环壳理论与直交异性板理论在计算三圆弧波纹膜片上的比较
Comparison of the Calculations of Three-Convolution Circular Arc Corrugated Diaphragms by Toroidal Shell Theory and by Orthogonal Anisotropy Plate Theory
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摘要: 有人用直交异性板的理论计算[1]波纹板(膜片)的弹性位移,所得结果曾与实验对照比较满意.但是并没有人认真分析波纹数目、形状对直交异性板的弹性位移和应力分布的数量上的影响,以致未能对用直交异性板理论计算波纹板的范围作明确的说明.以前只是较一般地说,直交异性板理论用于计算波纹数目较多的膜片弹性特性(弹性位移与外力的关系)较满意,计算应力误差较大.本文利用环壳理论[2][3]分析了对称和不对称三圆弧波纹膜片的位移与应力,并与直交异性理论所得结果比较,明确了直交异性板理论的应用范围.Abstract: The calculation of elastic deformations of corrugated diaphragms has been given by orthogonal anisotropy plate theory[1],and its result agrees with the experimental results.But it has never beer discussed seriously how the number and form of convolutions affect the elastic deformations and stress distributions of anisotropy plate.As a result, adaptable limits of orthogonal anisotropy plate theory cannot be indicated when applied to calculate diaphragms. It is said that the theory is fairly good for calculating elastic deformations of the diaphragms which have more convolutions. It is also said that the error in calculating stresses is rather large. This paper, by using toroidal shell theory, presents the calculation of deformations and stresses of three-convolution circular arc corrugated diaphragms both symmetrical and unsymmetrical,compares its result with that of the orthogonal anisotropy plate theory and gives definite adaptable limits of the latter theory.
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[1] Андреева,Л,Е.,Расчет гоФрированных мембран как анизотропных плястинок.Инженерый Сбрнцк,АН СССР.Т ХХI(1955). [2] 钱伟长、郑思梁.轴对称圆环壳的复变量方程和轴对称细环壳的一般解.清华大学学报,19.1(1979),27-47. [3] Новожилов,В.В.,Теорця ТонкЦх Оболочек,Лениград(1962). [4] Wildhack,W.A.and V.H.Goerke,Corrugated metal diaphragms for aircraft pressure.measuring instruments,T,N.NACA,No,738(1939). [5] 樊大钧、黄黔,圆弧波纹膜片的理论分析和工程设计方法,在第二届仪器仪表学术年会上宣读.北京(1982.12). [6] 樊大钧、黄黔,三圆弧波纹膜片的设计,仪器仪表学报(排印中). [7] 黄黔.用数值积分的初参数法解波纹管.应用数学和力学,3.1(1982).101-112. -
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