非保守功能梯度弹性组合曲梁的精确模型及其数值解

基于直法线假设,采用可伸长梁的几何非线性理论,建立了功能梯度材料弹性组合曲梁受切线均布随从力作用下的静态大变形数学模型。该模型不仅计及了轴线伸长,同时也精确地考虑了梁的初始曲率对变形的影响以及轴向变形与弯曲变形之间的耦合效应。用打靶法数值求解了由金属和陶瓷两相材料所构成的一种FGM组合曲梁在沿轴线均布切向随动载荷作用下的非线性平面弯曲问题,给出了不同梯度指标下FGM弹性曲梁随载荷参数大范围变化的平衡路径,并与金属和陶瓷两种单相材料曲梁的相应特性进行了比较。

Analysis of nonlinear large deformation of functionally graded material elastic combination curved beam subjected to non-conservative forces

Based on the assumption of straight normal line of beams and by employing geometrically nonlinear theory for the extensible elastic beams,governing equations of large static deformation of functionally graded material(FGM) combination elastic curved beam subjected to a distributed tangential follower force along the central axis were established.In the mathematical model,not only the effects of the axial elongation and the initial curvature of the FGM curved beam on the deformation were accurately taken into account but the coupling between elongation and bending was considered.By using shooting method,the nonlinear plane bending of a combination curved beam from a straight beam and a quarter semicircle FGM made of metal and ceramic subjected to tangentially distributed follower force along the axial line was analyzed.The equilibrium paths of the deformed FGM curved beams under the different graded index,varying with the load parameter in a large range,are presented,and compared with the properties of metal and ceramic material curved beams.