含裂纹功能梯度材料Timoshenko梁的非线性静力分析

Nonlinear Static Analysis of Cracked Functionally Graded Material Timoshenko Beam

利用转动弹簧模型模拟裂纹,给出由裂纹引起的局部柔度表达式。基于一阶剪切变形理论和Von Karman非线性理论建立含裂纹功能梯度材料Timoshenko梁的非线性力学模型,采用Hamilton原理推导了含裂纹功能梯度材料Timoshenko梁的非线性平衡微分方程,利用伽辽金方法对该非线性偏微分方程组进行求解。数值计算中分析了跨高比、裂纹位置、裂纹深度和弹性模量比值等因素对含裂纹FGM梁非线性静力响应的影响。

The rotating spring model is used to simulate the crack,and the local flexibility expression caused by the crack is given.Based on the first-order shear deformation theory and Von Karman nonlinear theory,the nonlinear model of the cracked functionally graded material Timoshenko beam is established.The Hamilton principle is used to derive the nonlinear balanced differential equation of the cracked functionally graded material Timoshenko beam.The system of differential equations is solved by the Galerkin method.In the numerical calculation,the effects of the factors such as span-depth ratio,crack location,crack depth and elastic modulus ratio on the nonlinear static response of cracked FGM beams are analyzed.