功能梯度梁纯弯曲特性研究

Analysis of functional gradient material beam subjected to pure bending

根据陶瓷和金属的体积分布,利用TTO模型,得到了功能梯度材料力学参数沿梁高度方向变化的规律。在小变形及平面假设下研究了功能梯度矩形截面梁纯弯曲特性。结果表明:弹性模量、屈服应力、切线模量的梯度分布使梁截面的应力呈现明显的不对称;在加载的弹性阶段,中性轴偏向陶瓷一侧并保持恒定;随着载荷的增大,在陶瓷一侧率先出现单边塑性区,中性层的高度先降低后增大;卸载阶段,中性层的高度、梁截面上的应力分布受卸载初始时的弯矩影响;功能梯度纯弯曲梁截面应力及弹塑性边界呈现出明显的不对称性。

The mechanical parameters of functional gradient material(FGM) along the height of the beam section are obtained according to the volume distribution of ceramic and alloy by using the TTO model. The FGM beam is subjected to pure bending is studied under the assumptions of small deformation and plane section. The gradient of elastic modulus, yielding stress and tangent modulus affect the curvature of the beam and the stresses of the beam section show asymmetry obviously. During the elastic stage of loading, the neutral axis moves towards the ceramic side and remains constant. With the increase of bending moment, a unilateral plastic zone appears on the ceramic side, and the neutral layer moves nonlinearly. During the unloading stage, the height of the neutral layer and the stress distribution on the beam cross-section are affected by the bending moments at the initial unloading.