Development of an Automatic Coupler for Railway Vehicles: A Topology Optimization Approach with Numerical and Experimental Validation

This thesis aims at understanding and improving topology optimization techniques focusing on density-based level-set methods and geometrical nonlinearities. Central in this work are the numerical modeling of the mechanical response of a design and the consistency of the optimization process itself. Concerning the first topic, we investigate different means to improve the robustness of density-based numerical models including geometrical nonlinearities. The conventional approach (scaling the local material properties) can result in convergence problems due to excessive deformation in low-stiffness finite elements. To avoid excessive deformation, we combine the element connectivity parameterization method (adapting the connectivity between finite elements) with level-set-based topology optimization. Furthermore, we achieve greater robustness of analysis method using a second and improved approach called element deformation scaling. This approach eliminates the need for solving internal equilibrium equations (needed for the element connectivity parameterization method) via an explicit relation between the local internal and global external displacement field. The second focus of this thesis is on the optimization process of level-set-based topology optimization, and in particular its numerical consistency. We observe that signed-distance reinitialization of the level-set function affects the shape of a design in the optimization process. To minimize this effect, we propose a discrete level-set method that is based on an approximate Heaviside function and focusing on the implementation. Furthermore, we also propose a level-set-based topology optimization method using an exact Heaviside function and mathematical programming that effectively eliminates the need for reinitialization. We demonstrate that our density-based level-set method is closely related to conventional density-based topology optimization methods, while offering the advantage of more control over the geometrical complexity. On the other hand, we confirm that the dependence of the final result on the initial design which remains one of the big challenges for level-set-based topology optimization. The potential of the proposed level-set method is shown by applying it on problems with stress constraints and geometrical nonlinearities and performing manufacturing tolerant topology optimization. Finally, this thesis offers a review of level-set methods for structural topology optimization to identify and discuss the different approaches that are available in literature. We can distinguish between level-set methods by examination of their design parameterization, sensitivities, update procedures and regularization techniques. A level-set-based design parameterization offers the advantage of a crisp distinction between subdomains. For this reason, X-FEM approaches and conforming discretizations are an interesting option to retain the crisp nature of the level-set-based description of the design. Many level-set methods are combined with density-based numerical models and are, therefore, closely related to conventional density-based topology optimization methods. In particular, recently proposed projection methods have much in common with a level-set-based design description. The results of level-set-based TO methods often rely heavily on regularization techniques that introduce inconsistencies in the optimization process. Numerical consistency does not necessarily lead to the best search direction, but is essential to find a Karush-Kuhn-Tucker point of the discretized optimization problem.

The structural design must ensure suitable working conditions by attending for safe and economic criteria. However, the optimal solution is not easily available, because these conditions depend on the bodies’ dimensions, materials strength and structural system configuration. In this regard, topology optimization aims for achieving the optimal structural geometry, i.e. the shape that leads to the minimum requirement of material, respecting constraints related to the stress state at each material point. The present study applies an evolutionary approach for determining the optimal geometry of 2D structures using the coupling of the boundary element method (BEM) and the level set method (LSM). The proposed algorithm consists of mechanical modelling, topology optimization approach and structural reconstruction. The mechanical model is composed of singular and hyper-singular BEM algebraic equations. The topology optimization is performed through the LSM. Internal and external geometries are evolved by the LS function evaluated at its zero level. The reconstruction process concerns the remeshing. Because the structural boundary moves at each iteration, the body’s geometry change and, consequently, a new mesh has to be defined. The proposed algorithm, which is based on the direct coupling of such approaches, introduces internal cavities automatically during the optimization process, according to the intensity of Von Mises stress. The developed optimization model was applied in two benchmarks available in the literature. Good agreement was observed among the results, which demonstrates its efficiency and accuracy.

The article presents an overview of the construction of automatic couplers and their digital version of the DAC for freight wagons. In the article, particular attention was paid to the process related to the development and popularization of the design of automatic digital couplers in the European Union countries. Poland, the automatic coupler train was presented in July 2022 and tested under various conditions. This is related to the current trend of improving rail safety and accelerating the procedure of forming trains, and, consequently, sending a freight train on its way. Automatic digital couplers will allow, in addition to mechanical connection, also pneumatic and electrical connection without the participation of an employee for coupling and uncoupling carriages.

Research on multi-stage topology optimization method based on latent diffusion model

Topological design of microstructured materials using energy-based homogenization theory and proportional topology optimization with the level-set method

• A modified Tsai-Hill stress interpolation model for lattices is proposed. • Multiscale lattice structure topology optimization under stress constraints for static and dynamic loads is addressed. • Full-scale analysis and experimental validation of the optimized structures are conducted. This study presents a topology optimization method for heterogeneous lattice structures subject to stress constraints. The proposed approach extends the ordered SIMP (Solid Isotropic Material with Penalization) framework to incorporate a composite material failure criterion. Specifically, a modified Tsai–Hill yield criterion is employed to characterize the anisotropic yielding behavior of the heterogeneous lattice, which is subsequently integrated into the optimization as a stress constraint. To address the variation in yield strength across different lattice configurations, a normalization strategy is applied to the stress field. Additionally, a P-norm aggregation scheme is introduced to efficiently handle local stress constraints while reducing computational cost. The equivalent elastic tensor and yield strength of each lattice configuration are obtained using a representative volume element (RVE) based on homogenization theory. The effectiveness of the proposed method is demonstrated through a series of 2D cases, achieving lightweight structural designs that satisfy stress constraints. Finally, full-scale mechanical analysis and 3D printing experimental validation further confirm the strength reinforcement of the optimized results.

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

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.

The SIMP (solid isotropic material with penalization) approach is perhaps the most popular density variable relaxation method in topology optimization. This method has been very successful in many applications, but the optimization solution convergence can be improved when new variables, not the direct density variables, are used as the design variables. In this work, we newly propose S-shape functions mapping the original density variables nonlinearly to new design variables. The main role of S-shape function is to push intermediate densities to either lower or upper bounds. In particular, this method works well with nonlinear mathematical programming methods. A method of feasible directions is chosen as a nonlinear mathematical programming method in order to show the effects of the S-shape scaling function on the solution convergence.

A boundary element and level set based topology optimisation using sensitivity analysis

Topological optimization is an innovative method to realize the lightweight design. This paper proposes a hybrid topology optimization method that combines the SIMP (solid isotropic material with penalization) method and genetic algorithm (GA), called the SIMP-GA method. In the method, SIMP is used to update the chromosomes, which can accelerate convergence. The filtering scheme in the SIMP method can filter unconnected elements to ensure the connectivity of the structure. We studied the influence of varying the filtering radius on the optimized structure. Simultaneously, in the SIMP-GA method, each element is regarded as a gene, which controls the population number to a certain extent, reduces the amount of calculation, and improves the calculation efficiency. The calculation of some typical examples proves that the SIMP-GA method can obtain a better solution than the gradient-based method. Compared with the conventional genetic algorithm and GA-BESO (Bi-directional Evolutionary Structural Optimization) method, the calculation efficiency of the proposed method is higher and similar results are obtained. The innovative topology optimization method could be an effective way for structural lightweight design.

This paper discusses a geometrical optimization method for thermoelectric generators. Our method provides the optimized geometry in accord with various arbitrary conditions such as types of materials, volume of materials, temperatures of installation position, and shape of installation position. It has the potential to contribute to improving thermoelectric devices in supporting design stages. By establishing the coupled equations of state for the thermoelectric problem, an analytical model subject to these equations is introduced that mimics the closed circuit composed of the thermoelectric materials, electrodes and a resistor. The total electric power lost through the resistor is formulated as an objective function for optimization. The proposed optimization method for thermoelectric generators is implemented as a geometrical optimization method using the solid isotropic material with penalization (SIMP) method used in topology optimizations. Simple relations are formulated between the density function of SIMP method and physical properties of thermoelectric material. Sensitivity analysis for the objective function is formulated with respect to the density function and the adjoint equations required for calculating it. Depending on the sensitivity, the density function is updated using the method of moving asymptotes, which has numerous benefits in various optimization problems by virtue of its combination with topology optimization. Finally, the numerical examples are provided to demonstrate the validity of our method.

SummaryIn this work, an asymptotically concentrated topology optimization method based on the solid isotropic material with logistic function interpolation is proposed. The asymptotically concentrated method is introduced into the process of optimization cycle after updating the design variables. At the same time, with the use of the solid isotropic material with logistic function interpolation, all the candidate densities are reasonably polarized, relying on the characteristic of the interpolation curve itself. The asymptotically concentrated method can effectively suppress the generation of intermediate density and speed up the process of updating the design variables, hence improving the optimization efficiency. Moreover, the above polarization can weaken the influence of low‐related‐density elements and enhance the influence of high‐related‐density elements. For the single‐material topology optimization problem, gray‐scale elements can be effectively eliminated, and clear boundary and smaller compliance can be obtained by this method. For the multimaterial topology optimization problem, minimum compliance with high efficiency can be achieved by this method. The proposed method mainly includes the following advantages: concentrated density variables, reasonable interpolation, high computational efficiency, and good topological results.

A Multi-volume constraint approach to diverse form designs from topology optimization

Since deterministic topology optimization (TO) does not consider the uncertainties in the structure, including materials, loading and geometric dimensions, it may provide the optimal designs with the lowest state of reliability and safety. To solve this problem, reliability-based topology optimization (RBTO) is used, which is actually a combination of TO methods with reliability-based design methods (RBDO) based on a mathematical framework and process. In this article, by considering four TO methods including moving iso-surface threshold (MIST), SIMP, evolutionary structural optimization-extended finite element (XFEM-ESO) and level-set (LS), and considering a constraint or objective function, an optimal volume fraction (Vf) is obtained for TO by the bisection method. Then, with the aid of mean volume fraction, TO is performed and its optimized results are applied by an advanced reliability analysis method, i.e. accelerated dynamical mean value (ADMV), taking into account the uncertainties and their standard deviations to extract the most probable probability point (MPP). Having the MPP and the constraint, the bisection algorithm is used again and the optimized volume fraction for the RBTO model, and thereby the optimal layout for the RBTO solution, is achieved. Several examples are presented to validate and highlight the optimization capability of the RBTO method using a structural model and the mentioned TO methods, and the results are compared together. Based on the results, it is shown that the combination of RBDO and TO approach is able to result in powerful, stable, safe, and reliable structures completely different from the TO results.