功能梯度材料Timoshenko梁的非线性大变形分析

采用打靶法研究了两端不可移简支功能梯度Timoshenko梁在横向非均匀升温下的大挠度弯曲问题.在精确考虑轴线伸长和基于一阶横向剪切变形理论的基础上建立了功能梯度Timoshenko梁受热-机载荷作用时的几何非线性控制方程,其中功能梯度梁的材料性质采用了沿厚度方向按照幂函数连续变化的形式.用打靶法数值求解所得强非线性边值问题,获得了横向非均匀升温时Timoshenko梁的静态非线性大变形数值解.绘出了梁的变形随温度载荷及材料梯度参数变化的特性关系曲线,并分析和讨论了温度载荷及材料的梯度性质参数对梁变形的影响.结果表明,由于材料的非均匀性,功能梯度梁中存在拉-弯耦合变形.

Analysis of nonlinear large deformation of Timoshenko beam made of functionally graded materials

By using shooting method, large deflection bending of the functionally graded Timoshenko beam with both pinned-pinned edges subjected to transversely non-uniform temperature rise was investigated. Accurately considering the axial extension and first order transverse shearing deformation, the geometrically nonlinear governing equations for functionally graded Timoshenko beam subjected to mechanical as well as thermal loads were established. In the analysis, it was assumed that the material properties of the beam vary continuously as a power function of the thickness. Using a shooting method, the nonlinear ordinary differential equations were solved and numerical solutions for the statically large deformation were obtained. Characteristic curves of the deformation versus the thermal loads and the parameter of gradient of the materials were plotted. The effects of material gradient property on bending deformation of the beam were discussed in detail. The results show that there exists the tension-bend coupling deformation in the uniformly heated beam because of the non-uniform characteristic of materials.