【作者】 侯国华；

【导师】 侯朝胜；

【作者基本信息】 天津大学 ， 结构工程， 2004， 硕士

【摘要】 随着夹层板的广泛应用，夹层板的受力分析成了一个很重要的课题。本文对计及表板抗弯刚度的夹层圆板在均布荷载作用下的非线性弯曲问题进行了研究。文中给出了计及表板抗弯刚度的夹层圆板非线性弯曲的弯矩公式。在求解由夹层圆板非线性弯曲问题的非线性平衡微分方程和变形协调方程组成的方程组时，取幂函数作为夹层圆板挠度的试函数，用加权残值法中的配点法得到了简化后的夹层圆板非线性微分方程组。由于得到的简化微分方程组为非线性微分方程组，因此本文选用牛顿迭代法来在求解此微分方程组。本文用牛顿迭代法解得了固定夹紧、可移夹紧、铰支承和简单支承4种常见边界条件下，夹层圆板在均布荷载作用下的应力、弯矩和挠度值，并对计算结果进行了分析。分析证明用配点法解夹层圆板的非线性弯曲问题，具有计算量小和结果精确的特点。解非线性方程组和夹层圆板的内力，均用Fortran77编制通用的计算机程序，计算方便准确。更多还原

【Abstract】 The analysis of circular sandwich plates bearing force becomes a very important question with the abroad applications of sandwich plates. In this paper, it is researched that the non-linear bending problem about circular sandwich plates counting their surface plates’ flexural rigidity in the distributed loads. The essay gives the bending moment formulas of non-linear bending problems of circular sandwich plates counting their surface plates’ flexural rigidity. The non-linear differential equations are acquired by using power functions as trial functions and through the collocation method when the results of equilibrium equations are sought. The Newton-iterative method is adopted in order to acquire the keys of the equilibrium equations because the equations are non-linear differential equations.Four boundary conditions being considered in this paper, they are fixation clamp, motive clamp, pinned bearing, simpleness bearing. The functions based on the four boundary conditions are calculated by the Newton-iterative method in this paper and the results of calculations are analyzed. The stresses and bending moments are gained through the results. The examples testify that the collocation method has the advantages of less calculation quantities and accurate results.All above are realized by a program on computer by using the computer language Fortran77. it is very convenience.更多还原