正交异性板三维高阶渐近分析的圣维南原理表述和应力边界条件

Saint-Venant's Principle and Stress Edge Conditions for Orthotropic Plates in Higher-order Asymptotic Analysis

提出正交异性板的三维高阶渐近分析,其内部区域各阶渐近解为各级精度的二维板理论解,首项与著名的Kirchhoff板理论一致;而其边界层解则分解为半无限板条的平面应变和扭转变形解,因而也缩减为二维边值问题的分析。由Laplace变换方法对边界层半无限板条的分析建立了指数型衰减解的应力边界数据应满足的充分必要条件,此即圣维南原理在板渐近理论研究中的列式或表述。由此导出高阶板理论的应力边界条件,首项时与Kirchhoff板理论缩减的力边界条件一致。

A higher order asymptotic analysis for orthotropic plates was presented with the leading order interior solutions reduced to the well known Kirchhoff plate theory; The boundarylayer solutions were decoupled into the plane strain and torsional deformations of a semi-infinite plane strip, which was analyzed by Laplace transform method. Saint-Venant＇s principle in plate studies was formulated by establishing the necessary and sufficient conditions for stress edge-data generating exponentially decaying solutions, and applied to derive the stress edge conditions for higher order plate theories.