非均匀热载荷作用下功能梯度梁的非线性静态响应

发布时间：2018-04-06 07:10

本文选题：精确解　切入点：静态响应　出处：《工程力学》2017年06期

【摘要】：由于功能梯度材料结构沿厚度方向的非均匀材料特性,使得夹紧和简支条件的功能梯度梁有着相当不同的行为特征。该文给出了热载荷作用下,功能梯度梁非线性静态响应的精确解。基于非线性经典梁理论和物理中面的概念导出了功能梯度梁的非线性控制方程。将两个方程化简为一个四阶积分-微分方程。对于两端夹紧的功能梯度梁,其方程和相应的边界条件构成微分特征值问题;但对于两端简支的功能梯度梁,由于非齐次边界条件,将不会得到一个特征值问题。导致了夹紧与简支的功能梯度梁有着完全不同的行为特征。直接求解该积分-微分方程,得到了梁过屈曲和弯曲变形的闭合形式解。利用这个解可以分析梁的屈曲、过屈曲和非线性弯曲等非线性变形现象。最后,利用数值结果研究了材料梯度性质和热载荷对功能梯度梁非线性静态响应的影响。
[Abstract]:Due to the non-uniform material characteristics of functionally graded material structure along the thickness direction, the clamping and simply supported functionally graded beams have quite different behavior characteristics.In this paper, the exact solution of nonlinear static response of functionally graded beam under thermal load is given.Based on the theory of nonlinear classical beam and the concept of physical midplane, the nonlinear governing equation of functionally graded beam is derived.The two equations are simplified into a fourth order integro-differential equation.For a functionally graded beam clamped at both ends, the equation and the corresponding boundary conditions constitute the differential eigenvalue problem, but for the functionally graded beam with simply supported ends, there will be no eigenvalue problem due to the inhomogeneous boundary conditions.As a result, the clamped and simply supported functionally gradient beams have completely different behavior characteristics.The closed form solutions of the post-buckling and bending deformation of the beam are obtained by solving the integro-differential equation directly.The nonlinear deformation phenomena such as buckling, hyperbuckling and nonlinear bending can be analyzed by using this solution.Finally, the effects of material gradient properties and thermal loads on the nonlinear static response of functionally graded beams are studied by numerical results.
【作者单位】：兰州理工大学理学院;西安交通大学机械结构强度与振动国家重点实验室;
【基金】：国家自然科学基金项目(11472123) 西安交通大学机械结构强度与振动国家重点实验室开放课题项目(SV2014-KF-04)
【分类号】：O344.1;TB34

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