带转动自由度的内参型非协调元研究

Investigation of internal parameter type incompatible elements with rotational degrees of freedom

非协调元虽然破坏了单元间位移的连续性,却能很好地反映弯曲类变形,然而在不增加单元结点自由度的情况下,非协调元的计算精度总是滞留在某一水平,无法得到较大改变。基于修正后的位移型Reissner泛函中引入独立转动场的变分原理,采用连续介质力学中的转动自由度的定义,转动场采用结点真实转角来插值,结合平面四结点单元讨论了有效附加非协调位移的合理形式,引入了适用于任何四边形单元的非协调位移函数,从而建立了一种带转动自由度的平面四结点内参型非协调元模型。本文单元能通过分片检验,并易于与带转动自由度的梁单元相容,数值算例表明具有较高的计算精度。

The continuity of displacements between elements is destroyed by the use of incompatible elements, but the bending deformations are well reflected by them. If the number of nodal freedoms is not added, the computational accuracy is restricted in certain level and has not been greatly changed. Based on variational principle employing modified Reissner functional, into which independent rotation field has been introduced, the rotational definition of continuum mechanics is used and the rotation field is interpolated by true rotation at each node. The rational type of incompatible fields of 4-node element is discussed. The incompatible displacement functions being suitable for arbitrary quadrilateral element are denoted. An internal parameter type incompatible element with rotational degrees of freedom is established. The element presented in this paper is proved to pass the patch test. The compatibility with beam elements with rotation degrees of freedom can be easily made. It is shown that the numerical results based on the element have good accuracy.