采用面积坐标方法和形函数谱方法构造四边形薄板元

QUADRILATERAL THIN PLATE ELEMENTS FORMULATED BY THE AREA COORDINATE METHOD AND THE SHAPE FUNCTION SPECTRUM METHOD

  • 摘要: 构造一个四边形薄板元,其构造方法有两个特点:1) 采用四边形面积坐标方法以代替等参元坐标方法,从而使单元对网格畸变不敏感。2) 采用形函数谱方法从已知的膜元推导出新的薄板元,换言之,利用已知的膜元形函数(低阶形函数)来导出待求的薄板元形函数(高阶形函数),此法的要点是:形函数谱是由低阶和高阶形函数所组成,而高阶形函数则是对低阶形函数加以升阶而导出。此法的优点是:使新单元的推导过程大为简化,而且导出的高阶形函数也非常简洁。

     

    Abstract: A quadrilateral thin plate element is developed in this paper. There are two distinguishing features in the formulation: 1) The quadrilateral area coordinate method is used instead of the isoparametric coordinate method, so that the element developed is insensitive to mesh distortion. 2) The shape function spectrum method is used to develop the new thin plate element. In other words, the new thin plate element and its shape functions (the higher order shape functions) are developed on the basis of the shape functions of the membrane element (the lower order shape functions). The main features of this method are: The shape function spectrum is composed of shape function of lower power and higher power, and the shape functions of higher power are developed on the basis of the shape functions of lower power. The advantages of this method are: The construction of new element is significantly simplified and the new higher power shape functions are succinct.

     

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