Variational geometry: A new method for modifying part geometry for finite element analysis
Variational geometry: A new method for modifying part geometry for finite element analysis
复制标题
DOI：
10.1016/0045-7949(83)90104-9
复制
发表时间：
1983
影响因子：
4.7
通讯作者：
R. Light;D. Gossard
中科院分区：
文献类型：
--
作者：
R. Light;D. Gossard
交互式图形方法有可能显着降低与有限元分析的前处理和后处理相关的成本。其中一个特别重要的领域是零件几何形状的创建和修改，本文描述了一种用于有限元分析前处理器的几何形状修改的强大方法。该方法称为“变分几何”，使用单个表示来描述共享通用形状的整个几何家族。组件的实体几何模型是相对于一组标量参数定义的。尺寸，如机械图纸上出现的尺寸，被视为这些参数允许值的约束。对几何形状的约束表示为一组非线性代数方程。通过求解这组非线性约束方程，可以确定参数的值，从而确定几何形状，并给出了一种使计算量最小化的方法。对于n个自由度的部分，求解时间为O（n）。
Interactive graphic methods have the potential to significantly reduce the cost associated with pre- and post-processing of finite element analyses. One area of particular importance is the creation and modification of part geometry.This paper describes a powerful method for modification of geometry for finite element analysis pre-processors. The method, called “Variational Geometry”, uses a single representation to describe the entire family of geometries that share a generic shape.A solid geometric model of a component is defined with respect to a set of scalar parameters. Dimensions, such as those which appear on a mechanical drawing, are treated as constraints on the permissible values of these parameters. Constraints on the geometry are expressed as a set of non-linear algebraic equations. The values of the parameters and hence the geometry may be determined by solving the set of non-linear constraint equations.A procedure for minimizing the computational requirements is presented. For a part withndegrees of freedom, the solution time is shown to be O(n).