinforced composites is a promising way to pursue lighter and stronger structures. However, the concurrent design problem of structural topologies and continuous orientations is a tough topic due to the issue of local optimum solutions. This paper presents a new parameterization of orthotropic materials with continuous orientations, which is labeled as discrete-continuous parameterization (DCP), to handle this difficulty. The starting point of DCP is that the risk of falling into local optima will be much smaller if the search range of orientation variables can be greatly reduced. To do so, the searching interval of orientation is averagely divided into several subintervals. Then, the original continuous orientation optimization problem is changed to a discrete subinterval selection problem and a continuous orientation optimization problem in a subinterval. Based on this, the new DCP is proposed to model orthotropic materials with continuously varying orientations by combining both discrete and continuous variables. Finally, a new and general concurrent topology optimization method is built based on the proposed DCP and a three-field topology optimization scheme. Verification studies with several benchmark examples are provided to validate the effectiveness of the proposed approach.

Multi-Objective Topological Optimization of an Electric Truck Frame Based on Orthogonal Design and Analytic Hierarchy Process

The electric truck frame as a vital load-bearing component has aroused growing attentions due to its enormous potential in lightweight. However, few systematic studies have been performed on the multi-objective topological design of the frame attributable to its complexity on loading and conflicting objectives. This paper aims to develop a multi-objective topology optimization strategy of the electric truck frame based on the hybrid decision making method combining orthogonal test design (OTD) and analytic hierarchy process (AHP). The hybrid strategy is performed to obtain a new set of weight ratio combination from objective data and subjective judgment. The topological results show that the overall performance of the optimal frame is better than any of the methods applied alone. By comparing, it is found that the strength and stiffness of the optimal frame is higher than that of the original frame from the perspective of static conditions, and the low-order natural frequency of the optimal frame is significantly improved. It demonstrates that the proposed approach could be as an effective tool for multi-objective topology optimization of the electric truck frame in seeking lightweight and comprehensive mechanical performance. The hybrid strategy might be expected to provide some guidance for more complicated engineering problems.

Efficient structure crash topology optimization strategy using a model order reduction method combined with equivalent static loads

In this study, an efficient topology optimization method under crash loads is proposed by combining the equivalent static loads with a model order reduction method, which is referred as the reduced model–based equivalent static loads method for nonlinear dynamic response topology optimization method. Considering that some parts of the vehicle experience large nonlinear deformations, whereas others exhibit only small linear deformations in a vehicle crash scenario, the linear and nonlinear behavior parts are identified and the whole model of the complete structure is divided into nonlinear and linear sub-models. At each cycle, the model order reduction method is used in the linear sub-model during crash analysis to solve the low-density-elements-induced mesh distortion problem and accelerate this process. In the linear static topology optimization, the nonlinear sub-model that was initially used to describe the nonlinear behavior part is linearized by the equivalent static loads method and then reduced by the Guyan reduction method. Then, the reduced equivalent static load model is assembled into the linear sub-model that is defined as the design space to formulate a reduced topology optimization model of the complete structure and the reduced equivalent static loads that only act on master degrees of freedom are calculated. Finally, the linear static topology optimization is performed based on the reduced topology optimization model with the reduced equivalent static loads to enhance the efficiency and improve the numerical stability. The process is repeated until the convergence criterion is satisfied. The effectiveness of the proposed method is demonstrated by investing a numerical example. The results show that the proposed method provides a feasible strategy for the topology optimization under crash loads, which can effectively improve the numerical stability and convergence.

Bionic Stiffener Layout Optimization with a Flexible Plate in Solar-Powered UAV Surface Structure Design

A cellular-based evolutionary topology optimization scheme over a small curvature big contour wing surface is proposed for the design of an ultralight surface structure. Using this method, a ground-structure technique is first applied to obtain homogeneous mesh generation with a predefined weight value over the design domain. Secondly, the stiffener path’s description is guided by a modified map L system topology method that simulates the growth of the bionic branch, and the structural components are obtained by the specified searching method according to weights of the previous mesh vertexes. Thirdly, an optimal curved stiffener layout is achieved using an agent-based algorithm to create individual instances of designs based on a small number of input parameters. These parameters can then be controlled by a genetic algorithm to optimize the final design according to goals like minimizing weight and structural weakness. A comparison is implemented for long-span panel stiffener layout generation between an initial straight case and a bionic optimal case via our method, thereby indicating the significant improvement of the buckling loads by steering the stiffener’s path. Finally, this bionic method is applied to the wing box structure design and achieves remarkable weight loss at last.

A Modified Big Bang–Big Crunch Algorithm for Structural Topology Optimization

The purpose of this study is to develop a topology optimization scheme based on big bang–big crunch (BB–BC) algorithm, inspired from the evolution of the universe called big bang and big crunch theory. In order to apply the BB–BC algorithm to topology optimization for static and dynamic stiffness problems, the parameters of the algorithm were transformed to those of topology optimization scheme. In addition, some parameters such as big bang (BB) range, BB search, population and non-exchange limit were newly introduced to topology optimization scheme. Also, a parametric study for the parameters involved in the topology optimization scheme was performed to reduce the number of parameters, and find the appropriate ranges for topology optimization. Some examples were provided to examine the effectiveness of the developed topology optimization scheme for both static and dynamic stiffness problems throughout comparing with other metaheuristic topology optimization algorithms and the BESO (bi-directional evolutionary structural optimization) method. It was verified that the suggested algorithm shows superior to the compared typical metaheuristic topology optimization algorithms in the viewpoints of stability, robustness, accuracy and the convergence rate.

Topological design of piezoelectric actuator layer for linear quadratic regulator control of thin-shell structures under transient excitation

The purpose of this work is to develop a topology optimization scheme for thin-shell piezoelectric smart structures under the linear quadratic regulator optimal control for suppressing transient vibrations. The transient responses of the dynamic system are found by the finite element method based on the classical plate theory and a time-integration algorithm. A mode superposition method is employed to improve the computational efficiency. The pseudo-densities indicating the layout of piezoelectric actuators are taken as the design variables. The sensitivity analysis for a general time-integral function of transient structure response under optimal control is derived with the adjoint-variable method. A Lyapunov equation is solved to determine the derivative of the feedback gain in the sensitivity analysis. In the numerical examples, the integral of the structural response over a specified time interval is chosen as the objective function. Then, the optimization problem is solved with a gradient-based programming algorithm. The optimization results illustrate the validity of the proposed method. It is shown that the effects of active control have been substantially improved through optimization. The influences of some key factors on the optimized design are also discussed.

An Efficient Strategy for Non-probabilistic Reliability-Based Multi-material Topology Optimization with Evidence Theory

It is essential to consider the effects of incomplete measurement, inaccurate information and inadequate cognition on structural topology optimization. For the multi-material structural topology optimization with non-probability uncertainty, the multi-material interpolation model is represented by the ordered rational approximation of material properties (ordered RAMP). Combined with structural compliance minimization, the multi-material topology optimization with reliability constraints is established. The corresponding non-probability uncertainties are described by the evidence theory, and the uniformity processing method is introduced to convert the evidence variables into random variables. The first-order reliability method is employed to search the most probable point under the reliability index constraint, and then the random variables are equivalent to the deterministic variables according to the geometric meaning of the reliability index and sensitivity information. Therefore, the non-probabilistic reliability-based multi-material topology optimization is transformed into the conventional deterministic optimization format, followed by the ordered RAMP method to solve the optimization problem. Finally, through numerical examples of 2D and 3D structures, the feasibility and effectiveness of the proposed method are verified to consider the geometrical dimensions and external loading uncertainties.

An isogeometric approach to topology optimization of spatially graded hierarchical structures

This paper presents an isogeometric approach to topology optimization of spatially graded hierarchical structures, which are assumed to be consisted of identical or spatially varying substructures. In this work, the isogeometric analysis (IGA) is adopted for an efficient and accurate performance assessment of spatially graded structures, especially for those with complex geometries. A multi-resolution topology optimization (MTOP) scheme with two distinct mesh discretization levels is used to achieve high-resolution topology representation. In specific, displacement field and topology field are approximated separately on two distinct levels of mesh discretization, where the IGA is performed on a coarse mesh and nodal-based topology design variables are defined on a refined mesh obtained by k-refinement scheme. A projection scheme with the use of non-uniform rational basis spline (NURBS) basis functions is employed to compute the densities at quadrature points from nodal densities variables. The proposed IGA-MTOP-based design framework has threefold merits: a) global structure and constituent substructures are strictly coupled with no assumption on the separation of scales as required in homogenization-based designs, which together with high continuous NURBS basis functions guarantee automatically smooth connection between substructures; b) high-resolution designs with detailed local structural features can be obtained in a computationally high-efficient manner; c) the substructures designed in the common parameter space can be freely transformed to conform the physical space. The effectiveness and robustness of the proposed method are validated by a series of benchmark designs.

TOSG: A Topology Optimization Scheme With Global Small World for Industrial Heterogeneous Internet of Things

In Industrial Internet of Things (IIoT), sensor nodes are vulnerable to withstand node failures due to energy exhaustion or external attacks, which leads to the low connectivity of networks. In this situation, how to improve network reliability has became a crucial problem. Adding a small amount of shortcuts to build a small world model in IIoT not only can reduce the delay, but also increases the reliability of networks. In this paper, we propose a Topology Optimization Scheme with Global Small World (TOSG) based on ant colony for IIoT. First, according to the number of appearing on the all shortest paths obtained by the ant colony optimization algorithm, we give the definition of importance for each node. The node with the highest importance in the communication range of a node is defined as an important node. We can find the important nodes in the network topology so that some shortcuts can be created between them to build a global small world model. The experiment results show that the TOSG model has a smaller average shortest path length and higher reliability compared with Greedy Model with Small World properties and Directed Angulation toward the Sink Node Model.

Crash Model Order Reduction for Efficient Topology Optimization Using the ESLs Method

This paper presents an efficient structural topology optimization strategy for crashworthiness. The proposed method combines the equivalent static loads (ESLs) method with the crash model order reduction method. The ESLs method transforms crashworthiness topology optimization problems into a series of linear static topology problems. The crash model order reduction scheme is applicable to speed up the crash simulation. Therefore, the crashworthiness topology optimization is performed in a reduction manner and the efficiency is improved. The topology optimization results are filtered into a black-white design for the crash simulation to avoid the element distortion problem. The process is repeated until the convergence criteria is satisfied. The effectiveness of proposed method is demonstrated by investing a numerical example. The results show that, the proposed method can efficiently solve structural topology optimization problems for crashworthiness.

NURBS hyper-surfaces for 3D topology optimization problems

A general topology optimization strategy is presented in this study for three-dimensional applications. The approach is based on the combination of a well-established density-based method and the Non-uniform rational basis spline (NURBS) hyper-surfaces formalism. The topology of the structure to be optimized can be embedded in a reference domain and it is opportunely described by means of a suitable NURBS hyper-surface. This choice implies several advantages. On the one hand, the number of design variables (control points and weights of the NURBS hyper-surface) is drastically reduced, when compared to classical density-based approaches, and it is unrelated to the mesh of the finite element model. On the other hand, the topology is described through a purely geometrical entity, while the mesh is utilized only to perform the computation of the relevant physical quantities for the problem at hand. A sensitivity analysis with respect to the new variables set is carried out. The effectiveness of the method as well as the effects of some discrete parameters tuning the NURBS hyper-surface shape are investigated on meaningful benchmarks and results are compared with those provided by the classical Solid Isotropic Material with Penalization approach.

Structural design considering the uncertainty of load positions using the phase field design method

Ordinary topology optimization methods generate a result that is effective only for a specific load position. However, loads are often applied at many uncertain positions rather than at a specific location in most structures. For stability of the structure, it is desirable to guarantee a small amount of structural compliance despite the uncertainty of the load position. In this study, a topology optimization method is proposed to minimize the variation of compliance and its magnitude considering the uncertainty due to the wide range of load locations changes. The mean and the variance of the design objective, i.e., the compliance for each load case at various positions, are directly incorporated into a multi-objective optimization problem so that a similar degree of compliance can be obtained for the entire load case. The phase field design method is used as a topology optimization scheme in conjunction with the finite element method for structural compliance analysis. The reaction-diffusion equation combined with the double well potential functions is employed as the update scheme. Numerical examples for cantilever beam and MBB beam design are presented to demonstrate the validity of the proposed method.

High-efficiency and broadband photonic polarization rotator based on multilevel shape optimization.

We report on a novel photonic polarization rotator design obtained by multilevel shape optimization. The numerical method consists of a topological optimization scheme, improving iteratively the efficiency of the component by modifying its shape on two discrete levels along the etching direction. We numerically show that, compared to state-of-the-art single-level shape optimization, the performances can be drastically improved for a given device length. Next, the polarization conversion efficiency can be further improved up to a computed value of 98.5% with less than 0.35dB insertion losses on a 100nm bandwidth for a 6 μm×1 μm footprint.

An Efficient Topology Optimization Strategy for Structural Crashworthiness Using Model and ESLs Reduction Method

This paper presents an efficient structural topology optimization strategy for crashworthiness. Although equivalent static loads (ESLs) provides a relatively effective way to solve nonlinear dynamic response topology optimization problems, efficiency is still required to improve. To overcome above disadvantage, the proposed method combines the ESLs with model reduction (MR) method. The ESLs method transforms crashworthiness topology optimization problems into a series of linear static topology problems. The model reduction scheme is applicable to reduce the linear matrix equation and ESLs to interface degrees of freedom (DOFs), by selecting interface DOFs between design and non-design space as master DOFs. Therefore, the linear static topology optimization is performed in a reduction manner and the efficiency is improved. The topology optimization results are filtered into a black-white design for the crash simulation to avoid the element distortion problem. The process is repeated until the convergence criteria is satisfied. A numerical example is used to verify the reliability of the proposed method. The results are compared with the dynamic response optimization method using ESLs (ESLSO). The results show that, the proposed method can efficiently solve structural topology optimization problems for crashworthiness.