1-型三角剖分上3次二元样条的力学模型  

Mechanical Model of Cubic Bivariate Spline over 1-Type Triangulation

作　　者：常锦才 祝弘扬 赵淑静 

机构地区：[1]华北理工大学理学院,河北唐山063009 [2]河北安平中学数学组,河北衡水053600

出　　处：《河北联合大学学报（自然科学版）》2015年第3期95-101,共7页Journal of Hebei Polytechnic University:Social Science Edition

基　　金：国家自然基金资助项目(61170317);河北省自然基金资助项目(A2013209295)

摘　　要：以板壳理论和力学分析为基础,研究1-型三角剖分上3次二元样条的力学模型。对矩形薄板做均匀矩形剖分并连接一条对角线生成1-型三角剖分,通过在剖分线上施加线性变化的线力偶或弯矩,分别在自由边界、简支边界和一般剖分情形下达到平衡状态,使得薄板弯曲变形的挠曲面成为分片形式的样条曲面,从而建立了此类二元样条与薄板挠曲面的对应关系。Based on the theory of plate and shell and mechanical analysis,the mechanical model of cubic bivariate spline function over 1-type triangulation was investigated.By establishing 1-type triangulation over the plate with free boundary condition,simple supported condition and acting linear couple or bending moment on the grid line to reach equilibrium,the deflection surface of bending plate become a class of bivariate spline.Thus,the relationship between this the bivariate spline and deflection of thin plate is built up.

关 键 词：1-型三角剖分 薄板弯曲 光滑余因子 协调条件 

分 类 号：O302[理学—力学]