摘要
本文简略讨论了有限载荷增量弹塑性有限元分析中传统切线刚度法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、保证一阶精度和无条件稳定性的一致性算法.一致性算法具备以下两个特征:1)采用路径无关计算格式;2)采用一致弹塑性切线模量。根据一致性算法构造出以弯矩和曲率为基本变量的弹塑性板弯曲有限元NIDKQ元。数值结果表明NIDKQ元具有令人满意的精度,同时验证了有限载荷增量下牛顿迭代一致性算法的平方收敛率特性,而传统切线刚度法随着塑性区的扩展将大大降低收敛速度。
The reasons in the loss of accuracy and asymptotic rate of quadratic conver-gency of Newton iteration in finite load increments when using classical tangent stiffness matrix methods of elastoplastic finite element analysis are briefly discussed. A consistent algorithm is proposed which preserves the asymptotic rate of quadratic convergency of Newton iteration and holds a first order accuracy and unconditional stability. It is characterized by the path-independent strategy and the consistent elastoplastic tangent moduli.Based upon the consistent algorithm, an elastoplastic plate bending element, NIDKQ, is developed with moments and curvatures as basic variables. Numerical results show a satisfactory accuracy of NIDKQ, and have verified the asymptotic rate of quadratic convergency of consistent algorithm of Newton iteration in the finite load increments, whereas the asymptotic convergent rate of classical tangent stiffness matrix methods is greatly reduced along with the expansion of plastic zone.
出处
《力学学报》
EI
CSCD
北大核心
1990年第5期579-588,共10页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金
关键词
牛顿迭代
一致性算法
板
弹塑性
Newton iteration, consistent algorithm, elastoplasticity, plate bending finite element
