Winkler地基上四边自由正交各向异性矩形中厚板弯曲的有限积分变换解  

Finite Integral Transform Solution ofthe Bending of Moderately ThickOrthotropic Rectangular Plate withFour Sides Free on WinklerFoundation

作　　者：宁进 额布日力吐[1] Ningjin;Eburilitu(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China)

机构地区：[1]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《应用数学》2024年第1期192-199,共8页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(12362001,11862019);the Natural Science Foundation of Inner Mongolia(2023MS01008)。

摘　　要：本文应用有限积分变换法研究Winkler地基上四边自由正交各向异性矩形中厚板的弯曲问题.具体由正交各向异性矩形中厚板弯曲的基本方程组和边界条件出发,结合有限积分变换法及其对应的逆变换法推导出正交各向异性矩形中厚板弯曲问题的解析解.该解析解统一适用于计算各向同性/正交各向异性矩形薄板、中厚板和厚板的弯曲问题,并且通过具体算例验证了所得解析解的正确性.The bending problem of a moderately thick orthotropic rectangular plate(ORP)with four sides free on Winkler foundation is studied by the finite integral transform(FIT)method.Based on the boundary conditions and basic equations of the bending of moderately thick ORP,the analytical bending solution of this plate is obtained by the FIT method and its corresponding inverse transform method.This analytical solution is uniformly applicable to the calculation of bending problems of thin,moderately thick and thick isotropic and orthotropic rectangular plates.Then by specific examples the correctness of the obtained analytical solution is verified.

关 键 词：正交各向异性中厚板 弯曲 解析解 有限积分变换法 

分 类 号：O343[理学—固体力学]