摘要
简略讨论了传统切线刚度法在有限载荷增量下丧失精度和牛顿迭代平方收敛速度的原因,并提出保持牛顿迭代平方收敛速度、具有一阶精度和无条件稳定性的一致性算法。根据一致性算法构造了以弯矩和曲率为基本变量的弹塑性板弯曲单元(NIDK Q 元)。数值结果表明 NIDK Q 元具有满意的精度,同时验证了一致性算法的平方收敛特性。
The reasons of loss of accuracy and asymptotic rate of quadratic convergency of Newton iteration for finite load increments with classical tangent stiffness matrix methods of elastoplastie finite element analysis are briefly discussed.A consistent algorithm is proposed which preserves the asymptotic rate of quadratic convergency of Newton iteration and possesses first order accuracy and unconditional stability.Based upon the consistent algorithm,an elastoplastic plate bending element,NIDKQ,is developed with moments and curvatures as basic variables.Numerical results indicate the satisfactory accuracy of NIDKQ,and verify the asymptotic rate of quadratic convergency of consistent algorithm of Newton iteration for finite load increments.
基金
国家自然科学基金
关键词
板
弹塑性
有限元分析
塑性力学
finite element method
elastoplasticity
Newton iteration
consistent algorithm
