最少自由度板弯有限元

The PLATE BENDING FINITE ELEMENTS WITH MINIMUM DEGREES OF FREEDOM

本文用混合刚度有限元方法构造了解薄板弯曲问题的6自由度三角形和8自由度四边形混合刚度板元。数值算例表明性能良好。

Two plate bending elements, a triangular element with 6 degrees of freedom and a quadrilateral element with 8 degrees of freedom, are developed according to Mixed Stiffness Method.A mixed element characteristic shared by these two elements is that piecewise linear polynomial deflection and piecewise constant moment components are indepndently assumed. But, different from the mixed methods, the unknown moment variables can be eliminated at element level and only the deflection variables are solved simultaneously. The rigid-body displacement condition is mathematically proved to be satisfied. It is pointed out that the triangular element and nonconfo-rniing Morley's element stiffness matrices are the same. A detailed numerical evaluation is performed.It may thus be seen that the quadrilateral element gives results of engineering accuracy for a variety of plates under different support and loading conditions even when element geometry is changed from quadrilateral to triangular.