线性找力分析中的自动几何对称性检测方法

Automatic geomtrical symmetry detection method for linear force finding analysis

针对力学对称的多自应力模态体系的线性找力分析问题,人工观察获取力学对称单元信息需要经验且容易出错,自动对称性检测方法是必要的.本文提出了一种基于节点云的自动几何对称性检测方法.首先,基于等距变换和对称的定义,给出对称体系在对称或反对称荷载作用下内力和位移等矢量场对称或反对称的证明.其次,给出求解正对称分布自应力模态的对称性条件的引入方法.最后,引入图形学中对称性检测的有关概念,提出一种几何对称性信息的自动检测算法,开发了相应的代码并进行算例验证.

Integral prestress design of multiple self-stress mode system with mechanical symmetry is of great importance. Classification of elements by manual observation according to one’s engineering experiences is not always reliable. Therefore, an automatic symmetry detection method is necessary. This paper puts forward an automatic symmetry detection method based on nodal cloud data. Firstly, a simple proof of symmetrical elemental internal forces and nodal displacements is presented based on the definition of geometrical symmetry and isometric transformation. Seconly, the method of taking account of mechanical symmetry into decomposition of equilibrium matrix is introduced. At last, based on sereral concepts of symmetry detection in graphics, an automatic symmetry detection algorithm is developed and verified by a numerical example.