混合微分求积法在功能梯度材料平板柱形弯曲问题中的应用

Analysis of Functionally Graded Plates in Cylindrical Bending Using Hybrid Differential Quadrature Method

利用混合微分求积法,对任意荷载作用下不同材料梯度分布的功能梯度材料平板柱形弯曲问题进行了分析。针对广义微分求积法求解集中荷载问题精度不高的缺点,本文利用小波微分求积法进行了改进。由于小波对突变信号具有良好的自适应描述能力,因此在平板宽度方向上,利用小波微分求积法可以有效地处理集中荷载;而在材料梯度变化的板厚方向上,则利用广义微分求积法计算量小且精度高的特点进行离散计算。计算表明,混合微分求积法不仅保留了广义微分求积法高效的特点,而且能有效地求解任意荷载作用的问题。通过算例,分析了在机械荷载作用下,材料不同梯度形式、平板上下表面材料性质差异对功能梯度平板结构响应的影响。

Cylindrical bending of functionally graded plates with arbitrary distributions of material properties under arbitrary loading are studied using hybrid differential quadrature method （HDQM）. The wavelet-based differential quadrature method （WDQM） is proposed to overcome the shortage of generalized differential quadrature method （GDQM） in treating the problem of concentrated loading. HDQM is a combined method with WDQM being used in the longitudinal direction due to its superiority in treating singularity and GDQM in the thickness direction for its higher computational efficiency. Numerical results show that HDQM keeps high computational efficiency and accuracy, The influence of material property distributions on structural response of the plate to mechanical stimuli is studied through examples.