构造薄板弯曲单元的新途径

为了简化Ｋｉｒｃｈｈｏｆｆ 薄板弯曲单元的推导过程，提出了一个构造此类单元的新途径——假定曲率第一不变量的方法．证明了单元的能量积分实际上可以分为两项：第一应变不变量的域内积分和边界项的线积分．因此，只要根据单元边界的网线函数确定出第一应变不变量．单元刚度阵也就唯一确定了．给出了一个九参三角形单元的推导过程，显示出本文方法对简化计算的确是十分有效的．

New approach to derive thin plate bending elements

To simplify the formulation of Kirchhoff thin plate element, a new approach, by assuming the first strain invariant, is presented. It is proved that the integration of energy in an element can be divided into two terms: the integration of the first strain invariant in the element and the integration of some terms around the elemental boundary. The formulation of thin plate bending elements is much simplified. So long as the first strain invariant is obtained from the elemental mesh functions, the elemental stiffness matrix will be determined uniquely. An example to derive a triangular element with nine parameters shows that the method is really very efficient.