板面为各向异性面的横观各向同性弯曲板的精化理论  

Refinrd theory of a transversely isotropic bending plate with anisotropic plane

作　　者：李荣荣[1] 赵宝生[1] 

机构地区：[1]辽宁科技大学机械工程与自动化学院,辽宁鞍山114051

出　　处：《辽宁科技大学学报》2015年第4期268-273,共6页Journal of University of Science and Technology Liaoning

基　　金：国家自然科学基金项目(11172319)

摘　　要：在板面为各向同性面的横观各向同性板精化理论的基础上,对板面为各向异性面的横观各向同性板进行了研究,并推导出其精化理论。根据横观各向同性弹性理论和Elliott-Lodge通解,在不作任何预先假设的条件下,获得了由板中面上的位移和转角表示的位移场和应力场,根据Lur’e方法和边界条件获得了板面受横向载荷的精化方程,略去高阶项后获得可直接应用的近似控制微分方程。令所有物理量与x2或x3无关,得出的精化理论分别与横观各向同性梁和各向同性梁的精化理论一致。In this paper, based on the transversely isotropic theory, the refined theory of a transversely isotropic bending plate with the anisotropic plane is studied and derived. By using Elliott-Lodge solution and transversely isotropic elastic theory, the displacement and stress components were obtained in terms of the mid-plane displacement and its derivatives without any assumptions. The refined equation for the plate with transverse surface loadings is obtained by using Lur＇e method and boundary conditions and then omitting the high orders,the approximate governing differential equation is obtained. Making all physical quantities are irrelevant to x2 or x3and the results are consistent with the refined theory of transversely isotropic beams and isotropic beams respectively.

关 键 词：弹性板 横观各向同性 精化理论 Elliott-Lodge通解 Lur’e方法 

分 类 号：O343[理学—固体力学]