Grant P. Steven

A performance-based optimization method for topology design of continuum structures with mean compliance constraints

A performance-based optimization (PBO) method for optimal topology design of linear elastic continuum structures with mean compliance constraints is presented in this paper. The performance-based design concept is incorporated in continuum topology optimization, which is treated as the problem of improving the performance of a continuum design domain in terms of the efficiency of material usage and overall stiffness. A simple scheme is employed in the proposed method to suppress the formation of checkerboard patterns. Two energy-based performance indices are derived for quantifying the topology performance of plane stress structures and plates in bending. Performance-based optimality criteria incorporating performance indices are proposed, and can be used in any continuum topology optimization methods for compliance minimization problems to obtain the optimum. Numerical examples are provided to demonstrate the effectiveness and validity of the PBO method in producing optimal topologies of continuum structures.

Evolutionary structural optimization for connection topology design of multi‐component systems

Most engineering products contain more than one component or structural element, a consideration that needs to be appreciated during the design process and beyond, to manufacturing, transportation, storage and maintenance. The allocation and design of component interconnections (such as bolts, rivets, or springs, spot‐welds, adhesives, others) usually play a crucial role in the design of the entire multi‐component system. This paper extends the evolutionary structural optimization method to the generic design problems of connection topology. The proposed approach consists of a simple cycle of a finite element analysis followed by a rule‐driven element removal process. To make the interconnection elements carry as close to uniform a load as possible, a “fully stressed” design criterion is adopted. To determine the presence and absence of the interconnection elements, the usage efficiencies of fastener elements are estimated in terms of their relative stress levels. This avoids the use of gradient‐based optimization algorithms and allows designers to readily seek an optimization of connection topology, which can be implemented in their familiar CAD/CAE design platforms. To demonstrate the capabilities of the proposed procedure, a number of design examples are presented in this paper.

Multicriteria optimization that minimizes maximum stress and maximizes stiffness

Abstract In presenting and discussing structural analysis and design an engineer/analyst is always emphasizing the importance of strength and stiffness and endeavoring to get a balance between them both that suits the design in hand. It seems logical therefore in presenting structural optimization that both these crucial items be objectives of the process rather than having one as the objective and the other as a constraint as has traditionally been the case. It initially feels more appropriate to be trying to maximize stiffness whilst simultaneously maximize the strength. Also the goal of maximizing strength of a structure should, to the authors mind, be in the form of minimizing the maximum stress under all load cases. Traditionally structural optimization has targeted stress equalization or the achievement of “fully stressed” design as the stress objective/constraint. The authors consider that such an objective, especially coupled in with FEA still can lead to high localized stresses which therefore do not improve the strength of the structure. This paper aims at exploring the application of the evolutionary structural optimization method to such multicriteria design problems. To evaluate the overall effect on the design of material variation due to these two optimality criteria, a weighting scheme is adopted, whereby the weight factors emphasize and/or balance the stiffness and stress criteria. The work can accommodate various situations involving shape and topology design with multiple criteria. Also the important practical aspects of possible multiple peak stresses and multiple load cases are taken into account. A number of examples demonstrate the capabilities of the proposed method for solving multicriteria design optimization structural design problems.

A performance index for topology and shape optimization of plate bending problems with displacement constraints

Abstract.This paper presents a performance index for topology and shape optimization of plate bending problems with displacement constraints. The performance index is developed based on the scaling design approach. This performance index is used in the Performance-Based Optimization (PBO) method for plates in bending to keep track of the performance history when inefficient material is gradually removed from the design and to identify optimal topologies and shapes from the optimization process. Several examples are provided to illustrate the validity and effectiveness of the proposed performance index for topology and shape optimization of bending plates with single and multiple displacement constraints under various loading conditions. The topology optimization and shape optimization are undertaken for the same plate in bending, and the results are evaluated by using the performance index. The proposed performance index is also employed to compare the efficiency of topologies and shapes produced by different optimization methods. It is demonstrated that the performance index developed is an effective indicator of material efficiency for bending plates. From the manufacturing and efficient point of view, the shape optimization technique is recommended for the optimization of plates in bending.

On the development of structural optimisation and its relevance in engineering design

Abstract In the past, we have seen extensive developments in computational applications in order to improve the efficiency of a design process — e.g. FEA; CAD/CAM; and virtual modelling. In more recent years, much research has been conducted in optimisation. The introduction of optimisation in design is revolutionary in that it aids both the efficiency and creativity of a designer, improving the quality of a design itself. This paper addresses the current status of engineering design and optimisation methods, and defines their relevance and considers their implications for the future of the design process.

An evolutionary approach to elastic contact optimization of frame structures

Many real structures are made up of trusses and beams as are their computational models. It may be important to the designer to consider such structures to be in contact and if so, then to ensure that such contact does not produce high localized stress. This study is concerned with such an issue in truss/beam structures involving a unilateral contact constraints. In this paper, the evolutionary structural optimization method is verified for the design of planar or three-dimensional structures that consist of truss or beam elements. An elastic frame in contact with a rigid foundation and two elastic frames in contact with either two-or three-dimensional structures have been studied. Since the truss and beam elements provide different structural responses, the difference of optimal frame designs between these two element types is also investigated in this paper.

Stiffness and inertia multicriteria evolutionary structural optimisation

In continuation of the recent development of Evolutionary Structural Optimisation (ESO) applied to the simultaneous objective to maximise the natural frequency and to minimise the mean compliance, presents the Multicriteria ESO optimisation of two new criteria. This has been done with the use of four different multicriteria methods. Three examples have been used to verify the usefulness and capability of these methods applied to ESO in the context of the aforementioned criteria. Concluded that the ESO weighting method is proficient in presenting the designer with a range of options (of Pareto attribute) taking into account multiple criteria, and the global criterion method has the tendency to produce shapes and topologies that resemble that of the weighted 50 per cent: 50 per cent method. Likewise, the logical OR operator method produced designs that corresponded directly to those of 100 per cent stiffness weighted criteria. No clear resemblance could be concluded with the case of the logical AND operator method.

Discrete sensitivity-based evolutionary design optimization

Publisher Summary This chapter describes a paper that elucidates the range of individual design sensitivities that have been used in an evolutionary design optimization algorithm and presents some applications using these design sensitivities, which involve multioptimality criteria and multiphysics. The process, the evolutionary structural optimization (ESO), has been developed over the last 1010 years. Recent developments have significantly extended the original structural concept to most engineering mechanics situations. This paper demonstrates that the method can now be regarded as a gradient-based semianalytic sensitivity approach whereby the sensitivities are element-based and all design modifications take place at the element level. It shows how such sensitivities can be derived jsut like any physical aspect of a design. Accordingly, the decision regarding element modification can be based on its fitness when subjected to a range of physical and structural behaviors. For multiobjective or/and multiconstraint cases, a composite sensitivity can be formed that accounts for a balance in all the individual objectives/constraints in a Pareto manner with equal weights or penalized weights dependent on the amount of constraint violation.