一个简洁有效的带旋转自由度的平面三角形单元

从原始的Allman单元1]出发,构造出一个简洁有效的带有旋转自由度的平面三角形单元。该单元基本保持了Allman单元的精度,同时消除了多余的零能模式,而且使转动自由度等同于连续介质力学中关于旋转分量的定义,并对旋转自由度自身的正确性进行了考核。

A simple and effective triangular element with rotating degree of freedom

Based on the original Allman's element with rotating degree of freedom,which has the well-known spurious zero energy mode,a modified element was derived.It was proved that the rotating degree of freedom in Allman's element had no exact physical meaning.To solve the problem,a parameter was introduced.By letting the rotating degree of freedom at the element's nodes equal to the rotation defined in elasticity,the value of the parameter was determined,which also led to an additional equation that eliminated the spurious zero energy mode.The concrete examples show that the new element has the same precision as the original Allman's element did,but no spurious zero energy mode.It is proved that the rotating degree of freedom in the present element can correctly pass the twist moment.