【作者】 孙凡；

【导师】 侯朝胜；

【作者基本信息】 天津大学 ， 结构工程， 2003， 硕士

【摘要】 本课题研究了基于Reissner理论的夹层圆板的非线性弯曲问题。文中采用配点法计算,以三次样条函数作为应力函数和挠度函数的试函数。求解夹层圆板的非线性微分方程组时选取了牛顿迭代法。考虑了工程中常见的四种边界条件:可移夹紧、固定夹紧、铰支承和简单支承。论文首先分析了夹层圆板在轴对称均布横向荷载作用下挠度和内力的变化规律,并与幂级数方法作了比较。所得结果很理想,验证了样条函数在此问题上的有效性,并在收敛速度、收敛范围、计算精度等方面体现了此法的优越性。此外,论文还分析了夹层圆板在均布边弯矩及均布边弯矩与均布横向荷载组合作用下的非线性弯曲问题。所得结果也比较理想,自身收敛性很好,而且收敛速度快、收敛范围大,有一定的理论和实际意义。本文用FORTRAN90算法语言编制了相应程序,对上述所有内容加以实现。程序应用简单、通用性强。更多还原

【Abstract】 In the dissertation, the nonlinear bending of circular sandwich plates based on Reissner theory is analyzedThe method of Point Collocation are used in the calculation,with the B-spline function taken as the trial function. The Newton-iterative method is used to solve the nonlinear differential equation of circular sandwich plate. Four boundary conditions such as rigidly clamped edge, clamped but free to slip edge, simply hinged edge and simply supported edge, are considered.The nonlinear bending of circular sandwich plates subjected to axisymmetric uniformly distributed load are studied firstly. Some examples are calculated and by comparing the results with those obtained by the power series method, the validity and some excellences of the B-spline function method, such as wider convergent range, higher precision and less amount of computing time, are demonstrated. In addition, The nonlinear bending is also analyzed of circular sandwich plates subjected to uniformly distributed moment and the combination of axisymmetric uniformly distributed load and uniformly distributed moment. The convergent results are obtained, which are valid and have academic and practical value.All of above contents have been programmed and tested on the computer. The program is simple in use and has good currency.更多还原