中文摘要：

对功能梯度梁在纯弯曲加载和卸载过程中的弹塑性变形行为进行了研究.假设梁由线弹性材料A和理想弹塑性材料B两相材料组成,其复合材料的屈服特性较复杂.为了获得纯弯曲的理论解,利用复合材料力学的方法,分别考虑两相材料的应力,并以此为基础对梁进行弹塑性分析,认为梁的屈服特性完全由材料B的应力决定,而并非整体应力.文中详细讨论了加载和卸载过程的各个阶段,并给出相应的解析解.最后通过算例,对中性轴的位置、截面应力分布、残余应力和残余曲率的变化规律进行了详细讨论.

英文摘要：

The elastoplastic behavior of a functionally graded beam subjected to pure bending is studied in this paper. The beam consists of the linear elastic material A and the ideal elastoplastic material B. Based on the stress of each material, the total behavior of the beam is entirely determined by stress of the beam is calculated. We consider the yield the stress of material B rather than the total stress. The loading and unloading process including elastic process and elastoplastic process is discussed in detail, and the analytical solution is obtained. At last the changing laws of the position of neutral axis, the distribution of stress on the cross section, the residual stress and residual curvature are discussed through numerical examples.