Pasternak地基上简支板问题的准格林函数方法  

Green quasifunction method for simply-supported thin plates on Pasternak foundation

作　　者：袁鸿[1] 陆伟[1] 

机构地区：[1]暨南大学应用力学研究所,广东广州510632

出　　处：《暨南大学学报（自然科学与医学版）》2006年第5期652-657,共6页Journal of Jinan University(Natural Science & Medicine Edition)

摘　　要：提出一种新的数值方法———准格林函数方法.以Pasternak地基上简支多边形薄板的弯曲问题为例,详细阐明了准格林函数方法的思想.即利用问题的基本解和边界方程构造一个准格林函数,这个函数满足了问题的齐次边界条件,采用格林公式将薄板的弯曲问题化为两个耦合的第二类Fredholm积分方程.边界方程有多种选择,在选定一种边界方程的基础上,可以通过建立一个新的规范化边界方程来表示问题的边界,以克服积分核的奇异性.A new numerical method -Green quasifunction method is proposed. The idea of this method is clarified in detail by taking bending problem of simply - supported thin polygonic plate on Pastemak foundation as an example. A Green quasifunction is established by using the fundamental solution and boundary equation of the problem. This function satisfies homogeneous boundary condition of the problem. The bending problem is reduced to two simultaneous Fredholm integral equations of second kind by Green formula. There are multiple choices for the normalized boundary equation. Based on a chosen boundary equation, a new normalized boundary equation can be established to overcome the irregularity of the kernel of the integral equations. Numerical results show high accuracy of the Green quasifunction method.

关 键 词：格林函数 积分方程 薄板 Pastemak地基 

分 类 号：O241.8[理学—计算数学] TU471.2[理学—数学]