摘要
针对四边固支(all edges clamped,CCCC)的弹性矩形薄板在两对边半余弦分布压力下的面内应力分布以及屈曲问题,基于辛弹性力学的平面矩形域Hamilton体系下的实数型面内应力分布通解,依据必须满足的应力边界条件,借助符号运算软件Maple,得到不同长宽比矩形薄板在半余弦分布压力下合理的面内应力分布。考虑到应力分布表达式的复杂性,运用Galerkin法,根据CCCC矩形薄板弯曲的位移边界条件,给出不同长宽比弹性矩形薄板在半余弦分布压力下的屈曲载荷系数。通过与已有文献结果的比较表明,文中求解方法更为有效和正确。基于所给出的结果,可望为解决矩形薄板在非线性分布载荷下的面内应力分布以及屈曲问题提供一种新的研究方法。
The distribution of in-plane stresses and buckling of thin rectangular plates having all edges clamped （CCCC）, with co- sine-distributed in-plane loadings along two opposite plate edges are studied. Based the general solutions of the in-plane stress distribution under the Hamilton system of sympleetie elasticity in plane rectangular domain, cousidered all in-plane stress boundary conditions, with the help of the symbolic computational software Maple, the formulae determining the stress distribution for various aspect ratios thin rectangular elastic plates subjected to in-plane compressive loads varyi＇ng cosine along two opposite edges are gained. Taking into account the complexity of the expressious of stress distribution, a set of buckling loads for the CCCC thin rectangular plates are obtained by using the Galerkin method. The efficiency and validity of the proposed method is confirmed by the comparisons made with the results existed in literatures. Based on the results reported herein, one may conclude that the proposed method could provide a new way for obtaining the inplane stresses and buckling analysis of thin rectangular plates subjected noulinearly distributed in-plane loadings.
出处
《机械强度》
CAS
CSCD
北大核心
2010年第4期627-631,共5页
Journal of Mechanical Strength
基金
江苏大学高级专业人才科研启动基金(06JDG079)
