功能梯度材料梁的非线性研究

研究了热/机械载荷作用下几何非线性对功能梯度材料梁的位移及应力的影响。首先根据一阶剪切变形梁理论推导了机械载荷条件下功能梯度材料梁位移和应力的平衡方程,热载荷条件通过求解一维热传导方程即可获得;然后采用解析法和摄动技术两种方法对平衡方程求解,并利用非线性应变-位移关系分析非线性对位移和应力的影响;最后引入算例采用不同方法计算功能梯度材料梁的位移及应力并对比分析。数值计算结果表明,几何非线性对梁的位移和应力的影响是显著的,材料常数和边界条件对梁的非线性弯曲也有一定的影响。这种求解非线性平衡方程解析解的新方法对高阶剪切变形和层理论有一定的指导意义。

Nonlinear Analysis of Functionally Graded Beams

It was the intention to examine the effect of geometric nonlinearity on displacements and stresses in beams made of functionally graded materials subjected to thermo-mechanical loadings. Firstly with the mechanical loading condition, the equilibrium equations about the displacement and stress were obtained based on the first-order shear deformation beam theory (FSDBT). Temperature distribution through the thickness of the beams in thermal loadings was obtained by solving the one-dimensional heat transfer equation. Then the nonlinear strain-displacement relations were used to study the effect of geometric nonlinearity. And the equations were solved exactly and also by using a perturbation technique. Finally the results obtained from those two methods were compared for various loadings and boundary conditions by an example. The numerical results showed that the nonlinearity effect on the displacements and stresses of the beams was significant. Also the effects on the nonlinear bending behavior of the beams of material constant and the boundary conditions were determined. This new method for getting the solutions of the nonlinear equilibrium equations was significant for the high order shear deformation and layer theory.