By Y. M. Xie, G. P. Steven (auth.)
Evolutionary Structural Optimization (ESO) is a layout technique in line with the straightforward notion of steadily elimination inefficient fabric from a constitution because it is being designed. via this technique, the ensuing constitution will evolve in the direction of its optimal form. the most recent innovations and result of ESO are offered the following, illustrated through a number of transparent and distinct examples. Sections disguise the basic features of the strategy, the appliance to a number of load instances and a number of aid environments, frequency optimization, stiffness and displacement constraints, buckling, jointed body constructions, form optimization, and pressure aid. this can be through a bit describing Evolve97, a software program package deal on the way to enable readers to aim the tips of ESO themselves and to resolve their optimization difficulties. This software program is equipped on a working laptop or computer diskette which accompanies the book.
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1991; Zhou and Rozvany 1991 ; Jog et al. 1994). The MBB beam, as it is known, has the function of carrying the floor in the fuselage of an Airbus passenger carrier. The beam is 2400 mm long and 400 mm deep with a point load of 20 kN acting at the middle. 5. 4 mm under the given load. Because of symmetry, only half of the structure is modelled with 60 x 20 four node elements. 3 are assumed. 3 mm. 4 mm. In this example a removal ratio of 1% of the current number of elements is used. 33% of the initial volume.
12 which are obtained for individual support environments. RR = RR=5% IOo/~ (b) (a) . ~ . . " . , , , .. . , ... , ... , .... . .. . , . . ,.. o..... . . ...... .. , ... . . , .... . , RR= 15% (c) Fig. S. ESO solutions for an arch structure with two support environments. 4 again. It could arise that the bridge may have one of its four supports in a river bed. and the design needs to allow for the possibility of that support sinking or being swept away after a collision with a boat.
This sensitivity number indicates the change in the strain energy as a result of removing the ith element. In fact u i is the element strain energy and it can be easily calculated at the element level using the element stiffness matrix and the displacement vector of the element. It is worth pointing out that both C and u i always have positive values. 7) where C is a prescribed limit for C. In general, when an element is removed, the overall stiffness of a structure reduces and correspondingly the strain energy C increases.