应变梯度塑性理论下超薄梁弯曲中尺度效应的数值研究  

NUMERICAL STUDY ON THE SCALE EFFECTS PHENOMENA OF ULTRA-THIN BEAMS' BENDING WITH STRAIN GRADIENT PLASTICITY

作　　者：李雷[1] 谢水生[1] 黄国杰[1] 

机构地区：[1]有色金属研究总院有色金属材料制备加工国家重点实验室,北京新街口外大街二号100088

出　　处：《工程力学》2006年第3期44-48,共5页Engineering Mechanics

基　　金：国家自然科学基金资助项目(10172078;50175006)

摘　　要：构造了一个在物理空间二次完备的应变梯度非协调单元,在验证了单元数值可靠性后,采用该单元详细研究了均布载荷作用下超薄梁弯曲中的尺度效应现象。计算结果与实验观测一致,即随着梁厚度的减小,其尺度效应增强。并发现在平面应力状态下,梁的梯度效应略强于平面应变状态。最后指出,尽管梁越薄,其梯度效应越强,但梁抗弯刚度仍随厚度的增加而增大。An incompatible element with quadratic completeness in the physical space is developed based on strain gradient theory. After verifying the element, scale effects of ultra-thin beams＇ bending under the uniform load are studied with this element. Numerical results agree with the experiment observations that the thinner the bean, the more significant the scale effects. Results also show that the scale effect in plane stress state is slightly stronger than that in plane strain state. In the end, it is indicated that the bending stiffness increases when the beam＇s thickness increases.

关 键 词：有限元方法 尺度效应 非协调元 应变梯度塑性理论 材料特征长度 

分 类 号：O302[理学—力学]