Topology Optimization Algorithm Research Articles

Lightweight Design Optimization of Nonpneumatic Tires under Radial-Stiffness Constraints

Nonpneumatic tires (NPTs) have good safety and a good load-carrying capacity, and they replace the function of air in pneumatic tires with a solid spoke component. The radial stiffness and weight are the important indexes for evaluating the performance of an NPT. In this research, we designed an NPT according to the requirements of vehicle Chery eQ1 based on weight minimization. Taking the radial stiffness related to the bearing-capacity performance as the constraint condition, a topology-optimization algorithm is proposed to find the best thickness distribution of the spokes with the objective of minimizing the mass. First, the mechanical properties of the material were obtained with the test. Then, the FE model of an NPT with a Fibonacci spoke structure was built and validated with a radial-stiffness test on a five rigid test machine. The optimization algorithm was carried out by searching for the best thickness distribution of the spoke after verifying the reliability of the FE model. Finally, the optimized tire was manufactured, and the stiffness test was carried out to verify the feasibility of the optimization results. The results show that the spoke mass can be reduced by 9% by using the proposed optimization algorithm while satisfying the radial-stiffness constraint.

Broadband acoustic lens design using gradient-based optimization and adjusting radii and positions of scatterers

In this talk, we present the semi-analytical gradient-based optimization (GBO) technique for an efficient design of the broadband acoustic lens. This idea differs from earlier inverse designs that use topology optimization, shape optimization, and generic algorithms. We derived a formula for the gradients of the absolute pressure at the focal point with respect to positions and radii of a set of cylindrical scatterers. The derived analytic form of gradients of absolute pressure complements the modeling when combined with optimization and parallel computing. The GBO algorithm maximizes the sound amplification at focal point by evaluating pressure derivative with respect to the cylinder positions and radii, and then perturbatively optimizing the position and radius of each cylinder in the lens while considering acoustic multiple scattering between the cylinders. Computations are performed using the MultiStart Global optimization solver with fmincon while supplying the gradient of pressure at the focus and the gradient of nonlinear geometrical constraints. The GBO of the broadband acoustic lens is illustrated performing several performance measures for the dependency on the wavenumber and the incidence angle. The method is presented giving numerical examples for non-uniform configurations of the cylindrical structures of various radii and material submerged in water.

Cellular topology optimization on differentiable Voronoi diagrams

AbstractCellular structures manifest their outstanding mechanical properties in many biological systems. One key challenge for designing and optimizing these geometrically complicated structures lies in devising an effective geometric representation to characterize the system's spatially varying cellular evolution driven by objective sensitivities. A conventional discrete cellular structure, for example, a Voronoi diagram, whose representation relies on discrete Voronoi cells and faces, lacks its differentiability to facilitate large‐scale, gradient‐based topology optimizations. We propose a topology optimization algorithm based on a differentiable and generalized Voronoi representation that can evolve the cellular structure as a continuous field. The central piece of our method is a hybrid particle‐grid representation to encode the previously discrete Voronoi diagram into a continuous density field defined in a Euclidean space. Based on this differentiable representation, we further extend it to tackle anisotropic cells, free boundaries, and functionally‐graded cellular structures. Our differentiable Voronoi diagram enables the integration of an effective cellular representation into the state‐of‐the‐art topology optimization pipelines, which defines a novel design space for cellular structures to explore design options effectively that were impractical for previous approaches. We showcase the efficacy of our approach by optimizing cellular structures with up to thousands of anisotropic cells, including femur bone and Odonata wing.

Concurrent multiscale topology optimization: A hybrid approach

This paper presents a hybrid approach for multiscale topology optimization of structures. The topological shape of both macro-structure and micro-structure are concurrently optimized, based on the solid isotropic material with penalization (SIMP) technique in combination with finite element method (FEM). The material is assumed to have periodically patterned micro-structures, such that the effective properties can be evaluated via energy-based homogenization method (EBHM). In every iteration, the effective properties of material are passed to the macroscopic problem, and the macroscopic behavior (e.g. strain energy) is transferred back to the micro-scale problem, where the unit cell representing the micro-structure of material is determined for the next iteration. It is found that the update process can be done separately, i.e., the sensitivity of macro-scale design variables is not required during the update of micro-scale design variables, and vice versa. Hence, the proposal is that the macro-structure is updated by the gradient-free Proportional Topology Optimization (PTO) algorithm to utilize the computational efficiency of PTO. The micro-structure is still updated by the common gradient-based algorithm, namely Optimality Criteria (OC). Three benchmark numerical examples are investigated, demonstrating the feasibility and efficiency of the proposed hybrid approach.

Vibration Reduction of Reactor Using Global Magneto-Structural Topology Optimization

The global topology optimization algorithms used in vibration reduction of gapped-iron reactors will achieve the optimal performance under certain constraints, but with a long computational time and poor convergence. To shorten the calculation time, a global magneto-structural topology optimization algorithm (GMS) is proposed, in which the magnetic topology optimization result is used as the initial seed of the structural topology optimization. Firstly, the air gaps areas are set as the optimized area due to the large vibration in this area. And the relative permeability and the young's modulus of the reactor core material in the optimized area are presented as the interpolation function of the defined material density. Secondly, combined with the finite element method (FEM), the gapped-iron core reactor model is optimized, in which the parameters are obtained by measuring the magnetic properties of silicon steel. And the threshold function is presented to eliminate the intermediate density and improve the optimal material boundary. Finally, the stress and vibration displacement curves of the reactor before and after the optimization are calculated. The vibration displacement of the reactor with the optimal topology is reduced by 31% and the number of iterations is reduced by 6 times.

Singular geometry perturbation based method for shape-topology optimization in unsteady Stokes flow

This paper concerns the topological derivatives and its applications for solving shape and topology optimization problems in fluid mechanics. The fluid flow is governed by the unsteady incompressible Stokes equations in the two dimensional case. We derive a topological sensitivity analysis for this parabolic-type operator. The proposed approach is based on a preliminary estimate describing the variation of the velocity field caused by the presence of a small obstacle inside the fluid flow. We obtain a topological asymptotic expansion for the unsteady Stokes operator valid for a large class of shape functions and an arbitrarily shaped geometric perturbation. Then, the topological gradient is exploited for building an efficient and accurate topology optimization algorithm. Finally, we present some numerical investigations showing the efficiency of the proposed approach.

Topology optimization of shell-infill structures for natural frequencies

PurposeThe purpose of this paper is to develop a topology optimization algorithm considering natural frequencies.Design/methodology/approachTo incorporate natural frequency as design criteria of shell-infill structures, two types of design models are formulated: (1) type I model: frequency objective with mass constraint; (2) type II model: mass objective with frequency constraint. The interpolation functions are constructed by the two-step density filtering approach to describe the fundamental topology of shell-infill structure. Sensitivities of natural frequencies and mass with respect to the original element densities are derived, which will be used for both type I model and type II model. The method of moving asymptotes is used to solve both models in combination with derived sensitivities.FindingsMode switching is one of the challenges faced in eigenfrequency optimization problems, which can be overcome by the modal-assurance-criterion-based mode-tracking strategy. Furthermore, a shifting-frequency-constraint strategy is recommended for type II model to deal with the unsatisfactory topology obtained under direct frequency constraint. Numerical examples are systematically investigated to demonstrate the effectiveness of the proposed method.Originality/valueIn this paper, a topology optimization method considering natural frequencies is proposed by the author, which is useful for the design of shell-infill structures to avoid the occurrence of resonance in dynamic conditions.

Derivation of a continuous adjoint topology optimization method applied on heat transfer for incompressible flow

With the development of additive manufacturing, the freedom in developing complex cooling structures has been enlarged greatly. Topology optimization is one of the methods that can give out cooling structures beyond the limits of geometric parameters. In this research, an algorithm of topology optimization with heat transfer is derived. The detailed optimization procedure is presented in this work. The basic assumptions of this optimization method are steady state, incompressible and frozen turbulent flow with constant physical properties. The governing equations, optimization sensitivity formula and boundary conditions are presented, which are essential to the implementation of this method. A detailed derivation process is included. This method is applied in a 2-D flow domain using an open-source platform named OpenFOAM.

Concurrent topology and fiber orientation optimization of CFRP structures in space-borne optical remote sensor

Lightweight design is one of the most important concepts in the design of space-borne optical remote sensors. Carbon fiber reinforced polymer (CFRP), as one material with high ratio of modulus to density, is widely employed to realize the lightweight design. To maximize the stiffness and strength of CFRP with prescribed mass, fiber orientation and topology optimization are accomplished and optimum design result is acquired in this paper. First, the optimization algorithm of fiber orientation is put forward to find the optimal fiber direction and verified by theoretical analysis and simulations, illustrating that [90°/+ 45°/− 45°/0°] fiber orientation and symmetrical laminas are indispensable. Furthermore, the topology optimization algorithm including the density interpolation method and sensitivity analysis method is brought about to find the optimal material distribution. The algorithm is validated to be convergent and can provide a conceptual model which offers a reference for the critical design. Finally, acquired in the mechanical test is the performance of the optical remote sensor whose first three characteristic frequencies are respectively 66.95 Hz, 70.37 Hz, and 98.84 Hz. The mechanical amplification factor is 5.29, which meet the performance requirement of the stiffness and strength for the optical remote sensor.

Topology optimization of periodic mechanical structures with orthotropic materials based on the element-free Galerkin method

A topology optimization (TO) algorithm for periodic mechanical structures with orthotropic materials is established by using the element-free Galerkin method (EFGM) and imposing periodic constraints on design subdomains. The effectiveness of the presented TO algorithm is verified by two numerical examples compared with the finite element method (FEM). The comparisons demonstrate that the EFGM periodic structures without using any filtering techniques have smoother boundaries and fewer intermediate relative densities. These optimal periodic structures can be manufactured by 3D printing from the extracted "*.stl" files. The effects of the number of design subdomains, Poisson's ratio factor, and off-angle on minimum compliance and periodic structures are studied, and reasonable ranges of parameters are recommended to improve the mechanical performance of periodic structures. The results indicate that the increase of the number of design subdomains in any direction leads to inevitable stiffness loss, but the minimum compliance can be further reduced by decreasing Poisson's ratio factor and adjusting off-angle properly for specific number of design subdomains. Optimal periodic structures with orthotropic materials are of better mechanical performance to resist deformation and reduce von Mises stress than those with isotropic materials.

Application of a modular topology optimization framework to an aerospace bracket design

Abstract In aerospace industry, optimizing designs has become inevitable in terms of weight and performance requirements. Topology optimization is the most suitable optimization type for use in the conceptual design phase. Even though academic topology optimization algorithms have a modular structure (open to development), they are often useable for a regular design domain. Alternatively, commercial topology optimization software products, on the other hand, are very useful in terms of their solution speed, accuracy, and ability to handle complex or irregular design domains. However, the user is restricted with the optimization algorithms available in the software, and these software do not usually have a modular structure. In this study, a modular topology optimization framework that combines useful features of the academic codes (e.g., modularity) and the commercial software tools (e.g., capability of easily handling complex design domains) is developed. The developed framework is tested on two popular academic topology optimization problems, followed by aerospace bracket design problem. It is observed that the proposed framework usually provides lower objective function values and converges to the optimum result in fewer iterations than the Altair Optistruct topology optimization software.

Allying topology and shape optimization through machine learning algorithms

Structural optimization is part of the mechanical engineering field and, in most cases, tries to minimize the overall weight of a given design domain, subjected to functionality constraints given in terms of stresses or displacements. The most relevant techniques are topology and shape optimization. Topology optimization provides the optimal material distribution layout into a given, static, design domain. On the other hand, shape optimization provides the optimal combination of the parameters that define the required parametrization of the domain's boundary. Both techniques have strengths and weaknesses, thus a hybrid optimization approach that combines the former techniques will define a more general structural optimization framework that will take advantage of their synergistic combination. The difficulty arises when communicating both techniques for which, in this paper, we propose a machine learning-based methodology. • We proposed a methodology that allies topology and parametrized shape optimization algorithms, obtaining an hybrid optimization algorithm. • We studied the strengths and weaknesses of topology and shape optimization algorithms, which justified its combination to obtain a synergetic effect. • The use of manifold learning techniques, such as the Locally Linear Embedding (LLE), to extract the principal geometrical modes from a set of material distributions that topology optimization algorithm provides. • In order to properly use the LLE technique, the quasi-boolean material distribution provided by the topology optimization algorithm must be transformed into a richer level-set with the distance information. • The geometrical modes, extracted with the LLE algorithm, may be used to generate brand new geometries, as they define a parametric geometrical model. • The parametric space of geometrical modes may be considered by a shape optimization algorithm as its design space.

Intelligent design algorithm for branching structures based on updated force density method

Form-finding analysis has been deeply investigated with the extensive application of branching structures. In addition to the form-finding analysis, another important scientific problem to be resolved is determining the optimal topology of branching structures. The topological study of branching structure is inseparable from form-finding analysis because they are coupled together. An intelligent design algorithm for branching structures based on updated force density method is proposed to deeply investigate the topological form of branching structures. The intelligent design algorithm comprises three sub-algorithms, namely, form-finding algorithm based on force density method, length optimization algorithm based on updated force density method, and topology optimization algorithm. The proposed algorithm can automatically select the effective component to support the load while decreasing the sectional area of the inefficient component. Thus, topology optimization can be achieved by “killing” inefficient components. The component section can be determined in two ways, namely, fully stressed design algorithm and section library selection. The component length can be optimized through the proposed method to maximize the structural stability. The proposed method and research results can lay a foundation for the intelligent design of branching structures.

The Management of Educational Talents in Vocational Colleges Based on Wireless Network in the Artificial Intelligence Era.

Faced with the AI (artificial intelligence) era, it is both theoretically and practically important to examine the challenges and opportunities that vocational college education in China faces, as well as to actively explore how vocational college education can overcome the challenges and achieve a realistic path. This paper proposes and implements a wireless network-based vocational college talent management system. The main personnel management system primarily completes business operations related to daily personnel file management, while the data mining subsystem mines talent data using the DT (decision tree) classification algorithm to aid talent selection. At the same time, a new topology optimization algorithm based on the principle of minimum rigidity graph is proposed for talent management system wireless network optimization. The maximum-minimum balance criterion and the user-by-user optimization mechanism are designed to obtain the optimal relay selection and subchannel allocation strategy, ensuring the system's reliability and fairness. The optimized algorithm has a user security satisfaction of 0.93 in the range of 250 m, which is higher than other algorithms. It demonstrates that this algorithm's communication link is short, and it has good network connectivity and structural stability.

Topology optimization of multi-material structures with explicitly graded interfaces

The rapid development of additive manufacturing (AM) offers new opportunities to fabricate multi-material structures, whose performance can be optimized by the integrated design of multiple materials distribution and their interface behaviors. However, the graded-interface assumption between different materials often caused some numerical difficulties during topology optimization, e.g., poor applicability in weak interface and difficulty in accurately controlling interface width. This work develops a new element-based topology optimization algorithm by explicitly considering strong, weak or intermediate interfaces, and the interfacial width can also be controlled precisely. Under the explicit expression of a graded interface, a linear multi-material interpolation scheme is proposed to gradually achieve realistic graded physical field within the interfacial zone, where the interdiffusion or reaction inevitably happens and leads to the gradual transition of the interface property. The compliance minimization of multi-material structures with different types of graded interfaces is formulated under multiple volume fraction constraints. The sensitivity of the objective function and constraints with respect to design variables are derived. Numerical examples demonstrate that the optimized designs resulting from the proposed method always achieve a lower compliance, compared with those of the traditional multi-material designs. A phase diagram is presented to describe the sensitivity of the topological design on the interface behavior.

An SQP Algorithm for Structural Topology Optimization Based on Majorization–Minimization Method

When applying the sequential quadratic programming (SQP) algorithm to topology optimization, using the quasi-Newton methods or calculating the Hessian matrix directly will result in a considerable amount of calculation, making it computationally infeasible when the number of optimization variables is large. To solve the above problems, this paper creatively proposes a method for calculating the approximate Hessian matrix for structural topology optimization with minimum compliance problems. Then, the second-order Taylor expansion transforms the original problem into a series of separable and easy-to-solve convex quadratic programming (QP) subproblems. Finally, the quadratic programming optimality criteria (QPOC) method and the QP solver of MATLAB are used to solve the subproblems. Compared with other sequential quadratic programming methods, the advantage of the proposed method is that the Hessian matrix is diagonally positive definite and its calculation is simple. Numerical experiments on an MBB beam and cantilever beam verify the feasibility and efficiency of the proposed method.

Topology optimization of dispersive plasmonic nanostructures in the time-domain.

Topology optimization techniques have been applied in integrated optics and nanophotonics for the inverse design of devices with shapes that cannot be conceived by human intuition. At optical frequencies, these techniques have only been utilized to optimize nondispersive materials using frequency-domain methods. However, a time-domain formulation is more efficient to optimize materials with dispersion. We introduce such a formulation for the Drude model, which is widely used to simulate the dispersive properties of metals, conductive oxides, and conductive polymers. Our topology optimization algorithm is based on the finite-difference time-domain (FDTD) method, and we introduce a time-domain sensitivity analysis that enables the evaluation of the gradient information by using one additional FDTD simulation. The existence of dielectric and metallic structures in the design space produces plasmonic field enhancement that causes convergence issues. We employ an artificial damping approach during the optimization iterations that, by reducing the plasmonic effects, solves the convergence problem. We present several design examples of 2D and 3D plasmonic nanoantennas with optimized field localization and enhancement in frequency bands of choice. Our method has the potential to speed up the design of wideband optical nanostructures made of dispersive materials for applications in nanoplasmonics, integrated optics, ultrafast photonics, and nonlinear optics.

Heavy-water-based moderator design for an AB-BNCT unit using a topology optimization algorithm

Objective. The design of neutron moderators for BNCT treatment units currently relies on parametric approaches, which yield quality results but are ultimately limited by human imagination. Efficient but non-intuitive design solutions may thus be missed out. This limitation needs to be addressed. Approach. To overcome this limitation, we propose to use a topology optimization algorithm coupled with a state-of-the-art Monte-Carlo transport code. This approach recently proved capable of finding complex optimal configurations of particle propagators with limited human intervention. Main results. In this study, we apply this algorithmic solution to optimize some heavy-water neutron moderators for a specific AB-BNCT treatment unit. The moderators thus generated are compact yet succeed in limiting the exposure of patient’s healthy tissues to levels below recommended limits. They present subtle, original geometries inaccessible to standard parametric approaches or human intuition. Significance. This approach could be used to automatically fit the design of a BNCT moderator to the location and shape of the tumor or to the morphology of the patient to be treated, opening a path for more targeted BNCT treatment.

A nested algorithm of truss topology optimization for maximum plastic shakedown loading capacity

Abstract This paper proposes a nested algorithm for truss topology optimization under plastic shakedown theory, which aims at maximizing the shakedown loading capacity. The nested algorithm consists of shakedown analysis and sensitivity-based optimization. Analytical sensitivity of shakedown load with respect to the design variables is derived in a concise form for the first time in conjunction with the adjoint variable scheme. A primal-dual shakedown algorithm is implemented for the determination of the shakedown load limit of structures and adjoint variables needed in the sensitivity analysis. The ground structure approach is applied to formulate the optimization problem for determining the optimized topology and cross-sections of the truss structure. Based on the analytical sensitivity above, the nested algorithm of truss structure topology optimization can be done efficiently by a gradient-based mathematical programming algorithm. Through independent shakedown analysis and optimization processes, the proposed approach facilitates the computation scale and efficiency for large-scale structure optimization design. Several numerical examples involving two- and three-dimensional truss illustrate the effectiveness of the proposed approach.

Simulation on bone remodeling with stochastic nature of adult and elderly using topology optimization algorithm

Reliable and accurate predictions of bone remodeling provide essential assistance for personalized implant design and orthopedic diagnosis. However, the bone remodeling simulations fail to accurately mimic the sophisticated architecture of trabecular bone so far, due to the neglection of the stochastic behaviors of bone remodeling. In this study, we coupled the Physiological Stochasticity in Bone Remodeling into the conventional Topology Optimization algorithm (named PSBR-TO method) to predict the cancellous structure of human femur. The sensitivity function of topology optimization was amended according to the bone remodeling rules from in vivo study (Razi et al., 2015) to reflect the stochastic process of bone remodeling in various physiological conditions. To demonstrate the algorithm, the bone structures of adults and the elderly were simulated by adopting the corresponding remodeling rules. The results showed that PSBR-TO gives rise to highly similar morphological features with the natural femur bone, in terms of the trabecular orientations and bone content distribution. The predicted femurs for adults and the elderly showed that the region-dependent variations in trabecular structural parameters during aging, including BV/TV, Tb.Th, and Tb.Sp, were consistent with the natural bone. Additionally, a loading collection of thirteen activities was employed in the algorithm and succeeded in driving the femur model to reproduce cancellous structure without extra constraint of structure perimeter or local density. By means of PSBR-TO, the trabecular structure in diverse physiological conditions can be accurately predicted, showing the valuable contribution on the clinical diagnosis and patient-specific design of bone implants.