考虑尺度依赖的平面正交各向异性功能梯度Mindlin板静弯曲模型  

Static bending model of size-dependent plane orthotropic functionally graded Mindlin plate

作　　者：贺丹[1] 杨子豪[1] HE Dan YANG Zi-hao(Key Laboratory of Liaoning Province for Composite Structural Analysis of Aerocraft and Simulation, Shenyang Aerospace University, Shenyang 110136, China)

机构地区：[1]沈阳航空航天大学辽宁省飞行器复合材料结构分析与仿真重点实验室,沈阳110136

出　　处：《沈阳航空航天大学学报》2017年第4期41-47,共7页Journal of Shenyang Aerospace University

基　　金：国家自然科学基金(项目编号:11572204;11572081)

摘　　要：基于各向异性修正偶应力理论建立了能够考虑尺度依赖的平面正交各向异性功能梯度板静弯曲模型。模型中引入两个正交材料尺度参数,因此能够分别描述正交方向上不同程度的尺度效应。基于虚功原理推导了平衡方程和边界条件,并以受双向正弦载荷作用的简支板为例分析了尺度效应对板弯曲挠度产生的影响。算例结果表明:基于模型得到的板弯曲挠度总是小于传统一阶剪切板理论给出的结果,即捕捉到了尺度效应;尺度效应在尺度参数与几何尺寸接近时显著,而在几何尺寸远大于尺度参数时消失;此外,功能梯度变化指数和板跨厚比也会对尺度效应产生一定影响。A static bending model of size-dependent plane orthotropic functionally graded plate was proposed based on an anisotropic modified couple stress theory. The model included two orthogonal material length scale parameters, and thus can describe separately effects with different scale in orthogonal directions. The equilibrium equations and boundary conditions were deduced by the virtual work principle. The effects of scale effect on bending deflections were analyzed for a simply supported plate with a double sinusoidal load. Numerical results indicated that the scale effect was depicted well, and deflections calculated by the present model were smaller than those from the classical one. The scale effect was obvious as the geometry size approached the material length scale parameters, but it disappeared when the geometry size was much higher than those parameters. In addition, both grading index and span-to-thickness ratio have specific impacts on the scale effect.

关 键 词：修正偶应力理论 功能梯度材料 正交各向异性 尺度效应 材料尺度参数 

分 类 号：TB330.1[一般工业技术—材料科学与工程]