自由变形技术在有限元网格重用中的应用

Free-Form Deformation for Reuse of Mesh Models of Finite Element Analysis

在现有自由变形技术的基础上,提出了基于三变量B样条空间的局部变形方法和对变形晶格顶点的控制方法,以及几何特征-变形晶格顶点-有限元网格节点的3层控制架构,克服了现有自由变形技术不能维持2次几何特征的缺点,实现了有限元网格模型中几何特征的参数化和有限元网格的重用;当几何模型的设计变量变化时,能够直接修改初始网格模型,节省了重复划分网格的工作量;同时,以复杂零件斜齿轮轴为例进行有限元网格模型几何特征参数的构建,更改部分关键尺寸,并校验了所生成的网格模型.结果表明,由所建模型变形后所得网格质量符合要求,从而验证了所提出的有限元网格重用方法的有效性与实用性.

Meshing, which is very important to the result of finite element analysis （FEA）, is often con- ducted manually. It takes a long time while the geometry model has to be re-meshed every time if the de- sign is changed. A new method was presented in this paper that helped to reuse FEA meshes to improve efficiency with an extended technology of free-form deformation （FFD）. This method generalized the pre- vious FFD by allowing local deformation based on trivariate B-spline and proposing a way to control verte- xes of the FFD lattice. A three-level framework was presented that was ＂geometry feature-FFD lattice ver- texes-FEA nodes＂ to realize the reuse of FEA meshes with preserving geometry features continuous to the 2nd derivative and parameterizing mesh models. This approach saved time to re-mesh when the design vari- ables change within a relatively narrow range. The result of a case study of helical gear shaft at the end of this paper shows that this method is able to apply deformation on the FEA meshes directly, keeping topol- ogy structures and geometry features stable instead of re-meshing from computer-aided design models.