利兹法求解正交各向异性矩形板的弯曲  

Bending of orthotropic rectangular plates by Ritz method

作　　者：冯立华[1] 杨加明[1] 戴良忠[1] 王旭[1] 

机构地区：[1]无损检测技术教育部重点实验室(南昌航空大学),南昌330063

出　　处：《失效分析与预防》2012年第4期207-212,共6页Failure Analysis and Prevention

基　　金：江西省自然科学基金(20114BAB202010);无损检测技术教育部重点实验室基金(ZD201129006)

摘　　要：主要分析正交各向异性矩形板在四边固支条件下弯曲问题。用双重Fourier级数表达弯曲挠度函数,该函数须满足固支边界条件。用能量法求出正交各向异性板的总势能,分别截断级数的第1项和前4项代入势能方程中,利用利兹法,即最小势能原理求出挠度级数的系数项,利用应力应变与挠度之间的关系求出板的应力。结合有限元分析软件计算板的挠度以及应力,最后将两者结果对比分析。研究表明,挠度和应力计算四级近似方程较一级近似方程更精确,应力计算需取到级数前4项才可达所需精度。Bending of orthotropic rectangular plates is analyzed under four edges damped boundary conditions. Double Fourier series are used to express the deflection function which satisfy the boundary conditions. The first item or previous 4 items of the double Fourier series is tnmcated to calculate the total potential energy of the orthotropic rectangular plates. The coefficients of the deflection series are obtained by the theorem of minimum potential or The Ritz Method. The stress of the plates is acquired using relationship between stress/strain and deflection. Numerical results of deflection and stress are shown and compared between The Ritz Method and The Finite Element solution. The conclusion is that the usage of 4 previous items of the double Fourier series for the deflection and stress is better than that of the first item, and the 4 previous items are also required to meet the need of accuracy of stress calculation.

关 键 词：正交各向异性 矩形板 弯曲 利兹法 有限元方法 

分 类 号：O342[理学—固体力学] TG33[理学—力学]