Computational efficiency and validation of bi-directional evolutionary structural optimisation

The evolutionary structural optimisation (ESO) method has been under continuous development since 1992. Originally 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. The ESO algorithm caters for topology optimisation by allowing the removal of material from all parts of the design space. With appropriate chequer-board controls and controls on the number of cavities formed, the method can reproduce traditional fully stressed topologies. If the algorithm was restricted to the removal of surface-only material, then a shape optimisation problem (along the lines of the Min-Max type problem) is solved. Recent research by the authors has presented and benchmarked an additive evolutionary structural optimisation (AESO) algorithm that, with appropriate decision making, starts the evolutionary optimisation procedure from a minimal kernel structure that connects the loading points to the mechanical constraints. Naturally this is unevenly and overly stressed, and material is subsequently added to the surface to reduce localised high stress regions. AESO only adds material to the surface, the present work describes the combining of basic ESO with the AESO to produce bi-directional ESO (BESO) whereby material can be added and removed. This paper shows that this method provides the same results as the traditional ESO. This has two benefits, it validates the ESO concept, and as the examples demonstrate, BESO can arrive at an optimum faster than ESO. This is especially true for 3D structures, since the structure grows from a small initial one rather than contracting from a, sometimes, huge initial one where around 90% of the material gets removed over many hundreds of finite element analysis (FEA) evolutionary cycles. Both 2D and 3D structures are examined and multiple load cases are applied. (C) 2000 Elsevier Science S.A. All rights reserved.