【摘要】 三角形单元是有限元分析中常用的单元.在平面单元内引入结点转动自由度,可以提高单元位移场的阶次,在不增加单元结点的前提下提高单元性能.论文利用问题基本解析解作为试函数来构造带旋转自由度的三角形单元ATF-R3H,采用了杂交应力函数单元模式,确保了单元优良的抗畸变性能和较高应力计算精度.论文利用直角坐标与三角形面积坐标的线性关系,以及面积坐标幂函数在三角形域内和边界上的积分公式,直接给出单元刚度矩阵的显式表达式,从而避免了大量数值积分,提高了计算效率.数值算例表明,显式格式的ATF-R3H单元具有良好的性能.更多还原

【Abstract】 Triangle unit is commonly used in finite element analysis unit.Nodal rotational degrees of freedom are introduced in planar element,which can improve the order of displacement field,improve the performance without any increase in unit node.The basic fundamental solutions of plane elasticity problem based on Airy stress functions are used as trial functions to construct triangular element with drilling degrees of freedom,which called ATF-R3 H.In order to ensure the element of high stress calculation precision and insensitive to mesh distortion,hybrid stress function unit model is introduced.During the construction of element model,the explicit expression of element stiffness matrix is deduced by means of triangular area coordinates integration method,instead of numerical integration method.Numerical calculation indicates that the element ATF-R3 Hconstructed in this paper is of good property.更多还原