Designing cutouts for optimum residual strength in plane structural elements

Abstract

The paper presents a new approach for shape optimisation of structures with residual strength as the design objective. It must be emphasized that flaws are inevitably present in most structures, and hence the influence of cracks on optimised shapes needs to be investigated. Numerical simulation of cracks using the finite element method requires a very fine mesh to model the singularity at crack tip. This makes fracture calculations computationally intensive. Furthermore, for a damage tolerance based optimisation numerous cracks are to be considered along the structural boundary, and fracture analysis needs to be repeated for each crack at every iteration, thus making the whole process extremely computationally expensive for practical purpose. Moreover, the lack of information concerning crack size, orientation, and location makes the formulation of the optimisation problem difficult. As a result, little attention has been paid to date to consider fracture parameters in the optimisation objective. To address this, the paper presents a methodology for the shape optimisation of structures with strength and durability as the design objectives. In particular, the damage tolerance optimisation is illustrated via the problem of optimal design of a 'cutout in a rectangular R. Das (B) CSIRO Mathematical and Information Sciences, block under biaxial loading'. A parametric shape representation has been used to describe the problem geometry. Damage tolerance based optimisation was performed using nonlinear programming algorithms, and NE-NASTRAN was used for finite element analysis. The first order mathematical programming algorithms, viz: the Broydon-Fletcher-Goldfarb-Shanno (BFGS) and the Fletcher-Reeves (Conjugate Direction) Methods were evaluated as the potential algorithms for optimising the residual strength in the presence of flaws. Another recently developed Sequential Unconstrained Minimisation Technique (SUMT), based on an exterior penalty function method and especially suited for large problems, was also investigated for fracture based optimisation. The effects of the orientation and the number of boundary cracks on the optimal solutions were also studied. It has been shown that the residual strength optimised shapes can be different from the corresponding and commonly adopted stress optimised solution. This emphasises the need to explicitly consider residual strength as the design objective. In all cases a significant reduction in the maximum stress intensity factor was achieved with the generation of a 'near' uniform fracture critical surface. The design space near the optimal region was found to be relatively flat. This is beneficial as a significant structural performance enhancement is important rather than precise identification of the local/global optimum solution. The optimal solutions obtained using the nonlinear programming algorithms were compared against those obtained in the literature using a heuristic optimisation 123 130 R. Das, R. Jones method (Biological algorithm). The results obtained using the ...

Design Space Exploration for Optimisation of Damage Tolerant Structures

“…In a previous paper, we have implemented a 3D Biological method for residual strength optimisation [3]. The optimisation results found using the Biological method were later validated by optimising the same problem using the 'fundamentally' different gradient-based nonlinear programming optimisation algorithms [6]. From the design space study, the optimum hole size and curvature index were found to be 23.1 mm and 2.1, respectively.…”

“…Two broad approaches can be adopted for damage tolerance design optimisation: structural optimisation using (gradient-based or heuristic) optimisation algorithms [1,[4][5][6][7] and design space exploration. One advantage of design space visualisation over traditional optimisation methods is that it allows us to focus on innovative designs that may have other useful features, e.g.…”

“…This specific problem was selected as it has been used in the previous optimisation studies by the present authors and others in the literature [3,4,6,7], and has a stress based analytical (for the plane stress version) optimal shape [8]. Hence, this will enable us to correlate and compare the 'optimum point(s)' observed in the design space with those obtained using different optimisation methods.…”

“…From the design space study, the optimum hole size and curvature index were found to be 23.1 mm and 2.1, respectively. The hole dimensions and curvatures obtained using the different optimisation methods [3,6] are compared with that observed from the design space in Table 1. Given that the resolutions in plotting the design space were 0.1 mm along b and 0.05 along p, it can be inferred that all the optimisation methods performed fairly well in locating the 'near' optimum solution.…”

Optimal topology design of industrial structures using an evolutionary algorithm

“…These methods thus attempt to optimise structures by emulating the growth principles. Biological methods have been developed and extended for various applications by many researchers, such as Arutyunyan and Drozdov (1988), Mattheck et al (1990), and Azegami (1990), and recently by Das and Jones for fracture and fatigue life based optimum designs (Das and Jones 2009a, 2009b, 2009c. Lastly, the hard/soft kill optimisation methodologies have become a popular approach because of their conceptual simplicity and easy implementation with the finite element method.…”