Expansions in terms of Papkovich–Fadle eigenfunctions in the problem for a half-strip with stiffeners,ZAMM - Journal of Applied Mathematics and Mechanics

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Expansions in terms of Papkovich–Fadle eigenfunctions in the problem for a half-strip with stiffeners
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2021-03-08 , DOI: 10.1002/zamm.202000093
Mikhail D. Kovalenko ₁ , Irina V. Menshova _{2,

3} , Alexander P. Kerzhaev ₂ , Guangming Yu _{4,

5}

Affiliation

We have constructed an exact solution to the boundary value problem in the theory of elasticity for a half-strip with identical stiffeners along its long sides and a load acting at its end (even-symmetric deformation). The solution is represented as series in Papkovich–Fadle eigenfunctions whose coefficients are determined from closed formulas. The solution includes two easily variable parameters that characterize the relative tensile-compressive and flexural rigidities of the stiffeners. The final formulas for the stresses and displacements in the plate as well as for the longitudinal and transverse forces and bending moment in the stiffeners are simple and can be easily used in engineering.

中文翻译：

带加劲肋的半带问题中 Papkovich-Fadle 特征函数的扩展

我们已经构建了弹性理论中边界值问题的精确解，用于半带的长边具有相同的加强筋和作用在其末端的载荷（偶对称变形）。该解表示为 Papkovich-Fadle 特征函数中的级数，其系数由封闭公式确定。该解决方案包括两个容易改变的参数，它们表征了加劲肋的相对拉伸-压缩和弯曲刚度。板中应力和位移以及加劲肋中的纵向和横向力和弯矩的最终公式很简单，很容易在工程中使用。

更新日期：2021-03-08

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