C1阶协调矩形薄板单元的对比分析
来源期刊：中南大学学报(自然科学版)2004年第4期
论文作者：张国祥 罗万象 魏伟
文章页码：676 - 680
关键词：薄板有限元;C1阶连续性;边界位移插值法
Key words：thin plate finite element;C1conforming; border displacement interpolating method
摘 要：提出了一种直接由协调单元边界位移插值单元位移的特殊插值法,用于构造对称协调和完备的12节点参数薄板矩形单元,分离单元完备性条件和C1阶连续条件的相互影响,构造C1阶连续协调且完备的薄板单元,并构造出一种对称性更好的新型矩形协调薄板单元。该薄板单元具有完备性和真正的C1阶连续性,列式清晰,形函数表达更符合常规函数,对有限元程序不必作大的改动,只需修改挠度插值函数,即可进行常规的有限元分析,从而解决了薄板矩形单元的C1阶连续性问题。研究结果表明:矩形协调单元的计算结果比非协调单元的计算结果精确,收敛速度快,稳定性强。
Abstract: A special method to directly interpolate the displacement field of element using the displacement along each side of element is proposed to construct a C1 conforming rectangle thin plate-bending element with 12 degrees of freedom by this method, the perfection conditions and C1 conforming conditions of element can be separated. The perfection and C1 conforming rectangle thin plate bending element with 12 degrees of freedom is constructed, as well as a new perfect and C1 conforming rectangle thin plate element. It is proved that the element has C1 conforming and perfection, and formulation of the element displacement field is more distinct and closer to the common expression. The common finite element analysis can be conducted only by modifying the interpolating function of element displacement rather than the thin plate finite element program and thus the C1 conforming problem can be solved preferably. The results show that the element has the advantage of higher accuracy, better convergence and better stability than that of the non-conforming elements.
