THREE-DIMENSIONAL BASIC FORMULATIONS OF ADDITIONAL INCOMPATIBLE DISPLACEMENT ON INTERNAL PARAMETERS
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摘要: 文献[12]在平面问题基础上推导出附加非协调位移基本项的通用公式。依据这一公式,在构造新型非协调位移元时,可以主动地来选择基本项,减少了过去盲目试凑的现象。本文在文献[12]的基础上,推广至三维情况,分别推导出以等参坐标和直角坐标表述的附加非协调位移基本项通用公式。依据这些公式,本文分别以H8和H20单元为例,发展了两个新的非协调元,数值试验表明它们能够保证收敛,有较高精度,对畸变不敏感,从而证明了本文方法的可行性。Abstract: The additional incompatible displacement terms on internal parameters for plane elasticity problems were given in a previous publication[12]. With reference to the general formulas in[12], new incompatible displacement elements can be constructed directly, avoiding the previous tedious trial and error process. This paper aims to extend the previous work [12] to three-dimensional cases. Formulations of the additional incompatible displacement terms are established in terms of isoparametric coordinates and Cartesian coordinates, respectively. Taking H8 and H20 solid elements as examples, two new incompatible elements are developed. To illustrate the feasibility of the present approach, numerical examples are provided. It is shown that the two new elements produce convergent and highly accurate results.
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