An evaluative study on ESO and SIMP for optimising a cantilever tie—beam

We examine both the evolutionary structural optimisation (ESO) and solid isotropic microstructure with penalisation (SIMP) methodologies by investigating a cantilever tie–beam. Initially, both ESO and SIMP produce designs with higher objective function values relative to a previously published ‘intuitive’ design. However, after careful investigation of the numerical parameters such as the initial design domain and the mesh size, both methods obtain designs that have lower objective function values relative to the intuitive design. Thus, a clearer understanding of the numerical parame- ters and their influence on optimisation methods is achieved.     

Toolbox for super-structured and super-structure free multi-disciplinary building spatial design optimisation

Multi-disciplinary optimisation of building spatial designs is characterised by large solution spaces. Here two approaches are introduced, one being super-structured and the other super-structure free. Both are different in nature and perform differently for large solution spaces and each requires its own representation of a building spatial design, which are also presented here. A method to combine the two approaches is proposed, because the two are prospected to supplement each other. Accordingly a toolbox is presented, which can evaluate the structural and thermal performances of a building spatial design to provide a user with the means to define optimisation procedures. A demonstration of the toolbox is given where the toolbox has been used for an elementary implementation of a simulation of co-evolutionary design processes. The optimisation approaches and the toolbox that are presented in this paper will be used in future efforts for research into- and development of optimisation methods for multi-disciplinary building spatial design optimisation.     

Deep learning driven real time topology optimisation based on initial stress learning

Topology optimisation can facilitate engineers in proposing efficient and novel conceptual design schemes, but the traditional FEM based optimization demands significant computing power and makes the real time optimization impossible. Based on the convolutional neural network (CNN) method, a new deep learning approximate algorithm for real time topology optimisation is proposed. The algorithm learns from the initial stress (LIS), which is defined as the major principal stress matrix obtained from finite element analysis in the first iteration of classical topology optimisation. The initial major principal stress matrix of the structure is used to replace the load cases and boundary conditions of the structure as independent variables, which can produce topological prediction results with high accuracy based on a relatively small number of samples. Compared with the traditional topology optimisation method, the new method can produce a similar result in real time without repeated iterations. A classic short cantilever problem was used as an example, and the optimized topology of the cantilever structure is predicted successfully by the established approximate algorithm. By comparing the prediction results to the structural optimisation results obtained by the classical topology optimisation method, it is discovered that the two results are highly approximate, which verifies the validity of the established algorithm. Furthermore, a new algorithm evaluation method is proposed to evaluate the effects of using different methods to select samples on the prediction performance of the optimized topology, and the results were promising and concluded in the end.     

A genetic algorithm for combined topology and shape optimisations

A method to find optimal topology and shape of structures is presented. With the first the optimal distribution of an assigned mass is found using an approach based on homogenisation theory, that seeks in which elements of a meshed domain it is present mass; with the second the discontinuous boundaries are smoothed. The problem of the optimal topology search has an ON/OFF nature and has suggested the employment of genetic algorithms. Thus in this paper a genetic algorithm has been developed, which uses as design variables, in the topology optimisation, the relative densities (with respect to effective material density) 0 or 1 of each element of the structure and, in the shape one, the coordinates of the keypoints of changeable boundaries constituted by curves. In both the steps the aim is that to find the variable sets producing the maximum stiffness of the structure, respecting an upper limit on the employed mass. The structural evaluations are carried out with a FEM commercial code, linked to the algorithm. Some applications have been performed and results compared with solutions reported in literature.     

Multidisciplinary design optimisation and robust design approaches applied to concurrent design

The increasing economic competition of all industrial markets and growing complexity of engineering problems lead to a progressive specialisation and distribution of expertise, tools and work sites. Most industrial sectors manage this fragmentation using the concurrent engineering approach, which is based on tools integration and shared databases and requires significant investments in design and work organisation. Besides, the multidisciplinary design optimisation (MDO) is more and more used as a method for optimal solutions search with regard to multiple coupled disciplines. The paper describes a quite innovative multidisciplinary optimisation method based on robust design techniques: MORDACE (multidisciplinary optimisation and robust design approaches applied to concurrent engineering). Managing uncertainty due to design teams collaboration, our automatic optimisation strategy allows concurrently designing different aspects or parts of a complex product. The method assures effective design work distribution and high optimisation results, containing the CPU time. In addition, our strategy is suited to the early stages of the design cycle, where evolutions of design goals and constraints are possible and exhaustive information about the design space is necessary. A roll stabiliser fin optimisation is presented as an example of this method applied to an industrial design problem.     

A CAD-based on biological method for designing optimal fatigue life

This paper presents an innovative approach to shape optimisation of three-dimensional, damage-tolerant structures. In this approach, a new and simple method, which we termed Failure Analysis of Structures (FAST), is used to estimate the stress-intensity factor for cracks at a notch. The methodology and software used to automate damage-tolerance calculations are developed using computer-aided design and FAST codes. The worst crack locations are found by modeling many cracks along fractured critical edges of the structure by using FAST. This software is then used to evaluate damage-tolerance objective functions for optimisation algorithms. A particular stress-based biological growth method is employed to study the problem of optimisation with fatigue life as the design objective. This work confirms that a stress-optimised structure does not necessarily give the longest fatigue life by numerical examples.     

Structural topology and element sizing design optimisation of tall steel frameworks using a hybrid OC–GA method

This paper presents a hybrid optimisation method in which a local search operator based on a rigorously derived optimality criteria (OC) technique is embedded in the framework of a genetic algorithm (GA). The GA framework is particularly useful in the global exploration for optimal topologies, while the OC technique serves as a local search operator for efficient element sizing optimisation of given topologies. The hybrid OC–GA method was developed to strike a balance between the exploration of global search algorithms and the exploitation of efficient local search methods so as to make the hybrid method suitable for optimising tall building structures involving a large number of structural elements. The applicability and efficiency of the hybrid OC–GA method were tested with two 40-storey steel frameworks. The results show that the hybrid method can generate superior designs to pure GA while exhibiting rapid and smooth convergence, suggesting its great potential for optimising both structural form and element size of practical tall building structures.     

一种应用于柔性作业车间成组调度问题的分级优化算法

提出一种求解柔性作业车间成组调度FGJSS(flexible grouped job-shop scheduling)问题的蚁群粒子群求解算法。算法采用主从递阶形式,主级为蚁群优化算法,选择零件加工设备;从级为粒子群优化算法,在主级零件加工设备约束下优化设备作业排序以实现流通时间最小的目标。算法中,以工序加工时间和设备承载的作业族数为启发式信息设计蚂蚁在工序可用设备间转移概率;以粒子向量优先权值和作业族号为依据设计解码方法实现设备上的成组作业排序。最后,通过仿真实验,验证了该算法的有效性。     

Bridge topology optimisation with stress, displacement and frequency constraints

The principal stress based evolutionary structural optimisation method is presented herein for topology optimisation of arch, tied arch, cable-stayed and suspension bridges with both stress and displacement constraints. Two performance index formulas are developed to determine the efficiency of the topology design. A refined mesh scheme is proposed to improve the details of the final topology without resorting to the complete analysis of a finer mesh. Furthermore, cable-supported bridges are optimised with frequency constraint incorporating the “nibbling” technique. The applicability, simplicity and effectiveness of the method are demonstrated through the topology optimisation of the four types of bridges.     

Optimal control of LQR for discrete time-varying systems with input delays

In this work, we consider the optimal control problem of linear quadratic regulation for discrete time-variant systems with single input and multiple input delays. An innovative and simple method to derive the optimal controller is given. The studied problem is first equivalently converted into a problem subject to a constraint condition. Last, with the established duality, the problem is transformed into a static mathematical optimisation problem without input delays. The optimal control input solution to minimise performance index function is derived by solving this optimisation problem with two methods. A numerical simulation example is carried out and its results show that our two approaches are both feasible and very effective.