Shakedown theory in perfect elastoplasticity with associated and nonassociated flow-laws: A finite element, linear programming approach
Shakedown theory in perfect elastoplasticity with associated and nonassociated flow-laws: A finite element, linear programming approach
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DOI：
10.1007/bf02133439
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发表时间：
1969-09
期刊：
影响因子：
2.7
通讯作者：
G. Maier
中科院分区：
文献类型：
--
作者：
G. Maier
采用基于有限元离散化和屈服面分段线性化的力学行为矩阵描述代替传统的连续场描述。通过使用线性规划概念，以紧凑的形式呈现了一般安定理论的本质和相关求解过程的基础。对于具有相关流动定律的系统，扩展了第二个安定定理（Koiter's），以允许可变位错（例如温度循环）。对于具有非关联流动定律的系统，给出了两个定理，它们提供了安全系数的下限和上限。
The matrix description of the mechanical behaviour resting on finite element discretization and piecewise linearization of yield surfaces, is adopted instead of the traditional continuous field description. By the use of linear programming concepts, the essential of a general shakedown theory and the basis of relevant solution procedures are presented in compact form. For systems with associated flow-laws, the second shakedown theorem (Koiter's) is extended in order to allow for variable dislocations (e. g. temperature cycles). For systems with nonassociated flow-laws two theorems are given which supply lower and upper bounds to the safety factor.