弹性半空间地基与四边自由异性矩形板相互作用的研究  

Interaction between the elastic half-space and the anisotropic rectangular plates with four free edges

作　　者：王春玲[1] 周波[1] 胡勇[1] 

机构地区：[1]西安建筑科技大学理学院,西安710055

出　　处：《应用力学学报》2013年第4期469-474,641,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(51178387);陕西省教育厅专项基金(11JK0526)

摘　　要：选用弹性半空间地基模型分析四边自由各向异性矩形地基板的弯曲和稳态振动解析解。将异性薄板控制微分方程与基于弹性半空间地基位移解建立的板与地基变形协调方程相结合,先按对称性分解,然后采用三角级数法得出了弹性半空间地基上四边自由各向异性矩形薄板的弯曲和稳态振动解析解,包括地基反力(幅值)、板的挠度(幅值)、板的内力(幅值)的解析表达式。克服了数值法的弊端,取消了对地基反力的假设,得到了板的内力(幅值)及地基反力(幅值)更切实际的分布规律。算例结果不但与文献结果吻合良好,而且表明对于异形板,对称载荷能引起反对称的内力和变形。该方法使得半空间地基上各向异性矩形薄板这一复杂的接触问题的求解统一化、简单化、规律化。The analytical solution of an anisotropic rectangular thin plate with four free edges on the elastic half-space is analyzed.It combines the governing equation of anisotropic rectangular thin plate with the deformation compatibility equation of the plate and foundation based on the solution of the displacement for the elastic half-space.According to symmetric decomposition and then using triangular series method,the analytical solutions of the bending and steady vibration for anisotropic rectangular thin plate with four free edges on the elastic half-space are obtained.The solutions include the analytical expressions of the foundation reaction force,deflection of the plate and the internal force of the plate.The method not only overcomes some defects appear in traditional numerical methods,but also avoids the assumption of Winkler foundation mode or two-parameter foundation model,accordingly,the gained distributions of the inner forces in the plate and the contact pressure are more reasonable and accurate.The good agreement between the numerical results and the literature results proves that the proposed method is practical and achievable.This method makes the solution of the complex contact problems of anisotropic thin plate on the elastic half-space foundation to be unified,simplified and regulated.

关 键 词：弹性半空间地基 各向异性 四边自由矩形薄板 稳态振动 解析解 

分 类 号：TU311[建筑科学—结构工程] O342[理学—固体力学]