摘要
假设功能梯度材料为一理想弹塑性材料,其弹性模量和屈服强度沿梁高度方向按照幂函数变化,在小变形及平截面假设下研究功能梯度材料纯弯曲梁的弹塑性性能。根据Mises屈服准则导出了纯弯曲梁的弹性极限弯矩的解析表达式,建立了梁在弹塑性状态时截面弯矩与截面弹、塑性区分布之间的关系式,给出了梁进入塑性极限状态时中性轴的位置以及塑性极限弯矩的解析计算公式。数值算例的结果表明,功能梯度材料梁的弹塑性性能与均匀材料梁不同,其屈服不一定首先产生于截面最大应力点,而可能有多种不同的屈服模态及相应的塑性扩展。弹性模量及屈服强度的梯度变化对功能梯度材料纯弯曲梁的中性轴位置、截面弹塑性应力分布以及塑性极限弯矩均有较大影响。研究结果可为功能梯度材料梁的弹塑性分析提供一定的参考。
The elastoplastic behavior of a functionally graded beam subjected to pure bending is studied un- der the assumptions of small deformation and plane section. The material is assumed to be elastic, per- fectly plastic and its elastic modulus and yield limit vary through the thickness according to power func- tions. The explicit expression of elastic limit bending moment is obtained based on Mises＇ yield criterion. The relation between a given bending moment and the distribution of elastoplastic zones is established and the expression of plastic limit bending moment is also given. The results of numerical examples show that the elastoplastic behavior of a functionally graded beam is different from that of the beam composed of homogeneous materials. There are several possible cases of different yielding modes and different elasto- plastic stress distributions for a functionally graded beam. And the variations of material properties along the thickness have great influence on the position of the neutral axis, elastoplastic stress distribution and plastic limit bending moment of a functionally graded beam. The results presented here may be helpful for the elastoplastic analysis of a functionally graded beam subjected to pure bending.
出处
《力学季刊》
CSCD
北大核心
2013年第2期220-227,共8页
Chinese Quarterly of Mechanics
基金
国家自然科学基金(11072177)
教育部留学回国人员科研启动基金
关键词
功能梯度材料
纯弯曲梁
弹塑性分析
functionally graded materials
pure bending beam
elastoplastic analysis
