Multi-material topology optimization for automotive design problems

In the laser powder bed fusion process (PBF-LB), components are built up incrementally by locally melting metal powder with a laser beam. This process leads to inhomogeneous material properties of the manufactured components. By integrating these specific material properties into a topology optimization algorithm, product developers can be supported in the early phases of the product development process, such as design finding. For this purpose, a topology optimization method was developed, which takes the inhomogeneous material properties of components fabricated in the PBF-LB process into account. The complex pore architecture in PBF-LB components was studied with micro-computed tomography (µCT). Thereby, three characteristic regions of different porosity were identified and analyzed. The effective stiffness in each of these regions was determined by means of resonant ultrasonic spectroscopy (RUS) as well as finite element analysis. Afterward, the effective stiffness is iteratively considered in the developed topology optimization method. The resulting design proposals of two optimization cases were analyzed and compared to design proposals derived from a standard topology optimization. To evaluate the developed topology optimization method, the derived design proposals were additionally manufactured in the PBF-LB process, and the characteristic pore architecture was analyzed by means of µCT.

<div class="section abstract"><div class="htmlview paragraph">Evolving fuel efficiency and emissions standards, along with consumer demand for performance, are strong pressures for light-weighting of performance oriented motorcycles. The field of topology optimization (TO), with the extension of multi-material topology optimization (MMTO) provide manufacturers with advanced structural light-weighting methodology. TO methodology has been adopted in many industries, including automotive where light-weighting assists in meeting efficiency regulations. The development of process specific manufacturing constraints within MMTO is a critical step in increasing adoption within industries dealing with manufacturing cost restrictions. This capability can decrease design complexity, lowering manufacturing costs of optimization solutions.</div><div class="htmlview paragraph">A conventional all-aluminum perimeter style motorcycle chassis is analyzed to develop baseline compliance (total strain energy) metrics. An MMTO design space is created and optimized with steel and aluminum, such that results match the baseline design weight. This formulation demonstrates increased structural efficiency through stiffer structures at equivalent weight. Results are generated with standard MMTO, symmetry, and extrusion constraints to demonstrate utility of these manufacturing constraints. Material ratios are used to enforce lower cost material distribution selections.</div><div class="htmlview paragraph">The usage of MMTO with manufacturing and material ratio constraints has resulted in up to 60.4% reduction in structural compliance of designs, and a multitude of lower cost alternative designs. The usage of symmetry constraints provides effectively identical results to standard MMTO, with a computational time reduction of 29%. Extrusion constraints demonstrate decreased manufacturing difficulty with a computational time reduction of 52% and structural performance penalty of 58.6% from the lowest compliance MMTO result. The enforcement of steel has demonstrated a decrease in structural performance (increase in compliance) and material costs, with varying degrees depending on manufacturing constraints and enforcement limits. The MMTO based designs provide a range of solutions to designers, which can be selected based on the importance of structural efficiency, manufacturing difficulty, and material costs.</div></div>

Topology optimization considering multiple loading

ABSTRACTA comprehensive solution for bus frame design is proposed to bridge multi-material topology optimization and cross-sectional size optimization. Three types of variables (material, topology and size) and two types of constraints (static stiffness and frequencies) are considered to promote this practical design. For multi-material topology optimization, an ordered solid isotropic material with penalization interpolation is used to transform the multi-material selection problem into a pure topology optimization problem, without introducing new design variables. Then, based on the previously optimal topology result, cross-sectional sizes of the bus frame are optimized to further seek the least mass. Sequential linear programming is preferred to solve the two structural optimization problems. Finally, an engineering example verifies the effectiveness of the presented method, which bridges the gap between topology optimization and size optimization, and achieves a more lightweight bus frame than traditional single-material topology optimization.

The purpose of this paper is to present an important strength issue in the design of multi-fasteners jointed structures. Multi-fastener joints such as bolts and rivets are widely used in assembled structures and always act as critical elements in damage tolerance design. Therefore, fasteners static strength and fatigue performance are simultaneously considered in this paper. On one hand, constraints on joint loads are issued to avoid the fasteners failure. On the other hand, two multiaxial fatigue criterion, i.e., Sines criterion and Crossland criterion are introduced to avoid the failure in the connection areas around fasteners. In addition, the total material usage is limited for the light-weight design. The standard topology optimization is thus extended to minimize the structural compliance with joint load constraints and fatigue failure constraints. Beam elements are used to model the fasteners. The joint loads can therefore be derived easily based on the finite element formulation. In order to eliminate the high stresses caused by the nodal connections of the beam elements, compositional modeling method is used to evaluate the stress level around the fasteners, in which beam elements are used to simulate the stiffness of fasteners and spring/shell elements are used to simulate the interaction of multi-fastener joints. Fatigue constraints are handled in the context of stress-based topology optimization while the corresponding analysis is based on static finite element due to the decomposition of harmonic loads. To address the singularity problems related to stress constraints, q - p relaxation is used and p ≥ q ≥1. Fatigue constraints should be evaluated in every element which inevitably brings in a large number of constraints. P-norm is therefore used as the constraints aggregation scheme. The aggregation factor of P-norm, i.e., Pn is assigned as 6 in this paper. With respect to the constraints aggregation process, the design sensitivities of fatigue constraints and joint load constraints are derived and calculated. Two numerical examples, namely an assembled I-shape beam and a cabin of the high-speed flight vehicle are tested. Optimized results with the proposed method are compared with standard topology optimization design. All the constraints are completely controlled by the prescribed upper level and the loss of stiffness in the optimized configuration can be seen as a trade-off for the strength. It is shown that the fatigue performance is strongly affected by the structural layout and the load carrying path. The effects of different fatigue constraints on the optimized configuration are studied.

The development of multimaterial topology optimization offers significant advancements in the design of lightweight aerospace structures. A three-field multimaterial topology optimization method with a material selection function under a mass constraint is developed. By integrating a multimaterial linear interpolation model with floating projection techniques, design variables are refined to the expected 0/1 level, ensuring accurate smooth design. The approach demonstrates smooth convergence even when applied to more than three material phases, producing optimized structures with distinct material boundaries and interfaces. A case study of the aircraft engine pylon design is presented, utilizing real material properties, including Poisson’s ratio, to meet lightweight design requirements. The requirement of lightweight design is realized by introducing effective lightweight materials and automatically adjusting the distribution and volume fraction of materials. Additionally, the three-field density representation technique is applied to improve the optimization efficiency and is extended to design considering manufacturing uncertainty. The robust manufacturing multimaterial structure is designed with the potential for manufacturing errors in mind. It can provide valuable guidance for multimaterial lightweight design of aerospace structures.

Despite the growing interest in applying reinforcement learning (RL) to design optimization, its high computational cost limits its applicability to problems involving expensive function evaluations. In this study, we propose an efficient RL action strategy specifically designed for acoustic topology optimization. The key idea is to assign action values ( Q -values) to each element individually and select material-filled elements in descending order of their Q -values until the target volume fraction is met, instead of evaluating Q -values for complete combinations of elements that satisfy the volume constraint. This formulation decouples the learning complexity from the combinatorial explosion of candidate layouts, making the training of the Q -value-estimating neural network more efficient and thus the RL-based approach is more suitable for topology optimization problems requiring fine meshes. As a representative application, we consider the design of a muffler’s internal layout to maximize sound transmission loss—a problem where conventional gradient-based methods often fail to achieve near-global optimal solutions. By integrating the proposed method with finite element simulations and a reward function shaped by transmission loss at one or more target frequencies, the RL agent learns policies that directly determine the material distribution for single- or multi-frequency objectives. The resulting muffler designs, based on a two-dimensional finite element model, exhibit near-global optimal performance and outperform those generated by conventional gradient-based methods. The advantages of the proposed approach over standard RL-based topology optimization methods are also clearly demonstrated.

This paper presents an application of topology optimization and response surface method to optimize the geometry of a bicycle crank arm and the experimental validation of it. This is purposely to reduce the crank arm mass and create a preliminary design of a lightweight structure necessary for the high-performance bicycle development. A three-dimensional bike crank arm model was made in the SpaceClaim software followed by a static finite element analysis using ANSYS Workbench 2019 R1. A multiple cycling load was applied simultaneously in seven crank angles of 30, 45, 60, 90, 120, 135, and 150° relative to the horizontal position to create the multiple loads to the crank. From there, topology optimization was then conducted to investigate the effect of mass constraint, stress constraint, angle of cycling, and crank materials on the topological pattern result. To minimize stress concentration at corners, a shape optimization using the response surface method was conducted and obtained the final geometry. From the result, it is shown that both optimization methods not only successfully reduce the crank arm mass and provide several optimum design options but also are able to reduce the maximum stress in the crank arm up to 20% after the optimization process. The experimental validation using a newly developed wireless measurement system shows a considerable agreement to the numerical results.

An incremental form interpolation model together with the Smolyak method for multi-material topology optimization

An integrated method of topological optimization and path design for 3D concrete printing

In this article, we demonstrate the state-of-the-art of multi-scale topology optimization for 3D structural design. Many structures designed for additive manufacturing consist of a solid shell surrounding repeated microstructures, so-called infill material. We demonstrate the performance of different types of infill microstructures, such as isotropic truss or plate lattice structures and show that the best results can be obtained using spatially varying and oriented orthotropic microstructures. Furthermore, we demonstrate how implicit geometry modeling using nTop platform can help to interpret these multi-scale designs as single-scale manufacturable designs (de-homogenization). More importantly, we demonstrate the small difference in performance between these multi-scale and single-scale designs through extensive numerical testing. The presented method is at least 3 orders of magnitude more efficient compared to standard density-based topology optimization, allowing for high-resolution 3D structures to be obtained on a standard workstation PC.

Maximizing the fundamental eigenfrequency of geometrically nonlinear structures by topology optimization based on element connectivity parameterization

Microstructure design of porous viscoelastic composites with prescribed relaxation moduli by multi-material topology optimization

This paper presents a new strategy to distribute two different materials for multi-material topology optimization. Extended from the bi-directional evolutionary structural optimization (BESO) method for a single material, the multi-material bidirectional evolutionary structural optimization (MBESO) method has been developed, which can effectively handle the topology optimization problems involving two materials like steel and concrete. However, in some special cases, overloading of part of the compressed material occurs in the multi-material structures designed by using the MBESO method. Aimed to solve this critical problem, a simple but effective strategy is proposed in this paper. In steel-concrete composite structures, for instance, the overloaded compressed concrete elements with exceedingly high stress are replaced with steel material. The small amount of steel material added to the highly compressed region can effectively reduce the maximum compressive stress of the concrete material to a safe level. The comparison between the original MBESO method and the improved strategy based on a series of two-dimensional and three-dimensional examples clearly demonstrates the effectiveness of the proposed strategy in enhancing the structural safety and strength of the topologically optimized composite structures. This distinctly different material distribution strategy shows its potential and value in multi-material topology optimization research and applications.

A new method for performing topology optimization while considering multiple load cases is presented. The technique is demonstrated using two classes of problems, the first of which seeks to minimize the maximum deflection under a series of fixed, point loads subject to a material volume constraint. The second is a classical weight minimization problem subject to constraints on the maximum deflection caused by each load case. Because the topology optimization problem involving SIMP materials is inherently non-convex, the optimized solution is highly sensitive to the starting point and search path followed during the optimization. Therefore, the proposed technique calls for the use of a composite objective function, which is defined as the Kreisselmeier–Steinhauser aggregate of the individual objectives corresponding to the different load cases. The technique is also applied to the weight minimization problem, in which case the KS function is used to construct an aggregate constraint function. In this way, sensitivity information from inactive load cases is taken into account throughout the optimization making the method less susceptible to local minima. Furthermore, by beginning with a low value for the