基于等几何样条有限元法的二维弹性力学问题研究  

Research on two-dimensional elasticity problems based on isogeometric spline finite element method

作　　者：刘树勇[1] 陈家兴 苏攀 向家伟[2] LIU Shuyong;CHEN Jiaxing;SU Pan;XIANG Jiawei(Naval Univ.of Engineering,Wuhan 430033,China;Wenzhou Univ.,Wenzhou 325035,China)

机构地区：[1]海军工程大学,武汉430033 [2]温州大学,浙江温州325035

出　　处：《海军工程大学学报》2025年第2期62-68,共7页Journal of Naval University of Engineering

基　　金：浙江省科技计划基金资助项目(2023C01069);海军工程大学自主立项基金资助项目(2022502100)。

摘　　要：针对传统几何有限元形函数不具有插值特性,分析单元难以直接施加本质边界条件的问题,提出了一种分析等几何样条有限元法。应用非均匀有理B样条和均匀B样条分别进行插值,构造几何精确的有限单元并引入转换矩阵,在物理场中构造了具有插值特性的形函数。算例分析表明:相比于常规的有限元方法,该方法无需网格细分,几何离散误差小,能将本质边界条件直接施加到分析单元上,从而在较少自由度下获得较高精度效果。Due to the non-interpolating nature of the shape function,it is difficult to directly apply essential boundary conditions in traditional isogeometric finite element method.In response to this problem,an isogeometric spline finite element method was presented.Non-uniform rational B-splines and uniform B-splines were used to interpolate geometric and physical fields,respectively to construct geo-metrically accurate finite elements.Among them,a transformation matrix was introduced to construct a shape function with interpolation characteristics in the physical field.Numerical analysis shows that the proposed method does not require mesh refinement,but has less geometric discretization error.And it can directly apply essential boundary conditions to nodes and can achieve higher precision results with fewer degrees of freedom compared to conventional isogeometric finite element method.

关 键 词：等几何样条有限元法 均匀B样条 非均匀有理B样条 弹性力学问题 

分 类 号：TB115[理学—数学]