无拉力Winkler地基上自由边矩形Reissner板的弯曲
Bending Problems of Rectangular Reissner Plate with Free Edges Laid on Tensionless Winkler Foundations
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摘要: 本文提出了一种求解无拉力Winkler地基上自由边矩形Reissner板受任意载荷的弯曲问题的解析方法.通过适当设定满足可导条件的Fourier级数加补充项形式的挠度函数和剪力函数,把给定边界条件下的微分方程化成最简形式的无穷代数方程组.对于常规的Winkler地基,可直接求解;而对于无拉力Winkler地基,方程组为一组弱非线性代数方程组.使用迭代法容易得到解.Abstract: In this paper, an analytical method for solving the bending problems of rectangular reissner plate with free edges under arbitrary loads laid on tensionless Winkier foundations is proposed. By assuming proper form of Fourier series with supplementary terms, which meet derivable conditions, for deflection and shear force functions, the basic differential equations with given boundary conditions can be transformed into a set of simple infinite algebraic equations. For common Winkier foundations, this set of equations can be solved directly and for tensionless Winkler foundations, it is a set of weak nonlinear algebraic equations, the solution of which can be obtained easily by using iterative procedures.
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Key words:
- tensionless Winkler foundation /
- Reissner plates /
- bending problems
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