Rapid Modeling and Design Optimization of Multi-Topology Lattice Structure Based on Unit-Cell Library

Optimal design and modeling of gyroid-based functionally graded cellular structures for additive manufacturing

Topology optimization for concurrent design of layer-wise graded lattice materials and structures

During the last 20 years, structural optimization has become one of the most important topics of engineering applications. Design optimization of structure has been an interesting area of research in the field of engineering design for its ability to short the design cycle and to enhance product quality. Significant research activity has occurred in the area of structural optimization in the last decade. Especially for topology optimization of structure, many new theoretical, algorithmic, and computational contributions have resulted by researchers and engineers. Topology optimization is a powerful tool for global and multi-scale design of macrostructures, microstructures, and the cell of prescribed composite materials. The population based evolutionary algorithms have emerged as powerful mechanism for finding optimum solutions of complex optimization problems in engineering during the last two decades. Evolutionary computation is the study of computational systems which use ideas and get inspiration from natural evolution and adaptation [1]. The thinking has wide application in various engineering fields, such as computer science, artificial intelligence, operations research. Genetic algorithm is another kind of bio-inspired optimization method and it is playing an increasingly important role in studies of complex adaptive systems. Its application ranges from adaptive agents in economic theory to the use of machine learning techniques in the design of complex devices and structures, such as aircraft turbines and integrated circuits [2]. Optimization of structures can be classified into three categories: sizing, shaping, and topology optimization. In the topology optimization, it is concerned with the structure members and connectivity between members. In general, it is easily represented by discrete variables rather than by those used for continuous optimization problems. Topology optimization is the most difficult and complex among three categories and it is special useful in developing innovative conceptual designs. Structural optimization, in particular the topology optimization, has been identified as one of the most challenging tasks in structural design. Various techniques and approaches have been established during the last two decades. Topology optimization usually referred to as layout optimization or general shape optimization [3]. It lets engineers get the optimal topology of structure or new configurations during product design phase, as they are implementing the design of the size

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.

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.

Topology design and structural optimization of Co-Cr frameworks for implant-supported prostheses.

The topology optimization (TO) process has the objective to structurally optimize products in various industries, such as in biomechanical engineering. Additive manufacturing facilitates this procedure and enables the utility of advanced structures in order to achieve the optimal product design. Currently, orthopedic implants are fabricated from metal or metal alloys with totally solid structure to withstand the applied loads; nevertheless, such a practice reduces the compatibility with human tissues and increases the manufacturing cost as more feedstock material is needed. This article investigates the possibility of applying bioinspired lattice structures (cellular materials) in order to topologically optimize an orthopedic hip implant, made of Inconel 718 superalloy. Lattice structures enable topology optimization of an object by reducing its weight and increasing its porosity without compromising its mechanical behavior. Specifically, three different bioinspired advanced lattice structures were investigated through finite element analysis (FEA) under in vivo loading. Furthermore, the regions with lattice structure were optimized through functional gradation of the cellular material. Results have shown that optimal design of hip implant geometry, in terms of stress behavior, was achieved through functionally graded lattice structures and the hip implant is capable of withstanding up to two times the in vivo loads, suggesting that this design is a suitable and effective replacement for a solid implant.

As an increasing need for metal implant species and quantities in the clinical application, the demands of structure for the implants have been increased, accompanying the rapid development of 3D printing technology and the progress of medical combination with engineering also made it possible to fabricate complex implants. On this basis, the topology optimization of structure in the finite element analysis technique has been developed gradually, and the application of this technique has greatly improved the biomechanical properties of implants. This review introduces the applications of topology optimization technology in implant structure design, and summarizes the researches of topology optimization technique in the field of medical implant mainly on the department of maxillofacial surgery and orthopedics. In the field of orthopedics, topology optimization technique is most widely used, and in the structural design of joint prosthesis, internal fixation and spinal implant, the obvious progress was obtained in both theory and practice. Finally, the paper put forward the prospect of the trend for the topology optimization design of metal implants in the future. Key words: Topology optimization; Implants; Maxillofacial surgery; Orthopedics.

This paper will give a short survey about topology optimization of structures. It is particularly focused on topological shape optimization of structures using level-set methods, including the level-set based standard methods and the level-set based alternative methods. The former often directly solve the Hamilton-Jacobi partial differential equation (H-J PDE) to obtain the boundary velocity field using Finite Differential Methods (FDM), and the later commonly employ parametric or equivalent methods to evaluate the velocity field without directly solving the H-J PDE. The unique characteristics of the level-set based topology optimization methods are discussed, and a future perspective and prospects in this research area is also included. A benchmark numerical example is used to showcase the effectiveness of the level-set based methods.

A methodology is developed for optimal structural topology design subject to several performance constraints. Eight-node solid elements are used to model the initial structure, which is a uniform solid block satisfying the boundary conditions and subjected to external loading. The Young modulus of each solid element or group of elements is used as redesign variable. A minimum change function is used as an optimality criterion. Performance constraints include static displacements, natural frequencies, forced response amplitudes, and static stresses. These constraints are treated by the large admissible perturbation methodology which makes it possible to achieve the performance objectives incrementally without trial and error or repetitive finite element analyses for changes in the order of 100–300%. Thus, the optimal topology is reached in about four to five iterations, where each iteration includes one finite element analysis and setting of an upper limit for the value of the modulus of elasticity to produce a manufacturable structure. Several numerical applications are presented using three different benchmark structures to demonstrate the methodology and the impact of performance constraints on the generated topology.

Additive manufacturing (AM) has enabled great application potential in several major industries. The footwear industry can customize shoe soles fabricated by AM. In this paper, lattice structures are discussed. They are used to design functional shoe soles that can have controllable stiffness. Different topologies such as Diamond, Grid, X shape, and Vintiles are used to generate conformal lattice structures that can fit the curved surface of the shoe sole. Finite element analysis is conducted to investigate stress distribution in different designs. The fused deposition modeling process is used to fabricate the designed shoe soles. Finally, compression tests compare the stiffness of shoe soles with different lattice topologies. It is found that the plantar stress is highly influenced by the lattice topology. From preliminary calculations, it has been found that the shoe sole designed with the Diamond topology can reduce the maximum stress on the foot. The Vintiles lattice structure and the X shape lattice structure are stiffer than the Diamond lattice. The Grid lattice structure buckles in the experiment and is not suitable for the design.

This article proposes an efficient parameterized level set method (PLSM) for structural topology optimization design with minimum compliance as the objective function and volume fraction as the constraint condition. In the stage of establishing the optimization model, the level set function (LSF) is interpolated using compactly-supported radial basis functions (CS-RBFs) to transform the Hamilton-Jacobi partial differential equation (PDE) into ordinary differential equations (ODEs), thereby making the evolution of the LSF more convenient and efficient, and ensuring the smoothness of the optimization result boundary. The method of moving asymptotes (MMA) is used for solving the established optimization model, and meanwhile the shape sensitivity constraint factor is added to improve computational efficiency. During the evolution of the LSF, an approximate re-initialization scheme is employed to prevent the gradient of the LSF boundary from being too large or too small, thereby improving the numerical stability and the convergence speed of structural topology optimization process. Furthermore, the proposed method is also extensible and applicable to topology optimization of multi-material structures. The feasibility and effectiveness of this method have been verified through several typical numerical examples involving topology optimization of single-material structures and multi-material structures within the framework of minimum compliance design. HIGHLIGHTS An efficient parameterized level set method using the approximate re-initialization scheme is proposed for structural topology optimization. The approximate re-initialization scheme is employed when solving the parameterized level set function via the MMA algorithm. This scheme can prevents the gradient of the level set function boundary from being too large or too small, making the level set function update more stable and accelerating the convergence speed of structural topology optimization. The effectiveness and feasibility of the proposed method are demonstrated through examples of single-material and multi-material structural topology optimization.

The robotic arm is one of the vital components of robot assembly. The purpose of the robotic arm is to transmit power and conduct the desired motion, i.e., translation or rotation. Robotic limbs are designed and constructed to execute certain tasks with a high degree of speed, accuracy, and efficiency. This research focuses on to enhancing the strength-to-weight ratio of robotic arm using certain techniques of additive manufacturing, i.e., topology optimization and lattice structure. Employing the finite element analysis, the impact of weight reduction optimization on structural parameters such as stress and deformation in the current design is assessed using ANSYS R18.1 for FE analysis and Creo parametric 7.0 design software for computer-aided design modeling. Observations reveal that the 0.5 and .4 scale lattice structure designs have deformation of 0.01453mm and 0.01453 mm respectively though the generic design has 0.01043 mm deformation. Notably, the 0.5 scale lattice of the robotic arm exhibits a 31.08% higher equivalent stress than the generic design with 29.3%. reduction in mass of the robotic arm. These findings highlight the efficacy of lattice structures for optimizing the robotic arm’s performance, contributing to advancements in power-efficient robot assembly processes.

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.

Isogeometric analysis (IGA) connects CAE with standard CAD design tools and has been utilized for a decade in structural optimization. FEA has a number of drawbacks, including a lack of linkage between analytic and geometric models, a shortage of continuity between components, and a lack of accuracy for high-order elements. Isogeometric analysis effectively overcomes these obstacles. This paper proposes the isogeometric topological optimization mathematical model depending on the asymmetric constitutive relationship of tension and compression microscopic materials. We provide a new density-based topology optimization formulation in which the design domain is limited to the B-spline space. A rectangular domain with a tensor-product is embedded in a design domain that is arbitrarily shaped. The density field is represented using B-splines. The intrinsic filter provided by the B-spline representation for topology optimization is governed by the degrees of B-spline and the knot spans. This B-spline effectively removes numerical artifacts and controls the minimum feature-length in; when the B-spline basis functions span many analysis elements. Benchmark problems in structural topology optimization are computed through Evolutionary Structural Optimization (ESO) algorithm. Comparisons of the optimal structure topologies using finite element analysis and isogeometric collocation methods are analyzed. The influence of different tension-compression stiffness ratios on the final structure topologies is listed and analyzed. The numerical results show the reliability and performance of the proposed mathematical formulation and asymmetry of natural structure.