Shape Control for Composite Structures of Photostrictive Actuators Using Topology Optimization Method

Shape morphing of laminated composite structures with photostrictive actuators via topology optimization

According to the requirements of the aerospace industry for high strength, high stiffness, and lightweight structural parts, topology optimization has been proved to be an effective product design method. As one of the most conceptual and prospective structural optimization design methods, topology optimization intends to seek the optimal layout of materials in an allowed design region under a given load and boundary conditions. Thus, the object of study in the article is the method of topological optimization of aircraft structures. The goal of this article is to analyze the existing approaches, algorithms, as well as application of the method of topological optimization in the aerospace field in applied problems. The tasks are to describe the existing various approaches methods, features, and research directions of topological optimization as well as to study the possibility of application in the manufacturing process of composite structures. The following results were obtained. The optimization methods are briefly explained and compared, and the advantages and limitations of each approach are discussed. The various ways of simultaneous optimization of fiber orientation and structural topology were described and analyzed. The features of different methods of continuous fiber orientation optimization method were reviewed. The discrete fiber orientation optimization methods were represented. The possibility of multi-scale concurrent topological optimization was described. The combination of topology optimization and additive manufacturing was considered. Finally, the topology optimization of FRC structures which have been resolved in literature are reviewed and the potential research fields requiring more investigation are pointed out. Conclusions. In the article, a comprehensive review of the topology optimization design of FRC structures was presented. The promising way is to combine topology optimization with additive manufacturing techniques. However, these proposed methods may not suitable for other more complex problems, such as bucking stability and natural frequency. Hence, the topology optimization design of complex FRC components under complicated conditions is the main challenge in the future. This can be a new trend in the topology design of FRC structures.

In recent years, additive manufacturing has been gaining ground among traditional manufacturing methods in many different applications. This is mainly due to its ease of prototyping, material savings and above all the highly complex geometries that can be achieved. Despite its many advantages, the use of additive manufacturing in electrical machines has been limited. The lack of maturity of the manufacturing processes and the increase in losses when applying additive approaches to some parts, mainly stators, have led little implementation in the field of electrical machines. The geometric freedom offered by additive manufacturing paves the way for the use of novel optimisation techniques, such as topology optimisation. Traditionally, topology optimisation has not been widely used because the complex geometries obtained by these algorithms are not easily produced by traditional manufacturing methods. However, thanks to additive manufacturing, topology optimisation has started to be used, mainly for mechanical applications and it has demonstrated its ability to reduce weight without compromising mechanical stability in several cases. Nevertheless, topology optimisation for physics other than mechanical has not been thoroughly studied, let alone for the simultaneous optimisation of different physics. In view of the scenario described, this thesis investigates the benefits that additive manufacturing and topology optimisation can bring to the design of electrical machines. For the additive manufacturing of electrical machines, a thorough literature review is carried out on the application of this manufacturing approach to different parts of electrical machines, active and non-active. Two main case studies are presented: in the first, the rotor, the shaft, the stator and the housing of an aerospace actuator are manufactured by L-PBF in FeCoV and the assembled actuator is tested. In the second case, a rotor is manufactured in FeSi by LP- DED. Finally, not considered an additive manufacturing case study itself in this thesis, but two electrical conductor prototypes are manufactured in CuCr1Zr and an additional geometry is manufactured in AlSi10Mg by L-PBF. With regard to topology optimisation of electrical machines, a description of the main topology optimisation methods used is given and their application to electrical machine components is presented. In a similar way to additive manufacturing, two case studies are analysed. First, a novel multiphysics - mechanical and electromagnetic - topology optimisation method is presented, in which the rotor and the stator of a permanent magnet motor are optimised simultaneously. This method is compared with two methods found in the literature, SIMP and on-off. Secondly, another topology optimisation method is described and applied to an electrical conductor model. The proposed algorithm involves a multiphysics - thermal and electromagnetic - hybrid parametric topology optimisation approach. Two reduced length geometries and one full length prototype are built via additive manufacturing. Finally, conclusions regarding additive manufacturing and topology optimisation of electrical machines are drawn from the work presented in this thesis. Future lines of work for additive manufacturing and topology optimisation of electrical machines are also presented.

The numerical method of stamp topological optimization taking into account fatigue strength is presented in the work. It is proposed to take into account the restrictions on the stress state in accordance with the curve of the dependence of the maximum stresses on the number of loading cycles in the ESO topological optimization method. An approach to the selection of the evolutionary coefficient with a step-by-step increase in the rejection coefficient is proposed when constructing an iterative scheme for the rejection of elements by the method of topological optimization. The calculation of the stamp optimal topology with a decrease in volume due to the removal and redistribution of material was carried out in the study. The new geometric model of the optimal topology stamp is based on the predicted distribution of elements with a minimum stress level. The verification calculation of the stress state of the stamp of optimal topology with an assessment of fatigue strength was carried out in the work. The numerical calculation was carried out using the finite element method in the Ansys software package. The minimized stamp volume decreased by 35% according to the calculation results. The results of the study can be further applied in the development of topological optimization methods and in the design of stamping tools of optimal topology.

Aiming at the problems of a low material utilization rate and uneven stress distribution of cast-steel support joints in cable dome structures, topology optimization and additive manufacturing methods are used for optimization design and integrated manufacturing. First, the basic principle and calculation process of topology optimization are briefly introduced. Then, the initial model of the support joint is calculated and analyzed by using the universal software ANSYS Workbench 2020R2 and Altair OptiStruct, and the optimized joint is imported into Discovery Live to smooth the surface. The static behaviors of three types of joints (topology-optimized joints, joints after the smoothing treatment, and joints from practical engineering) are compared and analyzed. Finally, the joints are printed by using fused deposition modeling (FDM) technology and laser-based powder bed fusion (LBPBF) technology in additive manufacturing. The results show that the new support joint in the cable dome structure obtained by the topology optimization method has the advantages of a novel shape, a high material utilization rate, and a uniform stress distribution. Additive manufacturing technology can allow the manufacture of complex shape components with high precision and high speed. The combination of topology optimization and additive manufacturing effectively realizes the advanced design and integrated manufacturing of support joints for cable dome structures.

Structural topology optimization.- On basic properties of Michell's structures.- Validation of numerical method by analytical benchmarks and verification of exact solutions by numerical methods.- Introduction to shape and topology optimization.- Homogenization method for shape and topology optimization.- Level set method for shape and topology optimization.- Compliance minimization of two-material elastic structures.- Some notes on topology optimization of vibrating continuum structures.- Topology optimization of vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps.- On optimum shape design and periodicity of band-gape beam structures.- Topological design for minimum dynamic compliance of continuum structures subjected to forced vibration.- Topological design for minimum sound emission from bi-material structures subjected to forced vibration.- Discrete material optimization of vibrating laminated composite plates for minimum sound emission.- Optimization of diffusive transport problems.- Fluid topology optimization: stokes and Navier-stokes models.- Topology optimization of coupled multi-physics problems.- Topology optimization based on the extended finite element method.- Topology optimization of meso- and nano-scale problems.- Topology optimization under uncertainty.- A brief review of numerical methods of structural topology optimization.- The free material design in planar elasticity.

Random variable of thermo-mechanical coupling (TMC) structure is analyzed first, then the topology optimization model of TMC compliant mechanism is established. According to the uncertainty factors such as temperature, load, volume ratio and thermal expansion coefficient in the process of topology optimization, the robust reliability optimal design method is introduced into the topology optimization process. The various factors on the sensitivity of topology optimization process is analyzed, the best match between various factors is find out, which make the product has robust reliability for the change of the uncertainty. The residual analysis for the most sensitive factors is carried out. Finally the correctness and validity of the method is verified with an example. Introduction When we study the compliant mechanisms by adopting topological optimization method, we only need to give design domain and allocate input and output position, no need from the perspective of a known rigidity. The mechanism come from this method have a input and output relationship of optimized “force—displacement”, thus it attracts people’s attention. Topology optimization research is developing from certain topology optimization direction to reliable topology optimization direction. Jinqing Zhan proposed a reliable topology optimization method of compliant mechanism based on infrastructure method. KHARMANDA proposed a reliable topology optimization method. Zhaokun Li proposed a geometric nonlinear topology optimization research method based on reliable compliant mechanism. Their research turned out that the mechanism based on reliable topology optimization is more reasonable than the mechanism based on certain topology optimization. Yongcong Kuang build a level set function to design variable, stiffness minimization, and proposed corresponding optimization algorithm. Mingtao Cui established a monolithic compliant mechanism multi-target reliable topology optimization design dual mathematical model. This paper combines topology optimization process of compliant mechanism and robust reliability optimal design, analyzes the sensitivity of uncertainty random variables such as design domain’s size, external load and temperature in topology optimization process. Then get the best combination among these random variables. Random Variable Coupling Field Analysis Hot objects will produce thermal expansion, thus caused by the thermal deformation and displacement of combined action of mechanical load and temperature load structure called a hot solid coupling structure, the finite element balance equation :

Non-contact wireless actuation offers many advantages to precision control, as compared with conventional hard-wired actuation mechanisms. High-energy laser or ultraviolet lights irradiating on photostrictive materials can induce a photodeformation process involving two fundamental effects: 1) the photovoltaic effect and 2) the converse piezoelectric effect. This photodeformation process transforms photonic energy to mechanical strain/stress that can be directly used for actuation and control applications. With specific design configurations, the photodeformation process of photostrictive actuators can induce various control forces and moments applied to precision manipulation and control of mechatronic and structronic systems. In this study, fundamental photodeformation coupling mechanisms among photo-thermo-electromechanical/control fields are investigated and parametric evaluation of various design parameters of a hybrid photostrictive/elastic beam is conducted. A mathematical model for a laminated beam with segmented photostrictive actuators is defined, followed by photodeformation induced modal control forces and moments of segmented actuators. Characteristics of actuation and control effectiveness of distributed photostrictive actuators at various locations, natural modes and illumination intensities are analyzed in case studies. The most effective actuator location(s) for controlling the first four beam modes are illustrated. Finally, with scheduling light irradiations on various photostrictive actuators, one can control multiple beam modes, allowed by control electronics and material response.

A smart structure involves distributed actuators and sensors, and one or more microprocessors that analyze the responses from the sensors and use distributed-parameter control theory to command the actuators to apply localized strains to minimize system response. A smart structure has the capability to respond to a changing external environment (such as loads or shape change) as well as to a changing internal environment (such as damage or failure). It incorporates smart actuators that allow the alteration of system characteristics (such as stiffness or damping) as well as of system response (such as strain or shape) in a controlled manner. Many types of actuators and sensors are being considered, such as piezoelectric materials, shape memory alloys, electrostrictive materials, magnetostrictive materials, electro- rheological fluids and fiber optics. These can be integrated with main load-carrying structures by surface bonding or embedding without causing any significant changes in the mass or structural stiffness of the system. Numerous applications of smart structures technology to various physical systems are evolving to actively control vibration, noise, aeroelastic stability, damping, shape and stress distribution. Applications range from space systems, fixed-wing and rotary-wing aircraft, automotive, civil structures and machine tools. Much of the early development of smart structures methodology was driven by space applications such as vibration and shape control of large flexible space structures, but now wider applications are envisaged for aeronautical and other systems. Embedded or surface-bonded smart actuators on an airplane wing or helicopter blade will induce alteration of twist/camber of airfoil (shape change), that in turn will cause variation of lift distribution and may help to control static and dynamic aeroelastic problems. Applications of smart structures technology to aerospace and other systems are expanding rapidly. Major barriers are: actuator stroke, reliable data base of smart material characteristics, non-availability of robust distributed parameter control strategies, and non-existent mathematical modeling of smart systems. The objective of this paper is to review the state-of-the-art of smart actuators and sensors and integrated systems and point out the needs for future research.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

This thesis aims at understanding and improving topology optimization techniques focusing on density-based level-set methods and geometrical nonlinearities. Central in this work are the numerical modeling of the mechanical response of a design and the consistency of the optimization process itself. Concerning the first topic, we investigate different means to improve the robustness of density-based numerical models including geometrical nonlinearities. The conventional approach (scaling the local material properties) can result in convergence problems due to excessive deformation in low-stiffness finite elements. To avoid excessive deformation, we combine the element connectivity parameterization method (adapting the connectivity between finite elements) with level-set-based topology optimization. Furthermore, we achieve greater robustness of analysis method using a second and improved approach called element deformation scaling. This approach eliminates the need for solving internal equilibrium equations (needed for the element connectivity parameterization method) via an explicit relation between the local internal and global external displacement field. The second focus of this thesis is on the optimization process of level-set-based topology optimization, and in particular its numerical consistency. We observe that signed-distance reinitialization of the level-set function affects the shape of a design in the optimization process. To minimize this effect, we propose a discrete level-set method that is based on an approximate Heaviside function and focusing on the implementation. Furthermore, we also propose a level-set-based topology optimization method using an exact Heaviside function and mathematical programming that effectively eliminates the need for reinitialization. We demonstrate that our density-based level-set method is closely related to conventional density-based topology optimization methods, while offering the advantage of more control over the geometrical complexity. On the other hand, we confirm that the dependence of the final result on the initial design which remains one of the big challenges for level-set-based topology optimization. The potential of the proposed level-set method is shown by applying it on problems with stress constraints and geometrical nonlinearities and performing manufacturing tolerant topology optimization. Finally, this thesis offers a review of level-set methods for structural topology optimization to identify and discuss the different approaches that are available in literature. We can distinguish between level-set methods by examination of their design parameterization, sensitivities, update procedures and regularization techniques. A level-set-based design parameterization offers the advantage of a crisp distinction between subdomains. For this reason, X-FEM approaches and conforming discretizations are an interesting option to retain the crisp nature of the level-set-based description of the design. Many level-set methods are combined with density-based numerical models and are, therefore, closely related to conventional density-based topology optimization methods. In particular, recently proposed projection methods have much in common with a level-set-based design description. The results of level-set-based TO methods often rely heavily on regularization techniques that introduce inconsistencies in the optimization process. Numerical consistency does not necessarily lead to the best search direction, but is essential to find a Karush-Kuhn-Tucker point of the discretized optimization problem.

With the rapid advancement of computing technology, mathematical modeling and computer simulations have become common and standard methods for design of complex systems. To exercise these models intelligently and eliminate the burden of manual iteration, manipulating inputs and reviewing outputs, optimization strategies are applied in a simulation-based design environment. In reality, the knowledge that engineers have about the design problem is imperfect and incomplete, uncertainty always exists in simulation-based design. The conventional deterministic optimization techniques do not consider the impact of such uncertainties. If the system responses driving the design decisions are very sensitive to these uncertainties, serious problems might confront the designer. Performance of the actual system may differ greatly from expected optimum performance. Again, if the design solution is near one or more constraint boundaries, then even slight uncertainties or changes in the operating environment could produce failed, unsafe designs, and/or result in substantial performance degradation. In recent years, the concept of reliability and robust design has become very popular. Probabilistic design analysis and statistical modeling allow the identification of designs that qualify as not only feasible, but as consistently feasible in the face of uncertainty. Reliability based topology optimization (RBTO) extends the reliability notion to the area of structural topology optimization. Although reliability based design optimization (RBDO) is a well established research area, very few work has been presented in the area of RBTO. In this study, we give an overview of the various works done in the field of RBTO. Ever since Bendsoe and Kikuchi introduced the topology optimization using a homogenization method, many topology optimization methods have been developed for the both linear and nonlinear structures. Traditional topology optimization methods drive the topology of a structure to an optimum design based on the constraint on mass. Kharmanda et al. introduced reliability constraints in deterministic topology optimization problem. They proposed a heuristic strategy that aims to reduce mass while improving the reliability level of the structure without greatly increasing its weight. But the limit state function used by them was not based on failure criteria for the structure. Their formulation considered uncertainty with respect to ∗Design Automation Laboratory †Advisor geometrical dimension and applied load only. Also their reliability analysis seems to be independent of the boundary and loading condition, so their results showed similar values for the uncertain variables for different structures. Tovar et al. have developed the Hybrid Cellular Automaton (HCA) method for structural synthesis of continuum material where the state of each cell is defined by both density and strain energy. In Agarwal, a decoupled RBDO approach is employed such that the topology optimization is separate from the reliability analysis. Patel et al. showed the use of RBTO using the gradient free Hybrid Cellular Automata (HCA) method. Their formulation incorporates uncertainty with respect to material property also. They considered limit state function based on failure modes on the output displacements. This study aims at giving a comparative study on these methods. It points out the advantages and disadvantages of the methods, and their significance in the field of RBTO. As large numbers of design variables are associated with continuum topology optimization problems, RBTO methods are inherently computationally expensive because of additional required system analysis associate with RBDO. Based on the observations, this study presents an efficient method for incorporating reliability analysis in topology optimization.

To date the design of structures via topology optimisation methods has mainly focused on single-objective problems. However, real-world design problems usually involve several different objectives, most of which counteract each other. Therefore, designers typically seek a set of Pareto optimal solutions, a solution for which no other solution is better in all objectives, which capture the trade-off between these objectives. This set is known as a smart Pareto set. Currently, only the weighted sums method has been used for generating Pareto fronts with topology optimisation methods. However, the weighted sums method is unable to produce evenly distributed smart Pareto sets. Furthermore, evenly distributed weights have been shown to not produce evenly spaced solutions. Therefore, the weighted sums method is not suitable for generating smart Pareto sets. Recently, the smart normal constraints method has been shown to be capable of directly generating smart Pareto sets. This work presents an updated smart normal constraint method, which is combined with a bi-directional evolutionary structural optimisation algorithm for multi-objective topology optimisation. The smart normal constraints method has been modified by further restricting the feasible design space for each optimisation run such that dominant and redundant points are not found. The algorithm is tested on several different structural optimisation problems. A number of different structural objectives are analysed, namely compliance, dynamic and buckling objectives. Therefore, the method is shown to be capable of solving various types of multi-objective structural optimisation problems. The goal of this work is to show that smart Pareto sets can be produced for complex topology optimisation problems. Furthermore, this research hopes to highlight the gap in the literature of topology optimisation for multi-objective problems.

Topology optimization method is a novel design method for MEMS actuators. In this paper, a multi-objective design method is introduced into topology optimization for MEMS actuators. Some important factors for multi-objective design of MEMS actuators are deeply researched. A multi-objective topology optimization method based on minimal structural compliance and maximal structural output displacement of MEMS actuators is proposed and the corresponding governing equation for topology optimization is established. A sensitivity analysis of adjoint method is proposed to analyze topology optimization design of multi-objective MEMS actuators. Meanwhile, GCMMA (globally convergent version of the method of moving asymptotes) algorithm is used in optimization. Two numerical examples of MEMS actuators verified the effectiveness of above theory and algorithm.

Static shape control of adaptive structures is currently an important and active research area in the smart structures field. Numerous actuation schemes using smart materials have been proposed and developed for shape control of structures. While the results of the smart material based technology is promising, it is also, however, showing more serious limitations such as scalability of laboratory-scale prototype models into real-scale models. In addition, the smart material based approach for shape control requires a multitude of actuators distributed throughout the host structure, the hence, complicates the control system. This paper introduces a novel alternative design concept for shape control of flexible adaptive structures using a single actuator which need not necessarily be smart material based. The novelty in this concept is that it employs distributed compliance in design--through compliant mechanisms, a class of mechanisms that transmit motion through inherent flexibility--rather than distributed actuation to accomplish the shape changes. The paper outlines a method for synthesis of such compliant mechanisms. The concept, and the synthesis method are illustrated through an example where a specified shape change in the leading edge of an airfoil structure is accomplished. The new concept has a great potential to not only eliminate the scalability problem, but also reduce the control complexity, the weight, and cost of the entire system as well.

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.