Topology Optimization Method For Design Research Articles

Topology optimization structure design of shape memory alloy with multiple constraints

As an emerging functional material, shape memory alloy (SMA) exhibits remarkable mechanical properties and finds diverse applications across industries. This paper presents a topology optimization framework based on the bi-directional evolutionary structural optimization (BESO) method for designing SMA structures, which maximizes structural stiffness under multiple constraints of specified volume fraction, displacement, and fundamental frequency. A phenomenological constitutive model is utilized to simulate the mechanical behavior of SMA accurately. The unit virtual load method is employed to determine sensitivities. Several optimized SMA beam structures and simply-supported cube structures are designed under different thermal-mechanical loads, and their displacement, mean compliance, and fundamental frequency are evaluated throughout the optimization process. The results demonstrate that the proposed framework successfully customizes the SMA topology structure with adjustable displacement and fundamental frequency, and the optimized schemes exhibit more considerable deformation and more uniform mechanical properties than their initial counterparts. The proposed framework has higher computational efficiency than the traditional SIMP-based SMA topology optimization design method.

Topology Optimization Design Method for Acoustic Imaging Array of Power Equipment.

Acoustic imaging technology has the advantages of non-contact and intuitive positioning. It is suitable for the rapid positioning of defects such as the mechanical loosening, discharge, and DC bias of power equipment. However, the existing research lacks the optimization design of microphone array topology. The acoustic frequency domain characteristics of typical power equipment are elaborately sorted out. After that, the cut-off frequencies of acoustic imaging instruments are determined, to meet the needs of the full bandwidth test requirements. Through a simulation calculation, the circular array is demonstrated to be the optimal shape. And the design parameters affect the imaging performance of the array to varying degrees, indicating that it is difficult to obtain the optimal array topology by an exhaustive method. Aimed at the complex working conditions of power equipment, a topology optimization design method of an acoustic imaging array for power equipment is proposed, and the global optimal solution of microphone array topology is obtained. Compared with the original array, the imaging performance of the improved LF and HF array is promoted by 54% and 49%, respectively. Combined with the simulation analysis and laboratory test, it is verified that the improved array can not only accurately locate the single sound source but also accurately identify the main sound source from the interference of the contiguous sound source.

A dynamic topology optimization design method based on multiple domain variable parameters

Topology optimization has been extensively studied for obtaining desired functional performances of a structure within a predefined design domain. However, existing topology optimization approaches mainly focus on the static structure. Additionally, a structure is generally consisted of multiple materials and its loading state is quite complicated in practical applications, which are seldom considered simultaneously during design optimization. In this paper, a dynamic topology optimization design method based on multiple domain variable parameters is proposed to solve these issues. First, a structure is divided into multiple domains, and an optimal topology model of discrete structure is proposed. Then, the constraints are relaxed and a per-element variable is introduced to process the design variables continuously. To eliminate the undesirable checkerboard patterns, a filtering method is proposed and an approach of projection is presented for determining the volume of the projected structure according to the practical design requirements. After that, a dynamic continuous optimization model is put forward for solving the optimal solution of the complex structure under various working conditions. Finally, the effectiveness and efficiency of the proposed method are validated by constructing a topology optimized link of the press.

Research on topology optimization method of surface support structure based on leaf vein growth process

In this paper, a biomimetic topology optimization design method that simulates the growth pattern of leaf veins is proposed for the design of the support structure of ultra-light airfoil-like solar cells in the solar powered unmanned aerial vehicle. This method simulates the optimal growth process of main vein morphology through the topology change of dynamic point groups to obtain an optimized topological main support structure and then generates a Voronoi grid structure in the area surrounded by the main support structure to increase the local support for the battery. The whole process is combined with genetic algorithm to simulate the optimal distribution strategy of leaf vein growth by inputting a small number of parameters. Compared with the traditional grid support structure, the support structure obtained by simulating the leaf vein growth optimization strategy can provide more efficient support for the solar panel and avoid damage to the solar cell.

Multiscale concurrent topology optimization of hierarchal multi-morphology lattice structures

This paper proposes a multiscale concurrent topology optimization method for design of hierarchal multi-morphology lattice structures (HMMLSs), which features in the Kriging metamodel assisted Uniform Multiphase Materials Interpolation (KUMMI) model and the sigmoid function (SF) based hybrid transition strategy. Specifically, level set functions are adopted to model hierarchal lattice unit cells (LUCs). Then LUCs with different morphology are treated as distinct lattice materials (LMs) and the SF-based hybrid transition strategy is employed to realize smooth transition between multi-morphology LUCs. Besides, Kriging metamodels are constructed to predict the equivalent properties of LUCs efficiently so that the topology optimization of HMMLSs can be achieved with an affordable computational cost. Two kinds of design variables are involved in the topology optimization of HMMLSs, where discrete variables indicate the categories of lattice materials and continuous variables determine the relative densities of lattice microstructures. The proposed KUMMI model can couple the two kinds of design variables dexterously to realize concurrent optimization of relative densities of LUCs, and distribution regions and percentages of different LMs within HMMLSs. Several numerical examples are presented to demonstrate the effectiveness and applicability of the proposed method. Results indicate the optimized HMMLSs exhibit rational distribution of hierarchal multi-morphology LUCs, hence achieving superior structural performance.

Multi-Scale Topology Optimization of Femoral Stem Structure Subject to Stress Shielding Reduce.

Hip replacement femoral implants are made of substantial materials that all have stiffness considerably higher than that of bone, which can cause significant bone resorption secondary to stress shielding and lead to severe complications. The topology optimization design method based on the uniform distribution of material micro-structure density can form a continuous mechanical transmission route, which can better solve the problem of reducing the stress shielding effect. A multi-scale parallel topology optimization method is proposed in this paper and a topological structure of type B femoral stem is derived. Using the traditional topology optimization method (Solid Isotropic Material with Penalization, SIMP), a topological structure of type A femoral stem is also derived. The sensitivity of the two kinds of femoral stems to the change of load direction is compared with the variation amplitude of the structural flexibility of the femoral stem. Furthermore, the finite element method is used to analyze the stress of type A and type B femoral stem under multiple conditions. Simulation and experimental results show that the average stress of type A and type B femoral stem on the femur are 14.80 MPa, 23.55 MPa, 16.94 MPa and 10.89 MPa, 20.92 MPa, 16.50 MPa, respectively. For type B femoral stem, the average error of strain is -1682με and the average relative error is 20.3% at the test points on the medial side and the mean error of strain is 1281με and the mean relative error is 19.5% at the test points on the outside.

A level set driven concurrent reliability-based topology optimization (LS-CRBTO) strategy considering hybrid uncertainty inputs and damage defects updating

With the diversification of engineering structure performance requirements and the continuous development of structural design refinement, it puts forward higher requirements for lightweight design of structures in terms of concurrent design and reliability design. It is necessary to develop advanced design technology. This paper focuses on the influence of multi-source hybrid uncertainties and defect damage in the design process and proposes a concurrent reliability-based topology optimization design method. Based on the collocation method, the propagation analysis of hybrid uncertainties is realized. A performance reduction method considering defect damage is proposed. Furthermore, the parameter iteration strategy of the optimization criterion method is improved. Based on the sensitivity analysis of a series of parameters, the gradient optimization algorithm is used to solve the optimization model. Finally, three numerical examples are given to illustrate the effectiveness and necessity of the proposed method.

基于BESO的产品结构拓扑优化设计方法研究

基于BESO的产品结构拓扑优化设计方法研究

Topology Optimization Design of an Active Deformable Mirror Based on Discrete Orthogonal Zernike Polynomials

In order to design an active deformation mirror for projection objective aberration imaging quality control, a topology optimization design method of active deformation mirrors based on discrete orthogonal Zernike polynomials is proposed in this paper. Firstly, in order to solve the problem that continuous Zernike polynomials do not have orthogonality on the discrete coordinates inside the unit circle, which causes the instability of topology optimization results, discrete orthogonal Zernike polynomials are used to characterize the active deformation mirror wave aberrations. Then, the optical and structural deformations are combined to establish an optical-mechanical coupling topology optimization model with the help of the variable density method to derive the sensitivity of the mathematical model. Finally, a wave aberration corrected deformation mirror in an optical machine system is used as an arithmetic example for topology optimization, and the results show that the absolute value of the Zernike coefficient Z4 after optimization is improved by nearly one order of magnitude compared with the value before optimization, and the vibration characteristics of the optimized structure meet the design requirements. The optimization effect is significant, which improves the optical performance of the deformed mirror and provides a new scheme for the design of the deformed mirror structure which has a certain practical value for engineering.

Topology and dimension synchronous optimization design of 5-DoF parallel robots for in-situ machining of large-scale steel components

Robotic machining has been successfully applied in thin-walled aluminum alloy components, but its ability to machine large steel components in-situ remains to be improved. To address this issue, a class of five-degree-of-freedom (5-DoF) parallel machining robots with high stiffness-mass ratio, easy installation, compact structure and reconfigurability is designed. To solve the problem of separation of topology and dimension designs, a topology and dimension synchronous optimization design method is proposed by parametric characterization and performance differential map of the robot. Three performance indices, namely, axial stiffness, feed stiffness, and mass are mainly considered. The influences of topology and layout on the performance are extensively investigated. We developed a full-size prototype according to the optimization results. Prototype data demonstrates that the 5-DoF parallel robot offers satisfactory static behavior, thereby fulfilling the essential requirements for the in-situ machining of large-scale steel components. Lastly, several in-situ machining robotic solutions are presented, thereby laying the foundation for other in-situ machining of large-scale steel components.

Topology optimization of structures subject to non-Newtonian fluid–structure interaction loads using integer linear programming

This paper proposes a topology optimization design method for fluid–structure interaction (FSI) problems considering Non-Newtonian fluid such as blood and polymer solution. Non-Newtonian fluid does not obey the Newtonian relationship between the shear stress and shear rate. Fluid–structure interaction involving Non-Newtonian fluid has a wide range of application in oil and gas, chemical, food industries, microfluidics, and bio-engineering. We solve a compliance minimization problem subject to volume constraints of structures under FSI loads considering Non-Newtonian laminar flow. The structure is considered to undergo small deformation. The TOBS (Topology Optimization of Binary Structures) method is applied to solve the material distribution problem. The TOBS approach uses binary {0,1} design variables, which can be advantageous when dealing with design-dependent physics interactions, e.g., in cases where fluid–structure boundaries are allowed to change during optimization. The finite elements method is used to solve the fluid–structure equations and output the sensitivities using automatic differentiation. The TOBS optimizer provides a new set of {0,1} variables at every iteration. Optimization results show that Non-Newtonian effects have a significant influence on FSI design.

Kriging-assisted design of functionally graded cellular structures with smoothly-varying lattice unit cells

Cellular structures in nature have attracted great attention in the field of structural optimization. This paper proposes a Kriging-assisted topology optimization method for design of functionally graded cellular structures (FGCS), which are infilled by smoothly-varying lattice unit cells (LUCs). Specifically, LUCs are depicted by level set functions and the shape interpolation method is employed to generate sample LUCs. Then, one Kriging metamodel is constructed to predict the mechanical properties of LUCs within FGCS, so as to reduce the computational expense involved in finite element analysis of LUCs. Meanwhile, the other Kriging metamodel is created to predict the values of shape interpolation function, and a Kriging-assisted morphological post-process method is put forward to achieve the smooth transition between adjacent graded LUCs. In the proposed method, the effective densities, mechanical properties, and geometrical configurations of LUCs are coupled by Kriging metamodels, so that the multiscale design of FGCS can be realized at a low computational burden by optimizing the distribution of elemental densities, and this also paves the way for design of FGCS with irregular geometries by morphological post-process and geometry reconstruction. Numerical examples are presented to validate the accuracy and effectiveness of the proposed method for design of FGCS. What is more, the design of a pillow bracket with a slightly complex geometry is provided to illustrate the engineering application of the proposed method. The results indicate that the proposed method is effective and universal for designing FGCS with smoothly-varying LUCs.

Topology optimization design and experimental validation of an acoustic metasurface for reflected wavefront modulation

Based on a level set-based topology optimization method, this study designs an acoustic metasurface capable of tailoring reflection wave arbitrarily. The present metasurface is composed of a periodic array of supercells and the supercell is constructed by eight inhomogeneous units possessing a full 2π reflection phase coverage with an interval of π/4. In the optimization, each unit in the supercell is designed through the topology optimization method to achieve a specific reflection phase, i.e., reaching a target reflection coefficient corresponding to the desired reflection phase. During the optimization process, the boundary of the unit is updated via solving the level set function, while the normal velocity is derived from the sensitivity analysis. The optimal unit configurations have relatively smooth and distinct boundaries and sample structures. The reflection fields of the designed optimal metasurface under normal and oblique plane wave incidences are investigated numerically and experimentally, and a generally good agreement between them is achieved. Results reveal that a desired reflection wave manipulation is realized by the designed metasurface based on diffraction theory, demonstrating the effectiveness and efficiency of the present topology optimization design method. Furthermore, applications of these optimal units to acoustic flat focusing and acoustic self-bending beam generation are successfully demonstrated by numerical simulations. The presented design approach is quite promising for metasurface design and may be generally used in a variety of metamaterials with a prescribed set of properties.

Topology Optimization and Prototype of a Multimaterial-Like Compliant Finger by Varying the Infill Density in 3D Printing.

This study presents a multimaterial topology optimization method for design of multimaterial compliant mechanisms. Traditionally, the objective function in topology optimization for design of structures is to minimize the strain energy (SE). For synthesis of compliant mechanisms, the objective function is usually to maximize the mutual potential energy (MPE). To design an adaptive compliant gripper for grasping size-varied objects, a multicriteria objective function considering both the SE and MPE at two different output ports is proposed in this study. In addition, based on the fact that different infill densities in three-dimensional (3D) printing leads to prototypes with different equivalent mechanical properties, this article proposes that a multimaterial design can be approximated by varying the values of infill densities in different portions of a 3D-printed component, which enables the multimaterial designs to be prototyped using the general low-cost, single-material fused deposition modeling 3D printing machines. The proposed method is used to design and prototype a bi-material compliant finger which is 3D printed using a flexible thermoplastic elastomer with infill densities of 30% and 100%. The experimental results demonstrate that the bi-material finger is a better design in terms of reducing the driving force while increasing the output displacement at the fingertip comparing to the single-material finger design with the same volume and weight. Furthermore, a two-finger gripper with two identical multimaterial-like compliant fingers is prototyped and installed on a six-axis industrial robot. The experimental tests are performed to demonstrate the effectiveness of the presented design.

Topology Optimization Design and Experimental Research of a 3D-Printed Metal Aerospace Bracket Considering Fatigue Performance

In the aerospace industry, spacecraft often serve in harsh operating environments, so the design of ultra-lightweight and high-performance structures is a major requirement in aerospace structure design. In this article, a lightweight aerospace bracket considering fatigue performance was designed by topology optimization and manufactured by 3D-printing. Considering the requirements of assembly with a fixture for fatigue testing and avoiding stress concentration, a reconstructed model was presented by CAD software before manufacturing. To improve the fatigue performance of the structure, this article proposes the design idea of abstracting the practiced working condition of the bracket subjected to cycle loads in the vertical direction via a multiple load-case topology optimization problem by minimizing compliance under a variety of asymmetric extreme loading conditions. Parameter sweeping was used to improve the computational efficiency. The mass of the new bracket was reduced by 37% compared to the original structure. Both numerical simulation and the fatigue test were implemented to support the validity of the new bracket. This work indicates that the integration of the proposed topology optimization design method and additive manufacturing can be a powerful tool for the design of lightweight structures considering fatigue performance.

Topology optimization of lattices with anisotropic struts

This work presents a topology optimization method for design of architected truss lattices made of anisotropic struts. Employing anisotropic materials for the lattice struts can result in better effective properties than those that can be obtained for a lattice in which each strut is made of a single isotropic material, but different struts may be made of different materials. This work focuses on lattice struts that are either hollow or fiber-reinforced, which effectively result in transverse isotropy. The proposed method simultaneously optimizes the spatial configuration of the struts and the volume fraction of the reinforcing fibers or the holes in each strut to extremize the lattice effective properties. A parametric description of the lattice struts is projected onto a density field for analysis via the geometry projection technique. The proposed method accommodates any number of specified material symmetries by performing appropriate reflections of the projected density with respect to the symmetry planes. To ensure the size variables converge to 0 or 1, we employ an explicit penalization by imposing a discreteness constraint. To improve manufacturability, a no-cut constraint is imposed to ensure that struts are not partially cut upon reflection by the symmetry planes or by the faces of the unit cell. The smallest angle at which two struts can intersect is also constrained to avoid overlaps that are difficult to manufacture. Examples of maximization of the effective bulk modulus and minimization of the effective Poisson’s ratio of the lattice demonstrate the effectiveness of the proposed method.

Topology optimization of multiphase materials with dynamic and static characteristics by BESO method

The demand for advanced manufacturing is gradually turning to the multi-functional integrated structure, so the effective and innovative functional structure topology optimization design method can maximize the performance of the structure. This paper proposes a parallel topology optimization design method for dynamic and static characteristics of multiphase materials. The inherent discrete design variables of bidirectional evolutionary structure optimization (BESO) can clearly distinguish the topological boundaries of multiphase materials without the intermediate density materials. The pre-processing density filtering scheme is introduced into the BESO method to eliminate the numerical calculation instability problem. Then, the improved multiphase materials interpolation scheme can overcome the local modal phenomenon of vibration problems. Finally, a series of typical numerical examples show that the method is effective, efficient and easy to implement in multiphase materials topology optimization with dynamic and static characteristics.

Topology optimization and shape design method for large-span tensegrity structures with reciprocal struts

Tensegrity is a kind of efficient structural system that is composed of continuous cables in tension and discontinuous struts in compression. Although the studies on tensegrity have been carried out by many researchers, there are few methods for assembling large-span tensegrity by multiple units. Inspired by the similarities between reciprocal units and tensegrity units, we present a novel method for designing large-span tensegrity structures with reciprocal struts, which is a kind of new tensegrity structural system that can cover a large area, while the rule of discontinuous struts is followed strictly. The proposed design method includes assembly, topology optimization, and shape design. The prototype; i.e., initial topology, of the tensegrity is generated from reciprocal struts. A topology optimization method using ground structure approach is proposed to remove the redundant cables from the initial topology. A shape design method using fictitious stiffness parameters is proposed to satisfy the architectural shape demand. The form-finding problem, which is to find the self-equilibrium shape in the topology optimization as well as shape design processes, is solved by using the non-rigid-body motion analysis method. Numerical examples demonstrate the effectiveness and applicability of the proposed method.

Topology optimization for transversely isotropic materials with high-cycle fatigue as a constraint

We propose a topology optimization method for design of transversely isotropic elastic continua subject to high-cycle fatigue. The method is applicable to design of additive manufactured components, where transverse isotropy is often manifested in the form of a lower Young’s modulus but a higher fatigue strength in the build direction. The fatigue constraint is based on a continuous-time model in the form of ordinary differential equations governing the time evolution of fatigue damage at each point in the design domain. Such evolution occurs when the stress state lies outside a so-called endurance surface that moves in stress space depending on the current stress and a back-stress tensor. Pointwise bounds on the fatigue damage are approximated using a smooth aggregation function, and the fatigue sensitivities are determined by the adjoint method. Several problems where the objective is to minimize mass are solved numerically. The problems involve non-periodic proportional and non-proportional load histories. Two alloy steels, AISI-SAE 4340 and 34CrMo6, are treated and the respective as well as the combined impact of transversely isotropic elastic and fatigue properties on the design are compared.

Lightweight design of the in-wheel motor considering the coupled electromagnetic-thermal effect

The lightweight problem of in-wheel motor is one of the key problems to be solved in the development of in-wheel motor driving electric vehicles. However, in-wheel motor involves the cross-coupling effect of multi-physical fields, such as the structure field, electromagnetic field and thermal field. The lightweight design for the in-wheel motor means the change in the structure, which will lead to the change in other physical field characteristics. Aiming at this problem, a lightweight design method is proposed in this paper. A 15Kw embedded permanent magnet synchronous in-wheel motor is taken as the research object, the minimum volume is set as the optimization objective, and the topology optimization design method is adopted to reduce the weight of the motor. And in the optimization design process, the bilateral coupling constraint of the electromagnetic field and thermal field is taken into account simultaneously. This study aims to find the optimal topology distribution considering the cross-coupling effect of structure-electromagnetic-thermal fields, and obtain the optimal structure of the in-wheel motor that meets the design requirements. Furthermore, the validity of the lightweight design method is verified by comparing and analyzing the characteristics of each physical field of the in-wheel motor before and after optimization.