基于应力及其灵敏度的结构拓扑渐进优化方法

在导出应力灵敏度的基础上，建立了一种改进的基于应力及其灵敏度的结构拓扑双方向渐进优化算法．该方法是对传统ESO和BESO方法的改进和完善．算例表明该方法能较大程度减少解的振荡状态数，获得更佳的拓扑结构．具有概念上的简洁性和应用上的有效性。

A STRUCTURAL TOPOLOGY EVOLUTIONARY OPTIMIZATION METHOD BASED ON STRESSES AND THEIR SENSITIVITY

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, and has been applied into the problems with static stress, stiffness, displacement etc. constraints. If the algorithm was restricted to the removal of surface-only material, then a shape optimisation problem is solved. Recent research (Q. M. Quern) has presented a bi-direction evolutionary structural optimisation (BESO) method whereby material can be added and removed. But the BESO method only consider elements' stress level, does not consider the effect of an element removal or adding on the maximum stress of the optimized structure. In order to improve the BESO method, in this paper, a set of stress sensitivity is introduced and derived at first. Based on stresses and their sensitivity, a procedure for an improved bi-directional structural topology optimization is given. It is the development and modification of the conventional ESO and BESO method. Two examples demonstrate that the proposed method can reduce the solution oscillatory state number, and obtain more optimal structural topology, and it is attractive due to its simplicity in concept and effectiveness in application.