针对局部横向载荷作用下四边刚性固定矩形板，运用能量法推导出板中挠度解答方程组，利用Matlab编程求解，可计算得到任意矩形板尺寸及横向载荷尺寸下弹性阶段的变形，将结果与有限元数值解进行对比，证明了该方法的精确与快速性，并将该公式应用于极地船舶冰区加强区域外板强度的快速校核中。
This paper derived the deflection formula of the rectangular plate by local distributed load with four edges clamped. Then it got the elastic load/deflection curve with Matlab programming. Compared the analytic solution with FEM solution and proved its accuracy and rapidity. Eventually, the paper applied the method to the rapid assessment method in a real case.
2019,41(7): 40-44 收稿日期：2018-05-07
DOI：10.3404/j.issn.1672-7649.2019.07.008
分类号：TU206
基金项目：工信部高技术舰船科研计划支持项目
作者简介：陆锁芳(1994-),女,硕士研究生,研究方向为船舶与海洋工程结构物设计制造
参考文献：
[1] UGURAL.A.C. Stresses in plates and shells[M]. McGraw-Hill Book Company 1981.
[2] 钟阳. 四边固支矩形弹性薄板的精确解析解[J]. 力学季刊, 2009, 30(2):297-303 ZHONG Yang. Exact analytic solution of rectangular thin plate with four edges clamped[J]. Chinese Quarterly of Mechanics, 2009, 30(2):297-303
[3] 李元媛. 矩形薄板弯曲的严格简明解析解[J]. 机械工程学报, 2008, 44(10):72-76 LI Yuan-yuan. Some concise exact analytical soluitons of rectangular plate bending[J]. Chinese Journal of Mechanical Engineering, 2008, 44(10):72-76
[4] CERDEM IMRAK, ISMAIL GERDEMELI. The problem of isotropic rectangular plate with four clamped edges[J]. Sahana-Academy Proceedings in Engineering Sciences, 2007, 32(3):181-186
[5] LIN Hong. Plastic design of laterally patch loaded plates for ships[J]. Marine Structures, 2007(3)
[6] TIAN Ximin. Review on advances in research of ice loads on ice-going ships[J]. Journal of Ship Mechanics, 2015, 19(3):337-348
[7] 张文福. 局部荷载作用下四边固支矩形板的计算用表[J]. 大庆石油学院学报, 2006, 30(6):66-69 ZHANG Wenfu. Calculating table of rectangular plate with four edges clamped[J]. Journal of Daqing Petroleum Institute, 2006, 30(6):66-69
[8] XU Dong, LIU Jun. Research on limit load criteria for polar ships under ice loads[J]. Journal of Ship Mechanics, 2014, 18(3):124-142
[9] 陈铁云, 陈伯真. 船舶结构力学[M]. 上海:上海交通大学出版社, 1991.
[10] 陈伟杰. 冰载下舷侧加强结构强度快速校核方法研究[D]. 上海:上海交通大学, 2015. CHEN Weijie. Study on rapid strength assessment method of enhanced side structure under ice load[D]. Shanghai:Shanghai Jiao Tong University, 2015.
[11] ABS. Guidance Notes on Ice Class[S]. 2011.
