An application of bi-directional evolutionary structural optimisation for optimising energy absorbing structures using a material damage model

The Bi-directional Evolutionary Structural Optimisation (BESO) method is a numerical topology optimisation method developed for use in finite element analysis. This paper presents a particular application of the BESO method to optimise the energy absorbing capability of metallic structures. The optimisation objective is to evolve a structural geometry of minimum mass while ensuring that the kinetic energy of an impacting projectile is reduced to a level which prevents perforation. Individual elements in a finite element mesh are deleted when a prescribed damage criterion is exceeded. An energy absorbing structure subjected to projectile impact will fail once the level of damage results in a critical perforation size. It is therefore necessary to constrain an optimisation algorithm from producing such candidate solutions. An algorithm to detect perforation was implemented within a BESO framework which incorporated a ductile material damage model.

pH-tunable hydrogelators for water purification: structural optimisation and evaluation

A focused library of potential hydrogelators each containing two substituted aromatic residues separated by a urea or thiourea linkage have been synthesised and characterized. Six of these novel compounds are highly efficient hydrogelators, forming gels in aqueous solution at low concentrations (0.03–0.60 wt %). Gels were formed through a pH switching methodology, by acidification of a basic solution (pH 14 to ≈4) either by addition of HCl or via the slow hydrolysis of glucono-δ-lactone. Frequently, gelation was accompanied by a dramatic switch in the absorption spectra of the gelators, resulting in a significant change in colour, typically from a vibrant orange to pale yellow. Each of the gels was capable of sequestering significant quantities of the aromatic cationic dye, methylene blue, from aqueous solution (up to 1.02 g of dye per gram of dry gelator). Cryo-transmission electron microscopy of two of the gels revealed an extensive network of high aspect ratio fibers. The structure of the fibers altered dramatically upon addition of 20 wt % of the dye, resulting in aggregation and significant shortening of the fibrils. This study demonstrates the feasibility for these novel gels finding application as inexpensive and effective water purification platforms.

Applying bi-directional evolutionary structural optimisation method for tunnel reinforcement design considering nonlinear material behaviour

In the empirical methods for reinforcement design of underground excavations, an even distribution of rock bolts is generally recommended. This work proves that this design is not necessarily optimal and shows how the state-of-the-art reinforcement design could be improved through topology optimisation techniques. The Bidirectional Evolutionary Structural Optimisation (BESO) method has been extended to consider nonlinear material behaviour. An elastic perfectly-plastic Mohr-Coulomb model is utilised for both original rock and reinforced rock. External work along the tunnel wall is considered as the objective function. Various in situ stress conditions with different horizontal stress ratios and different geostatic stress magnitudes are investigated through several examples. The outcomes show that the proposed approach is capable of improving tunnel reinforcement design. Also, significant difference in optimal reinforcement distribution for the cases of linear and nonlinear analysis results proves the importance of the influence of realistic nonlinear material properties on the final outcome.

A systems approach to shape and topology optimisation of mechanical structures

Optimisation techniques have become more and more important as the possibility of simulating complex mechanical structures has become a reality. A common tool in the layout design of structural parts is the topology optimisation method, which finds an optimum material distribution within a given geometrical design space to best meet loading conditions and constraints. Another important method is shape optimisation, which optimises weight given parametric geometric constraints. In the case of complex shaped parts or elaborate assemblies, for example automobile body structures, shape optimisation is still hard to do; mainly due to the difficulty in translating shape design parameters into meaningful analysis models. Tools like the parametric geometry package SFE CONCEPT are designed to mitigate these issues. Nevertheless, shape methods usually cannot suggest new load path configurations, while topology methods are often confined to single parts. To overcome these limitations the authors have developed a method that combines both approaches into an Integral Shape/Topology Method (IST) that is capable of finding new optimal solutions. This is achieved by an automated optimisation loop and can be applied for both thin walled structures as well as solid 3D geometries. When optimising structures by applying IST, global optimum solutions can be determined that may not be obtained with isolated shape- or topology-optimisation methods.

Axisymmetric shell structures for multi-use

Shell structures find use in many fields of engineering, notably structural, mechanical, aerospace and nuclear-reactor disciplines. Axisymmetric shell structures are used as dome type of roofs, hyperbolic cooling towers, silos for storage of grain, oil and industrial chemicals and water tanks. Despite their thin walls, strength is derived due to the curvature. The generally high strength-to-weight ratio of the shell form, combined with its inherent stiffness, has formed the basis of this vast application. With the advent in computation technology, the finite element method and optimisation techniques, structural engineers have extremely versatile tools for the optimum design of such structures. Optimisation of shell structures can result not only in improved designs, but also in a large saving of material. The finite element method being a general numerical procedure that could be used to treat any shell problem to any desired degree of accuracy, requires several runs in order to obtain a complete picture of the effect of one parameter on the shell structure. This redesign I re-analysis cycle has been achieved via structural optimisation in the present research, and MSC/NASTRAN (a commercially available finite element code) has been used in this context for volume optimisation of axisymmetric shell structures under axisymmetric and non-axisymmetric loading conditions. The parametric study of different axisymmetric shell structures has revealed that the hyperbolic shape is the most economical solution of shells of revolution. To establish this, axisymmetric loading; self-weight and hydrostatic pressure, and non-axisymmetric loading; wind pressure and earthquake dynamic forces have been modelled on graphical pre and post processor (PATRAN) and analysis has been performed on two finite element codes (ABAQUS and NASTRAN), numerical model verification studies are performed, and optimum material volume required in the walls of cylindrical, conical, parabolic and hyperbolic forms of axisymmetric shell structures are evaluated and reviewed. Free vibration and transient earthquake analysis of hyperbolic shells have been performed once it was established that hyperbolic shape is the most economical under all possible loading conditions. Effect of important parameters of hyperbolic shell structures; shell wall thickness, height and curvature, have been evaluated and empirical relationships have been developed to estimate an approximate value of the lowest (first) natural frequency of vibration. The outcome of this thesis has been the generation of new research information on performance characteristics of axisymmetric shell structures that will facilitate improved designs of shells with better choice of shapes and enhanced levels of economy and performance. Key words; Axisymmetric shell structures, Finite element analysis, Volume Optimisation_ Free vibration_ Transient response.

The use of a GA to improve the postbuckling strength of stiffened composite panels susceptible to secondary instabilities

The use of genetic algorithms (GAs) for structural optimisation is well established but little work has been reported on the inclusion of damage variables within an optimisation framework. This approach is particularly useful in the optimisation of composite structures which are prone to delamination damage. In this paper a challenging design problem is presented where the objective was to delay the catastrophic failure of a postbuckling secondary-bonded stiffened composite panel susceptible to secondary instabilities. It has been conjectured for some time that the sudden energy release associated with secondary instabilities may initiate structural failure, but this has proved difficult to observe experimentally. The optimisation methodology confirmed this indirectly by evolving a panel displaying a delayed secondary instability whilst meeting all other design requirements. This has important implication in the design of thin-skinned lightweight aerostructures which may exhibit this phenomenon.

Metodologias de optimização topológica em cálculo estrutural

A optimização estrutural é uma temática antiga em engenharia. No entanto, com o crescimento do método dos elementos finitos em décadas recentes, dá origem a um crescente número de aplicações. A optimização topológica, especificamente, surge associada a uma fase de definição de domínio efectivo de um processo global de optimização estrutural. Com base neste tipo de optimização, é possível obter a distribuição óptima de material para diversas aplicações e solicitações. Os materiais compósitos e alguns materiais celulares, em particular, encontram-se entre os materiais mais proeminentes dos nossos dias, em termos das suas aplicações e de investigação e desenvolvimento. No entanto, a sua estrutura potencialmente complexa e natureza heterogénea acarretam grandes complexidades, tanto ao nível da previsão das suas propriedades constitutivas quanto na obtenção das distribuições óptimas de constituintes. Procedimentos de homogeneização podem fornecer algumas respostas em ambos os casos. Em particular, a homogeneização por expansão assimptótica pode ser utilizada para determinar propriedades termomecânicas efectivas e globais a partir de volumes representativos, de forma flexível e independente da distribuição de constituintes. Além disso, integra processos de localização e fornece informação detalhada acerca de sensibilidades locais em metodologias de optimização multiescala. A conjugação destas áreas pode conduzir a metodologias de optimização topológica multiescala, nas quais de procede à obtenção não só de estruturas óptimas mas também das distribuições ideais de materiais constituintes. Os problemas associados a estas abordagens tendem, no entanto, a exigir recursos computacionais assinaláveis, criando muitas vezes sérias limitações à exequibilidade da sua resolução. Neste sentido, técnicas de cálculo paralelo e distribuído apresentam-se como uma potencial solução. Ao dividir os problemas por diferentes unidades memória e de processamento, é possível abordar problemas que, de outra forma, seriam proibitivos. O principal foco deste trabalho centra-se na importância do desenvolvimento de procedimentos computacionais para as aplicações referidas. Adicionalmente, estas conduzem a diversas abordagens alternativas na procura simultânea de estruturas e materiais para responder a aplicações termomecânicas. Face ao exposto, tudo isto é integrado numa plataforma computacional de optimização multiobjectivo multiescala em termoelasticidade, desenvolvida e implementada ao longo deste trabalho. Adicionalmente, o trabalho é complementado com a montagem e configuração de um cluster do tipo Beowulf, assim como com o desenvolvimento do código com vista ao cálculo paralelo e distribuído.

The ESO method revisited

This paper examines the evolutionary structural optimisation (ESO) method and its shortcomings. By proposing a problem statement for ESO followed by an accurate sensitivity analysis a framework is presented in which ESO is mathematically justifiable. It is shown that when using a sufficiently accurate sensitivity analysis, ESO method is not prone to the problem proposed by Zhou and Rozvany (Struct Multidiscip Optim 21(1):80–83, 2001). A complementary discussion on previous communications about ESO and strategies to overcome the Zhou-Rozvany problem is also presented. Finally it is shown that even the proposed rigorous ESO approach can result in highly inefficient local optima. It is discussed that the reason behind this shortcoming is ESO’s inherent unidirectional approach. It is thus concluded that the ESO method should only be used on a very limited class of optimisation problems where the problem’s constraints demand a unidirectional approach to final solutions. It is also discussed that the Bidirectional ESO (BESO) method is not prone to this shortcoming and it is suggested that the two methods be considered as completely separate optimisation techniques.