Topology Optimization Procedure Research Articles

Topology optimization of structures with infill-supported enclosed voids for additive manufacturing

This paper proposes a novel topology optimization procedure for designing structures with infill-supported enclosed voids for additive manufacturing (AM). In such structures, the open and enclosed regions are separately treated, where the open regions are the standard voids but the enclosed ones are filled by porous materials. The applied porous infill can work as supports in the AM process, but at the same time be part of the final structures and will never be removed. In this way, the difficulty of removing the supports in enclosed voids can be naturally avoided. However, whether the enclosed voids should be removed or kept if the porous material must be filled inside becomes a challenging problem, and thus this work develops a rational procedure to automatically determine it, and optimize the layout of these kept enclosed voids with infill. In the proposed procedure, a nonlinear virtual temperature (N-VTM) filter is utilized to separate the enclosed voids and open regions. Then, by combining the N-VTM filter, PDE filter and projection, a novel interpolation for structures with infill-supported enclosed voids is proposed, which at the same time can be used to provide structures without enclosed voids. The robust topology optimization formulation is applied to enhance the performance of the proposed procedure, and the sensitivity equations are deduced based on the adjoint method. Several numerical and experimental examples in two and three dimensions illustrate the effectiveness of the procedure. The results show that the procedure is capable of automatically determining whether to directly eliminate an enclosed void or to use infill to support it.

Two-level method part-scale thermal analysis of laser powder bed fusion additive manufacturing

Numerical simulations of a complete laser powder bed fusion (LPBF) additive manufacturing (AM) process are extremely challenging, or even impossible, to achieve without a radical model reduction of the complex physical phenomena occurring during the process. However, even when we adopt a reduced model with simplified physics, the complex geometries of parts usually produced by the LPBF AM processes make this kind of analysis computationally expensive. In fact, small geometrical features—which might be generated when the part is designed following the principle of the so-called design for AM, for instance, by means of topology optimization procedures—often require complex conformal meshes. Immersed boundary methods offer an alternative to deal with this kind of complexity, without requiring complicated meshing strategies. The two-level method lies within this family of numerical methods and presents a flexible tool to deal with multi-scale problems. In this contribution, we apply a modified version of the recently introduced two-level method to part-scale thermal analysis of LPBF manufactured components. We first validate the proposed part-scale model with respect to experimental measurements from the literature. Then, we apply the presented numerical framework to simulate a complete LPBF process of a topologically optimized structure, showing the capability of the method to easily deal with complex geometrical features.

On the topology design of a mechanical heterogeneous specimen using geometric and material nonlinearities

Material characterization and the calibration of constitutive models play an important role in the majority of the forming processes nowadays. For an accurate virtualization of the processes, the material mechanical behavior needs to be known a priori. The classical characterization procedure involves carrying out several standard mechanical tests to identify the required information about the material. However, this procedure turns out to be expensive and time-consuming. Heterogeneous mechanical tests have been used to overcome this issue. By providing richer information with a reduced number of tests, their use can enhance the actual material characterization process. This work aims at making a significant contribution towards this goal by designing a heterogeneous mechanical test using topology optimization. A specimen topology is obtained with a heterogeneous displacement field by applying the theory of compliant mechanisms. Due to the large displacements considered, a geometrically nonlinear finite element analysis and a topology optimization procedure are proposed. Material nonlinearity is taken into account as well, to design solutions closer to reality. An optimal mechanical test with a highly heterogeneous strain field is obtained and evaluated, considering its diversity, using mechanism theory and a mechanical indicator.

Reliability-Based Topology Optimization: An Extension of the SESO and SERA Methods for Three-Dimensional Structures

This study takes an approach to reliability-based topology optimization (RBTO) for 3D structures by applying an expansion of smoothing evolutionary structural optimization (SESO) and sequential element rejection and admission (SERA) for three-dimensional optimization. In the search for the stable optimal solution, and a more reliable structure, we present a performance index with the ability to monitor the evolutionary optimization procedure and adopt the filtering scheme usually applied in solid isotropic material with penalization (SIMP). The limit state functions are the maximum displacement constraints imposed in the topology optimization procedure and a structure’s performance control; a comparative analysis of the deterministic topology optimization (DTO) with the RBTO models is also explored. The obtained results suggest the importance of using the RBTO concept in 3D structures as part of the design analysis process.

Topology Optimization Design and Experiment of a Soft Pneumatic Bending Actuator for Grasping Applications

Soft pneumatic bending actuators are commonly used in robotic grasping applications and can be applied for handling both delicate and irregularlyshaped objects. Because these soft pneumatic actuators are typically embedded with multiple air chambers inside soft, thin structures, their maximum payloads are usually low compared to rigid designs of similar size. This article presents a soft pneumatic bending actuator design using a topology optimization procedure that can maximize the bending capability and thus increase the allowable payload of soft grippers that consist of multiple pneumatic bending actuators. After an optimum design is obtained, multiple identical actuators are prototyped through a molding process using a silicone rubber material. Both two-fingered and three-fingered soft grippers are developed using the topology-optimized pneumatic bending actuators. Experiments, including a bending angle test, an output force test, and a payload test, are conducted in this study,and the results are compared against the test results of the commercial SRT soft pneumatic actuator. The experimental results show that the bending angle for the developed bending actuator is 111 degrees on average of 10 tests at an input pressure of 50 kPa. The output force is 9.45 N at an input pressure of 80 kPa, while the maximum payloads of the two-fingered and three-fingered grippers are 2.66 kg and 5.12 kg, respectively.

Large-Scale Topology Optimization of Transient Incompressible Flow with Building-Cube Method

In recent years, topology optimization methods have been adopted not only for structural problems but also for fluid flow problems. Topology optimization for unsteady flows requires a fine mesh, which is computationally expensive. Therefore, we propose an transient incompressible flow topology optimization method based on the building cube method (BCM), which is suitable for massively parallel computing. BCM is a type of hierarchical Cartesian mesh method that has been reported to have very good scalability. The transient Navier-Stokes equations in the topology optimization procedure are solved by a finite volume discretization based on the BCM. The sensitivity of the objective function is obtained by continuous sensitivity analysis based on the adjoint variables method.

Infill topology optimization of porous structures with discrete variables by the sequential element rejection and admission method

This article presents an infill topology optimization procedure to generate lightweight porous structures. The proposed method is based on discrete variables and builds upon the sequential element rejection and admission method, extending previous work on topology optimization for infill structures. Local volume constraints are introduced in the conventional formulation of the topology optimization problem for maximum stiffness design instead of the global volume constraint. The local constraints are applied, dividing the interior of a given design shape into quadrangular subdomains with variable aspect ratios. The localized material within these subordinate cells is allowed to flow between two discrete material models, ‘real’ and ‘virtual’, where two separate criteria are considered for the rejection and admission of elements. The results demonstrate the effectiveness of the method, showing that detailed porous designs are efficiently achieved with the proposed strategy. Numerical examples demonstrate the effects of the different design parameters.

Effects of design sensitivity schemes for incorporating loading uncertainty in robust topology optimization

The effects of different design sensitivity schemes for an appropriate incorporation of the loading position uncertainty into a gradient-based topology optimization procedure are explored intensively, so that the robust optimal design of a continuum structure can be efficiently performed over the prescribed uncertain region. Three compliance sensitivity schemes are tested and the distinctive strategy offering the most reliable and competitive material layout of the load-bearing components is obtained from comprehensive comparisons. Three benchmark examples are used to demonstrate the diverse configurations of the material layouts. The numerical results show that the scheme with the largest absolute design sensitivity can most adequately integrate the load uncertainties into the topology optimization algorithm to make the structural performance insensitive to, or have less degradation in the presence of perturbations in the loading points.

Optimum topological bracing design of tall steel frames subjected to dynamic loading

In this paper, a frame structural topology optimization methodology for the generation of moment resisting braced frames for tall buildings, considering dynamic seismic loading, is presented. Real-world loading conditions along with standardized steel profiles of Euronorm are employed. In the literature, the studies that employ the ground structure topology optimization method are limited mostly to truss structures under static loading conditions. The dynamic response in the framework of structural topology optimization remains a challenging problem, especially when the ground structure method is used for deriving the structural system of tall buildings. The contribution of this study to the state of the art, relies on the implementation of the proposed methodology in the conceptual design phase of civil engineering frame structures, where both axial and flexural stiffness is considered. Direct time integration methods are used, to implement forced vibrations and real recorded earthquake data in the topology optimization procedure, resulting to novel layouts for lateral resisting systems of tall buildings. Aiming to aid the engineer to the final design phase, the response spectrum modal analysis is employed and the seismic loading is applied according to the Eurocode 8.

On tailoring fracture resistance of brittle structures: A level set interface-enriched topology optimization approach

We propose a fully immersed topology optimization procedure to design structures with tailored fracture resistance under linear elastic fracture mechanics assumptions for brittle materials. We use a level set function discretized by radial basis functions to represent the topology and the Interface-enriched Generalized Finite Element Method (IGFEM) to obtain an accurate structural response. The technique assumes that cracks can nucleate at right angles from the boundary, at the location of enriched nodes that are added to enhance the finite element approximation. Instead of performing multiple finite element analyses to evaluate the energy release rates (ERRs) of all potential cracks—a procedure that would be computationally intractable—we approximate them by means of topological derivatives after a single enriched finite element analysis of the uncracked domain. ERRs are then aggregated to construct the objective function, and the corresponding sensitivity formulation is derived analytically by means of an adjoint formulation. Several numerical examples demonstrate the technique’s ability to tailor fracture resistance, including the well-known benchmark L-shaped bracket and a multiple-loading optimization problem for obtaining a structure with fracture resistance anisotropy.

Re-engineering of Cast Product by Topology Optimization

Topology optimization is useful to carrying out the weight reduction and in process cost reduction can be achieved. This kind of optimization input shape and size modification and optimization give us improved product in reduction of material. For this study, planet pinion carrier is selected for topology optimization. Software gives an innovative real-time picture of company activities and ecosystem and links people, ideas and data in a single collaborative environment. The 3DEXPERIENCE platform as an operating system helps companies to achieve operational excellence. Casting is a process where allowances and other things are provided and if we could able to optimize the material and weight of the casting there is a scope for optimization the material size and shape in casting process. Planet pinion carrier which is a cast product is taken from well-known industry for topology optimization. For optimization that product first 3D model is done and this 3D model is given as an input for topology optimization software. Force analysis is carried out by using ANSYS software and then topology optimization procedure is applied accordingly product is optimized. After topology optimization again force analysis is carried out. It has been found that 20 percent reduction is observed in this study. The part details and load conditions are given by well-known industry for topology optimization. Size, shape and cost is reduced by giving various load conditions in FUSION 360 software. Modeling and remodeling is done using software. Comparative study has been done using AUTOCAST software. Part details are calculated and also casting flow and real time for actual casting is simulated by using software.

Numerical and experimental investigation on topology optimization of an elongated dynamic system

Minimizing vibration levels of dynamic components at their operating frequency range has been a widely studied topic in engineering. However, the design of structures that satisfy geometric constraints and technical performances is an ongoing challenge. In this work, a topology optimization procedure based on the Bi-directional Evolutionary Structural Optimization (BESO) algorithm is performed to maximize the natural frequency separation interval of an elongated structure. The issues of disconnected and trivial solutions are solved using a connectivity constraint. It is imposed by a proposed procedure based on the heat flux solution of an auxiliary system. An assessment of the feasibility of the structure is done by verifying its accordance with manufacturing and design constraints. The optimized structure was manufactured and validated experimentally. The implemented process produces topologies that maximize the natural frequency separation and reduce the mass of the structure. The obtained results demonstrate the effectiveness of the proposed procedure at satisfying geometric design constraints and technical performances.

Robust topology optimization of multi-material structures under load uncertainty using the alternating active-phase method

The synergy between different constituent materials can drastically improve the performance of composite structures. The optimal design of such structures for practical applications is complicated by the often-encountered non-deterministic loading conditions. This paper proposes an efficient method for robust multi-material topology optimization problems of continuum structures under load uncertainty. Specifically, the weighted sum of the mean and standard deviation of structural compliance is minimized under volume constraints for each material phase. Based on the theory of linear elasticity and using the orthogonal diagonalization of real symmetric matrices, the Monte Carlo sampling is separated from the topology optimization procedure and an efficient procedure for sensitivity analysis is established. By employing an alternating active-phase algorithm of the Gauss-Seidel version, the multi-material topology optimization problem is split into a series of binary topology optimization sub-problems, which can be easily solved using the modified SIMP model. Several 2D examples are presented to demonstrate the effectiveness of the proposed method.

A Topology Optimization Procedure for Assisting the Design of Nuclear Components

In this paper, we show that a module implemented in the MCNP transport code to perform sensitivity analyses can be diverted to perform topology optimizations of nuclear equipment. Component design with this approach leads to sophisticated solutions that outperform their human-designed counterparts.

A path-dependent level set topology optimization with fracture criterion

In this paper, a recently-developed phase-field damage model is incorporated into the topology optimization framework to take into account crack initiation and propagation in a path-dependent fashion. The proposed topological design can enhance fracture resistance of structures made of brittle materials such as advanced ceramics. For the first time, a path-dependent shape derivative is developed in a step-wise manner during the nonlinear fracture analysis, which enables to drive the topology optimization properly. To measure the fracture resistance of structure, a p-norm function is formulated to aggregate the phase-field variables into a single constraint. To demonstrate the effectiveness of the presented topology optimization procedure, three 2D benchmark examples with single-phasic material and one 3D biomedical example with biphasic materials are studied here. The comparison with the topological designs based upon conventional linear elastic finite element analysis without the damage model indicates that the proposed method can significantly improve the fracture resistance of structures with more efficient use of materials. The proposed method is anticipated to provide an effective approach for sophisticated path-dependent topological design of structures reducing severe stress concentration and high risks of fracture failure.

A Deep Learning Surrogate Model for Topology Optimization

In this work, a topology optimization procedure is proposed and applied to the TEAM 25 problem, i.e., a model of a die press with an electromagnet for orientation of magnetic powder. The shape of the press is described as a free discretized profile, and its relation to the flux density in the cavity is simulated by finite element analysis (FEA) and learned by a deep neural network (DNN) model. The DNN is used as a surrogate model for optimization, aiming to obtain a desired flux density distribution in the cavity. Results are promising, as better accuracy is obtained with respect to the full FEA-based optimization approach with the reduced time cost. Once trained, the surrogate model can be used to efficiently solve a whole family of problems where a different target field distribution is defined.

Accelerating Large-scale Topology Optimization: State-of-the-Art and Challenges

Large-scale structural topology optimization has always suffered from prohibitively high computational costs that have till date hindered its widespread use in industrial design. The first and major contributor to this problem is the cost of solving the Finite Element equations during each iteration of the optimization loop. This is compounded by the frequently very fine 3D models needed to accurately simulate mechanical or multi-physical performance. The second issue stems from the requirement to embed the high-fidelity simulation within the iterative design procedure in order to obtain the optimal design. The prohibitive number of calculations needed as a result of both these issues, is often beyond the capacities of existing industrial computers and software. To alleviate these issues, the last decade has opened promising pathways into accelerating the topology optimization procedure for large-scale industrial sized problems, using a variety of techniques, including re-analysis, multi-grid solvers, model reduction, machine learning and high-performance computing, and their combinations. This paper attempts to give a comprehensive review of the research activities in all of these areas, so as to give the engineer both an understanding as well as a critical appreciation for each of these developments.

A level-set approach based on reaction–diffusion equation applied to inversion problems in acoustic wave propagation

In this work, a topology optimization procedure based on the level-set method is applied to the solution of inverse problems for acoustic wave propagation in the time-domain. In this class of inverse problems the presence of obstacles in a background medium must be identified. Obstacles and background are defined by means of a level-set function that evolves by following the solution of a reaction–diffusion equation. Within this approach, no initial guess for the topology nor level-set reinitialization procedures are necessary, contrary to what is commonly observed when the Hamilton–Jacobi equation is used. The objective function is defined as the domain and time integration of the squared difference between experimental and simulation pressure signals. The finite element method is used for the spatial and level-set function discretizations and a time-marching procedure (Newmark scheme) is used to solve the wave propagation problem, as well as the adjoint problem for the sensitivity analysis. Both procedures provide the information needed to define the velocity field for the level set evolution. Results show that the proposed technique is capable to find the location and shape of obstacles within a background medium. Systematic tests show that, as expected, the distribution of sources and receivers shows to have a major influence on the final solution. Results also reproduce known difficulties; when the so called inverse crime is avoided, the identification procedure worsens its performance. Filters and smoothing are among different features that deserve further investigation. Although the formulation presented here focuses on the acoustic wave propagation problem, its extension to wave propagation in elastic media is straightforward.

A new model and direct slicer for lattice structures

This paper presents a model for generating strut-based lattice structures using topology optimization and their efficient direct slicing. These structures exhibit better physical properties and can represent the partial densities at the macro-scale level, which often appear in designs based on topology optimization. The fabrication of such large member structures with intricate geometries is possible by the additive manufacturing technologies which offer design freedom to produce the optimized parts for engineering applications. However, these structures generate millions of planer manifolds describing the strut members and result in large data files, thus making conventional procedures in additive manufacturing highly ineffective. Therefore, the design process for such structures requires efficient data manipulation and storage of the lattice topology. In the current work, a mathematical model for the strut primitive which connects two nodes in a cell is developed. Based on the proposed strut model, a structural optimization formulation is presented for lattice structures design under volume fraction constraint. A matrix-oriented compact data structure to express the lattice topology and the direct slicing algorithm which makes queries on the proposed compact data structure is presented as part of this work. The slicing kernel has been tailored for parallel implementation to handle engineering-scale applications which often consist of structures over a million struts. The article is organized into the “Introduction” section explaining the requirement and the novelty of this work. Following which, the automated design framework based on topology optimization procedure for lattice structures is given. The mathematical derivations and data structure of the strut-based lattice will be explained and the operations on model data for the direct slicing procedure are elaborated. Numerical experiments verifying the proposed method will be presented toward the end.

A Two-Scale Multi-Physics Deep Learning Model for Smart MEMS Sensors

Smart materials and structures, especially those bio-inspired, are often characterized by a hierarchy of length- and time-scales. Smart Micro Electro-Mechanical Systems (MEMS) are also characterized by different physical phenomena affecting their properties at different scales. Data-driven formulations can then be helpful to deal with the complexity of the multi-physics governing their response to the external stimuli, and optimize their performances. As an example, Lorentz force micro-magnetometers working principle rests on the interaction of a magnetic field with a current flowing inside a semiconducting, micro-structured medium. If an alternating current with a properly set frequency is let to flow longitudinally in a slender beam, the system is driven into resonance and the sensitivity to the magnetic field may result largely enhanced. In our former activity, a reduced-order physical model of the movable structure of a single-axis Lorentz force MEMS magnetometer was developed, to feed a multi-objective topology optimization procedure. That model-based approach did not account for stochastic effects, which lead to the scattering in the experimental data at the micrometric length-scale. The formulation is here improved to allow for stochastic effects through a two-scale deep learning model designed as follows: at the material scale, a neural network is adopted to learn the scattering in the mechanical properties of polysilicon induced by its polycrystalline morphology; at the device scale, a further neural network is adopted to learn the most important geometric features of the movable parts that affect the overall performance of the magnetometer. Some preliminary results are discussed, and an extension to allow for size effects is finally foreseen.