Osvaldo M. Querin

Evolutionary structural optimisation using an additive algorithm

Abstract The evolutionary structural optimisation (ESO) method has been under continuous development since 1992. Traditionally, the method was conceived from the engineering perspective that the topology and shape of structures were naturally conservative for safety reasons and therefore contained an excess of material. To move from the conservative design to a more optimum design would therefore involve the removal of material. Thus the ESO method started from a design space much bigger than the optimum and the final topology or shape emerged by a process of removal of unwanted/inefficient/lowly stresses material. The original algorithms allowed for two forms of evolution. One was there the understressed material could be removed from anywhere in the allowable design space, and with compensation for checker-boarding this produces an optimum topology under the prescribed environments. The second form only allows removal from the surface or parts of the surface (called nibbling in the ESO lexicon); this produces a Min–Max situation where the maximum surface stress is reduced to a minimum. It has been demonstrated that the ESO process produces a surface that is an iso-stress contour thus satisfying the Min–Max optimality criterion. The present paper addresses the opposite evolutionary process whereby the structure evolves from a base which is the minimum structural form required to carry the load regardless of the magnitude of the stress levels. Material is added in the proximity of high stress to ameliorate its effect and hence the final structural form emerges. Only singly connected regions are formed in the present analysis and thus the additive ESO process is the opposite of the nibbling SO, mentioned above, that produces optimum surface shapes. The paper presents a brief background to the current state of structural optimisation research. This is followed by a discussion of the strategies for the additive ESO (AESO) algorithm and two examples are presented.

Bilevel Optimization of Blended Composite Wing Panels

Two approaches are examined for finding the best stacking sequence of laminated composite wing structures with blending and manufacturing constraints: smeared-stiffness-based method and lamination-parameter-based method. In the firstmethod, thematerial volume is the objective function at the global level, and the stack shuffling to satisfy blending and manufacturing constraints is performed at the local level. The other method introduced in this paper is to use lamination parameters and numbers of plies of the predefined angles (0, 90, 45, and 45 deg) as design variables with buckling, strain, and ply percentage constraints while minimizing the material volume in the top-level optimization run.Given lamination parameters from the top-level optimization as targets for the local level, an optimal stacking sequence is determined to satisfy the global blending requirements. On a benchmark problem of an 18-panel wing box, the results from these two approaches are compared to published results to demonstrate their potential.

The use of topology optimisation in the conceptual design of next generation lattice composite aircraft fuselage structures

Conventional commercial aircraft fuselages use all-aluminium semi-monocoque structures where the skin carries the external loads, the internal fuselage pressurisation and is strengthen using frames and stringers. Environmental and economic issues force aircraft designers to minimise weight and costs to keep air transport competitive and safe. But as metal designs have reached a high degree of perfection, extraordinary weight and cost savings are unlikely in the future. Carbon composite materials combined with lattice structures and the use of topology optimisation have the potential to offer such weight reductions. The EU FP7 project Advanced Lattice Structures for Composite Airframes (ALaSCA) was started to investigate this. This article present some of this research which has now led to the development of a new airframe concept which consists of: a load carrying inner skin; transverse frames; CFRP-metal hybrid stiffeners helically arranged in a grid configuration; insulating foam and an additional aerodynamic outer skin.

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.

THEORETICAL FOUNDATIONS OF SEQUENTIAL ELEMENT REJECTIONS AND ADMISSIONS (SERA) METHODS AND THEIR COMPUTATIONAL IMPLEMENTATION IN TOPOLOGY OPTIMIZATION

The theoretical foundations of the heuristic topology optimization technique “Sequential Element Rejections and Admissions” (SERA) are examined. SERA has been publicized extensively, mostly under the term Evolutionary Structural Optimization (ESO). However, doubts about SERA’s validity have been often expressed in the past. Zhou and Rozvany (2001) have shown that SERA may result in highly nonoptimal solutions in isolated cases. In this paper, the concept of Iteration-wise Optimal Element Change (IOEC) and the Fundamental Assumption of SERA are introduced and the (in)correctness of this supposition is evaluated on various examples experimentally. Finally methods of improving element rejection/admission criteria for SERA are investigated.

Extension of the fixed grid finite element method to eigenvalue problems

This paper details the development of the fixed grid FEA (FGFEA) method to the solution of eigenvalue (natural frequency and buckling) problems, using a 4 node 20 degree of freedom shell element. The formulation of the FG element stiffness, buckling and natural frequency equations is presented. The first natural frequency and buckling load are determined for the simply supported plate with a central circular void. The void is then offset to three further locations to asses the applicability of FGFEA eigenvalue analysis at reduced symmetry. A correlation trend is formed by comparison with traditional FEA results at nine increasingly refined mesh densities for each example. In addition to this, a relationship between the FGFEA error and the boundary element intersection angle with the void is formed.

Determination of an optimal topology with a predefined number of cavities

In thee eldoftopology optimization,increasinginteresthasbeenappliedtowardimprovingthepracticalapplicabilityofthemethods.Mechanically, a cavity in a structureintroducesstressconcentrationsand, hence,structurally undesirableeffectsonthedesign.However, designssuch asaircraftfuselagesand wingribsoften requirea specie ed number of cavities for their functional capabilities. Cavities also have the favorable consequence of reducing the weight. In this study, intelligent cavity creation is discussed as a means of determining an optimal topology with a desired number of cavities, based on evolutionary structural optimization. After the effect is shown on the total number of cavities when a new cavity is introduced during an optimization process, a parameter C is introduced that delays cavity creation. An investigation is carried out to observe the effects of various parameters such as C and mesh density on the e nal number of cavities.

Bi-level Optimization of Blended composite Panels

Two approaches are examined for finding the best stacking sequence of laminated composite wing structures with blending and manufacturing constraints: smeared stiffnessbased method and lamination parameter-based method. In the first method, the material volume is the objective function at the global level and the stack shuffling to satisfy blending and manufacturing constraints is performed at the local level. The other method introduced in this paper is to use lamination parameters and numbers of plies of the pre-defined angles (0, 90, 45 and -45 degrees) as design variables with buckling, strength and ply percentage constraints while minimizing the material volume in the top level optimization run. Given lamination parameters from the top level optimization as targets for the local level, optimal stacking sequence is determined to satisfy the global blending requirements. On a benchmark problem of an 18-panel wing box, the results from these two approaches are compared to published results to demonstrate their potential.

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.

Optimization of Blended Composite Wing Panels Using Smeared Stiffness Technique and Lamination Parameters

§** The smeared stiffness-based method is examined for finding the best stacking sequence of laminated composite wing structures with blending and manufacturing constraints . In this method, numbers of plies of the pre-defined angles (0, 90, 45 and -45 degrees) are design variables, buckling, strain and ply angle percentages are constraints and the material volume is the objective function at the global level . The ply shuffling to satisfy global blending and manufacturing constraints is performed at the local level to match zero values of lamination parameters. The latter requirement is due to the ply angle homogeneity through the stack that is assumed in the top level optimization. This integrated process utilizing the smeared stiffness technique and lamination parameters is demonstrated by the optimization of the root part of a generic aircraft wing structure. The local level optimization can be seen as a postprocessing phase for determining the detailed ply-book of the laminate.