求解加筋板的位移与应力的一种解析计算方法  

An Analytical Calculation Method for Solving the Deflection and Stress of Stiffened Plates

作　　者：王小明[1] WANG Xiaoming(China Ship Development and Design Center,Wuhan 430064, China)

机构地区：[1]中国舰船研究设计中心,武汉430064

出　　处：《武汉理工大学学报（交通科学与工程版）》2021年第4期721-727,共7页Journal of Wuhan University of Technology（Transportation Science & Engineering）

基　　金：中国船舶重工集团联合基金项目(1B04010101);中国舰船研究设计中心研发基金项目(3130101)。

摘　　要：为了求解加筋板弯曲位移和应力,以加筋板中板与筋的耦合力和力矩为中间未知量,提出了一种“板筋分离法”的计算方法.板的运动模式采用一阶剪切变形理论,加强筋则采用铁木辛科梁理论.这种方法把板和筋拆开分析,加强筋受到板对其作用的力和力矩,成为加强筋的外力;板则受到加强筋的反作用,反作用力、反作用力矩和真实外力,一起构成了板的外力.根据上述受力分析,分别求解两者的弯曲位移.通过板与筋之间的位移协调条件,确定二者之间的耦合力和力矩,进而确定加筋板的位移.根据几何方程和本构关系,可以求出弯曲应力.通过算例验证,本文方法位移计算结果与有限元法吻合较好,局部最大误差3.5%;大部分区域的应力计算结果与有限元法接近,在局部区域差别略大,最大误差-13.5%.In order to solve the bending displacement and stress of stiffened plate,taking the coupling force and moment between plate and rib in stiffened plate as intermediate unknown quantities,a calculation method of“separation method of plate and rib”was proposed.The first-order shear deformation theory was adopted for plate motion mode,and Timoshenko beam theory was adopted for stiffener.By separating the plate from the rib,the force and moment exerted by the plate on the rib become the external force of the rib.The plate is reacted by the stiffener,and the reaction force,reaction moment and real external force together constitute the external force of the plate.According to the above-mentioned stress analysis,the bending displacements of the two were solved respectively.Through the displacement coordination condition between plate and reinforcement,the coupling force and moment between them were determined,and then the displacement of stiffened plate was determined.According to geometric equation and constitutive relation,bending stress can be obtained.The results of displacement calculation by this method are in good agreement with the finite element method,and the local maximum error is 3.5%.The stress calculation results in most areas are close to those of the finite element method,but the difference is slightly larger in some areas,with the maximum error of-13.5%.

关 键 词：加筋板 加肋板 板筋分离法 一阶剪切变形理论 正交异性板 

分 类 号：U446.1[建筑科学—桥梁与隧道工程]