摘要
矩形薄板边缘受非线性分布面内载荷作用的情况在工程中经常遇到,精确的应力分析也是薄板稳定性分析的基础,由于问题的复杂性目前还没有精确解。该文根据弹性力学理论,采用里兹法求解矩形薄板边缘受非线性分布载荷作用的面内应力,应力函数采用切比雪夫多项式并满足所有应力边界条件。结合数学计算软件Mathematica,分析了不同长宽比矩形板在单轴和双轴抛物线分布边缘载荷作用下的面内应力,得到的结果精确满足应力边界条件且与有限元法和微分求积法结果十分吻合,从而验证了方法的正确性和精确性。研究结果为受非线性分布面内载荷作用矩形板的屈曲分析奠定了基础。
Thin rectangular plates under non-linearly distributed edge loads are very common in engineering.Accurate stress distribution is required for buckling analysis of thin plates.Because of the complexity,no exact solution has been given thus far.Ritz method is used to find the distribution of in-plane stresses of thin rectangular plates under non-linearly distributed edge loads based on the theory of elasticity.Chebyshev polynomials are adopted as the stress functions which satisfy the stress boundary conditions.The stress distributions of rectangular plates with different aspect ratios under uniaxial or biaxial parabolic edge compressions are analyzed with the help of mathematic computational software Mathematica.It is seen that results satisfy exactly the stress boundary conditions and agree very well with numerical results given by finite element method and differential quadrature method,thus,verify the validity and accuracy of the proposed method.The results lay a foundation for the buckling analysis of rectangular plates under non-linearly distributed edge loads.
出处
《工程力学》
EI
CSCD
北大核心
2011年第1期37-42,共6页
Engineering Mechanics
基金
航空科学基金项目(04B52006)
关键词
弹性力学
非线性分布载荷
里兹法
应力分布
矩形板
屈曲
切比雪夫多项式
elasticity
non-linearly distributed load
Ritz method
stress distribution
rectangular plate
buckling
Chebyshev polynomial
