受应力约束的三维弹性体的拓扑优化

提出一种受应力约束的三维弹性体的拓扑优化方法:修改的满应力法,即通过反复迭代修改单元的弹性模量,使三维弹性体的每个单元均处于一种满应力的状态,然后删除弹性模量较低的单元,通过逐渐删除弹性模量较低的单元使单元最大弹性模量逐渐接近于材料实际的弹性模量,同时单元的最大应力也逐渐接近于材料的许可应力,从而获得满足应力约束条件的三维弹性体的最优拓扑.同时引入结构描述数组的概念,很方便地实现单元的重新划分.数值结果显示该方法很有效,且具有很好的通用性和稳健性.

Topological optimization of three -dimensional elastic continuum with stress constraints

The paper introduces a three-dimensional elastic continuum topological optimization method with stress constraints: amendatory full stress method,namely,it makes every element of the three-dimensional elastic continuum in a full stress state through amending the element modulus of elasticity repeatedly,then deletes the elements that their modulus of elasticity is small.And the maximum of the element elasticity modulus approaches gradually to the elasticity modulus of material through deleting the element their modulus of elasticity is small,at the same time,the maximum of the element Von Mises stress approaches gradually to the allowable stress of material,so the best topology of three-dimensional elastic continuum is gained.The concept of structure represent array is defined,so the next element division of the structure becomes easy.Numerical results illustrate the method is efficiency,robust and universal.