用有限元法确定弹塑性材料结构的极限承载力

确定弹塑性材料结构的极限承载能力是结构设计中极其重要的一个问题,它通常是采用弹塑性非线性有限元方法来进行分析的.本文提出了利用基于一系列线弹性有限元解来获得弹塑性材料结构的极限承载能力的试验误差法,并将它与切线法和割线法进行了比较和讨论.在计算的每一步中,根据应力松弛系数降低杨氏弹性模量,并将结构的应力松弛系数和作为误差指标.当结构的误差指标小于给定的误差容限时就得到收敛解.本文方法可计算出结构受载后直到崩溃时应力、应变和载荷-变形曲线.数值实验表明,本文方法是有效的和可行的.

Determination of Collapse Load-carrying Capacity of Structures Made of Elasto-plastic Material by Means of FEM

Determination of the collapse load-carrying capacity of elasto-plastic structure is very important in designing structures. The problem is commonly solved by elasto-plastic FEA.A trial and error method is suggested, and comparisons with the secant stiffness method and the tangential stiffness method are made in the paper. It can determinate the collapse load carrying capacity based on a series of linear-elastic solutions.In each calculation step,the Young's modulus is reduced according to a stress relaxation parameter. The sum of all stress relaxation parameters of the structure is defined as an error index. The convergence result is obtained when the error index is within the error tolerance.The method is developed for obtaining estimates of load-deflection curves,stresses and strains on the way to final collapse.Numerical experiments indicate that the algorithm is effective and reliable.