功能梯度变曲率曲梁的几何非线性模型及其数值解

基于弹性曲梁平面问题的精确几何非线性理论，建立了功能梯度变曲率曲梁在机械和热载荷共同作用下的无量纲控制方程和边界条件，其中基本未知量均被表示为变形前的轴线坐标的函数。以椭圆弧曲梁为例，采用打靶法求解非线性常微分方程的两点边值问题，获得了两端固定功能梯度椭圆弧曲梁在横向非均匀升温下的热弯曲变形数值解，分析了材料梯度指数、温度参数、结构几何参数等对曲梁受力及变形的影响。

GEOMETRICALLY NONLINEAR MODEL AND NUMERICAL SIMULATION OF FUNCTIONALLY GRADED VARIABLE CURVATURE CURVED BEAM

Based on an exact geometrically nonlinear theory of planar elastic curved beams, the dimensionless governing equations and boundary conditions for functionally graded variable curvature curved beam subjected to mechanical loads and thermal loads were formulated, in which the basic unknown quantities were expressed as the functions of axial coordinates before the deformation. Then, taking an example of elliptic arc curved beam, two-point boundary value problem of nonlinear ordinary differential equations were solved by using shooting method, and thermal bending responses of transversely non-uniformly heated FGM elliptic arc curved beam with fixed-fixed ends were obtained. The influences of material gradient index, temperature parameter and structural geometric parameters on the internal force and deformation of curved beam were discussed in detail.