基于等效系统假定的变厚度板弯曲广义积分变换解

针对等厚度薄板的弯曲问题,研究人员已给出了基于不同数值算法的经典数值解。针对变厚度薄板弯曲问题的解答较少,且以有限元数值模拟计算为主,计算耗时较大。本文基于广义积分变换原理建立了求解变厚度等效系统的广义积分变换算法,分析了线性和二次变化的变厚度板在多种边界条件下的弯曲问题,利用文献已发表结果同本文建立的广义积分变换解进行验证。计算结果表明,本文建立的基于广义积分变换的变厚度板弯曲求解方法具有较高准确性。同时,通过参数化分析手段,分别利用广义积分变换方法和有限元数值模拟方法讨论了不同边界约束和长宽比等条件对中心点处挠度的影响,计算结果具有较好的一致性,证明本文建立的广义积分变换方法可用于求解变厚度板弯曲问题,且具有较高的准确性。

Bending solution for equivalent system of variable thickness plate by the generalized integral transform technique

For the bending problem of thin plates with uniform thickness,some classical numerical solutions based on various numerical techniques have been developed by researchers.However,the bending problem solutions of plates with variable thickness have been rarely reported,and most of them were based on finite element calculation,which consumes a lot of CPU time.In the present work,the authors developed a hybrid numerical and analytical mothed based on the Generalized Integral Transform Technique (GITT) to solve the bending problem of plates with variable thickness of linear and quadratic variations.The calculated results were calibrated by the results which were reported in the literatures.Finally,the effects of boundary constraints and aspect ratio on the deflection at the center point is discussed by using the GITT method and finite element numerical simulation method,respectively and the results are in good agreement.It can be proven that the generalized integral transformation method established in this paper can be used to solve the bending problem of variable thickness plate with good accuracy.