基于变形分解的四边固支单向与双向薄板界定分析  

The distinguishing criterion of one-way and two-way plates with four sides fixed based on deformations decomposition

作　　者：王东炜[1] 孙攀旭 王栋[1] Wang Dongwei Sun Panxu Wang Dong(School of Civil Engineering, Zhengzhou Universit)

机构地区：[1]郑州大学土木工程学院,郑州450001

出　　处：《应用力学学报》2017年第1期8-13,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(50978232)

摘　　要：板是工程结构中的常用构件,但需区分单向板和双向板分别进行设计,故对两者的界定研究具有重要意义。本文通过构造8节点正方体单元24种基本位移与变形向量,形成用于变形分解的正方体单元完备正交基矩阵,及均布荷载作用下板的主要基本变形分解图。基于变形分解分析,总结出单向板三大变形特征,即短边弯曲变形为主特征、浅梁变形特征和长边弯曲变形为可略特征;进而确定以长宽比1.50、2.20、2.40作为不同精度下的单、双向薄板类型划分界限。工程设计人员可依据具体工程需求,采用不同的分类方法对任意薄板进行类型判别,进而采用单向薄板或双向薄板理论进行薄板设计。Plates are the common components in engineering structures. It must be distinguished between one-way and two-way plates in design. Therefore, the research on the definition of one-way plate and two-way plate is important. The 24 basic displacement and deformation vectors of eight nodes equilateral cube unit are constructed in this paper, and the complete orthogonal base matrix of the square unit is formed for the deformations decomposition. Then the main basic deformation decomposition graph of a plate under uniform load can be obtained. Based on the deformation decomposition analysis, this paper summarizes the three deformation characteristics for identifying the one-way plate. These characteristics consist of mainly short-side bending deformation characteristic, shallow beam deformation characteristic and slightly long-side bending deformation characteristic, respectively. And the three distinguishing criteria for one-way and two-way plate are provided with different accuracy requirements. The length-width ratio of 1.50, 2.20 and 2.40, are considered as the three distinguishing criteria. According to the different calculation accuracy requirements, the designers can use different classification methods to determine the type of the plate. Then, the plate design can be carried out based on the one-way or two-way plate codes.

关 键 词：固支薄板 单向板 双向板 正交理论 变形分解 

分 类 号：TU395.2[建筑科学—结构工程]