无剪切闭锁的厚薄通用板单元构造及计算  

Construction of Thickness Universal Plate Element without Shear Locking and its Calculation

作　　者：张广超 ZHANG Guangchao(Shanghai Urban Construction Design&Research Institute,Shanghai 200120,China)

机构地区：[1]上海市城市建设设计研究总院(集团)有限公司,上海200120

出　　处：《工业技术创新》2022年第2期133-140,共8页Industrial Technology Innovation

摘　　要：在采用有限单元法对厚度与跨度比值(厚跨比)较大的平板结构的力学参数进行计算时,往往因不同方向刚度相差过大等问题导致计算精度丧失甚至计算失败。以独立覆盖无网格法(Independent Cover Meshless Method,ICMM)为基础,构造一种厚薄通用板单元。根据Mindlin平板理论,提出一种厚薄板结构通用的数值计算方法——叠加剪切效应法,并与基于经典板理论的薄板计算方法进行对比。构造的板单元可以在相互独立的位移覆盖域内,以形式简洁的多项式作为位移近似函数,避免了构建C;阶连续函数的困难。实例分析表明,提出的叠加剪切效应法在计算薄板及厚板结构时均可获得较为精确的结果,从根本上消除了剪切闭锁现象。此外,该方法对各种网格划分形式均具有较强的适应性,在实际工程中具有较高的实用价值。When the finite element method was used to calculate the mechanical parameters of plate structures with large thickness-span ratio,the calculation often lost its accuracy or even failed due to the large stiffness difference in different directions.Based on the Independent Cover Meshless Method(ICMM),a general plate element with universal thickness was constructed.According to Mindlin’s plate theory,a general numerical calculation method of thickness universal structure,i.e.superposition shear effect method was proposed and compared with the thin plate calculation method based on classical plate theory.The constructed plate element can use simple polynomial as displacement approximation function in mutually independent displacement coverage domain,thus avoiding the difficulty of constructing C;-order continuous function.Examples show that the proposed superposition shear effect method can obtain more accurate results when calculating thin plate or thick plate structures,and fundamentally eliminate the shear locking phenomenon.In addition,such a method has strong adaptability to various grid division forms,and has high practical value in practical engineering.

关 键 词：独立覆盖无网格法(ICMM) 厚薄通用板单元 C 阶连续函数 叠加剪切效应法 剪切闭锁 

分 类 号：O31[理学—一般力学与力学基础]