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Phase field topology optimization of elasto-plastic contact problems with friction
Published in Alphose Zingoni, Current Perspectives and New Directions in Mechanics, Modelling and Design of Structural Systems, 2022
In many applications the areas where the contact occurs are very small It implies that the transmitted contact force densities are usually rather big in the contact zone and it leads to plastic deformations. Therefore it is reasonable to consider an elasto-plastic rather than elastic model for the material. The high contact stress may also lead to undesired vibrations or the degradation of surfaces of the contacting bodies as well as the deterioration of the working conditions for employees. The reduction of high contact stress or the obtaining the uniform distribution of this stress is the main aim of the topology or shape optimization problems for bodies in contact. The topology optimization consists in such distribution of the material filling the structure within the design domain to minimize the given cost functional describing the required features of the structure. Most research related to topology optimization has been concerned with linear elastic structures. The amount of papers dealing with non-linear elastic structures or nonlinear mechanical behavior is limited.
Design Optimization
Published in Xiaolin Chen, Yijun Liu, Finite Element Modeling and Simulation with ANSYS Workbench, 2018
A design's performance should be optimized from different perspectives as the design process evolves. In the early stage of a design, topology optimization can be used to help designers arrive at a good initial design concept. The goal of topology optimization is to find the ideal distribution of material within a predefined design space for a given set of loading and boundary conditions. The regions that contribute the least to the load bearing are identified and taken out from the design to minimize the weight. As a result, an optimal material layout is determined, from which a good design concept can be derived. Figure 11.1 illustrates topology optimization of a bridge structure. The 3-D design space of the bridge is shown as a solid rectangle box in Figure 11.1a. The bridge is fixed on the bottom two edges and applied a surface load on the top face. In Figure 11.1b, an arch is clearly suggested as the ideal layout by the topology optimization study aiming at 80% weight reduction. Materials are removed from the least stressed regions in the simulation model, that is, regions contributing the least to the overall stiffnesss of the structure. This optimization study perhaps helps elucidate why the arch continues to play an important part in bridge design after thousands of years of architectural use.
Additive manufacturing technologies
Published in Adedeji B. Badiru, Vhance V. Valencia, David Liu, Additive Manufacturing Handbook, 2017
Another challenge is to reduce weight and decrease the material used while keeping the product functions (mechanical, use…). Moreover, the main and support material can be expensive in the AM technology. Topology optimization is a mathematical approach that optimizes material layout within a given design space for a given set of loads and boundary conditions, so that the resulting layout meets a prescribed set of performance targets (Bendsoe and Sigmund 2003). Using topology optimization, engineers can find the best concept design that meets the design requirements. Any complex geometry is feasible in AM, the topological optimization implementation of a model leads to a new internal structure while maintaining conditions (mechanical, design shape, functions, etc.). Topologically, optimized parts have been created with internal geometry, using a narrow-waited structure that avoids the need for building supports (Galantucci et al. 2008). This method also creates new shapes of products.
Structural design and optimization of a guardrail for the train-to-train collision test platform
Published in Mechanics Based Design of Structures and Machines, 2023
Chengxing Yang, Wei Guo, Xianliang Xiao, Ping Xu, Shuguang Yao
In general, optimization methods for guardrail structures include three levels with increasing difficulty, i.e., size optimization (Kaveh and Ghazaan 2017; Liu et al. 2019; Zeng et al. 2019; Ma et al. 2020; Zhu, Liu, and Liu 2021), shape optimization (Kwak and Lee 2009; Wang et al. 2018; Zeng, Lu, and Wang 2020; Zahedan, Ahmadi, and Liaghat 2022), and topology optimization (Zhang et al. 2015; Sanz-Corretge and Echeverría 2018; Afrousheh, Marzbanrad, and Göhlich 2019; Bahramian and Khalkhali 2020; Alkalla and Fanni 2021; Gan and Wang 2021). Size optimization is widely used to find optimal solutions for key product characteristics, such as cross-sectional thicknesses, material choice, and other part parameters (Ponginan 2021). Shape optimization enhances an existing geometry by adjusting the height, length, or radii of the design (Ponginan 2021). Topology optimization is a mathematical method that optimizes material layout within a given design space, for a given set of loads, boundary conditions and constraints with the goal of maximizing the performance of the system (Bendsøe and Sigmund 2003). Size optimization refers to the physical size of the members within a structure, while shape refers to the geometric layout and topology to the internal member configuration of a structure (Mortazavi and Toğan 2016). In other words, topology optimization gives the product’s initial design, while size/shape optimization is used to update the current design (Gupta 2022).
An augmented Lagrangian method for multiple nodal displacement-constrained topology optimization
Published in Engineering Optimization, 2022
Nouman Saeed, Kai Long, Lixiao Li, Ayesha Saeed, Chengwan Zhang, Zhengkun Cheng
As a well-known mathematical process, topology optimization (TO) can achieve novel material layouts within a specific design domain to enhance the performance of a system. An inspiring inaugural study introduced by Bendsoe and Kikuchi (1988) proposed a practical topological design tool for structural optimization problems. To achieve the objective of maximum stiffness or minimum weight, the practice of TO has become increasingly prevalent in industrial engineering, particularly in the automobile and aerospace industries. Since the foundational work, outstanding achievements have been extended to stress constraints (Liu, Wen, and Xie 2016). Researchers in the field of TO have focused on developing more efficient and accurate methods for dealing with stress restrictions connected to problems concerning compliant mechanisms (Liu, Yan, and Yu 2021; Xu et al.2021).
Structural optimization with explicit geometric constraints using a B-spline representation
Published in Mechanics Based Design of Structures and Machines, 2022
Yosef M. Yoely, Iddo Hanniel, Oded Amir
Out of the various sub-disciplines of structural optimization, topology optimization can be seen as the most general and is becoming an integral part of the design process in aerospace, automotive and civil engineering (Bremicker et al. 1991; Vaidya et al. 2006; Zhang et al. 2015; Balogh, Bruggi, and Lógó 2018; Kook 2019). In essence, topology optimization aims to find the best possible distribution of material in a specified design space, such that a certain objective function is minimized subject to a set of design or response-based constraints. The method has been attracting tremendous research efforts since the pioneering work of Bendsøe and Kikuchi (1988) who proposed to formulate the problem based on homogenization of cells with a given microstructure. Several different approaches for formulating and solving topology optimization problems have been proposed over the years and the method has been extended also to other physical disciplines. For state-of-the-art reviews of the recent developments in topology optimization, the readers are referred to review articles and references therein (Sigmund and Maute 2013; Deaton and Grandhi 2014). It is worth noting that basic topology optimization functionalities have been embedded into all commercial CAD packages—indicating the important role that topology optimization has in the conceptual design phase in industry.