四边形平面应力等参元的无应力状态量研究  

Study on unstressed state amounts of quadrilateral plane stress iso-parametric element

作　　者：许磊平[1] 秦顺全[1] XU Leiping;QIN Shunquan(China Railway Major Bridge Reconnaissance&.Dcsign Institute Co.,Ltd.,Wuhan 430056,China)

机构地区：[1]中铁大桥勘测设计院集团有限公司,湖北武汉430056

出　　处：《武汉大学学报（工学版）》2020年第10期883-888,共6页Engineering Journal of Wuhan University

基　　金：国家自然科学基金青年基金(编号:51708455);国家自然科学基金面上项目(编号:51978578)。

摘　　要：为明确分阶段成形壳结构的成形状态与成形过程之间的关系,对平面应力单元的无应力状态量进行了研究。以四边形平面应力等参元为研究对象,通过几何分析确定了单元无应力状态量包含的独立参数,将弹性总势能计算的起点设在无应力状态,建立了单元的弹性总势能,根据最小势能原理,推导了基于四边形平面应力等参元的分阶段成形结构平衡方程,定义了单元的无应力状态量。基于理论推导编写了求解程序,对分阶段成形平面结构进行了分析,结果表明:对于分阶段成形的壳结构,当结构体系、外荷载及各平面应力单元无应力状态量一定时,结构的成形状态是一定的,与分阶段成形过程无关。In order to establish the relationship between ultimate state and forming process of shell structures constructed by stages,unstressed state amounts of plane stress element were studied.Independent parameters included in element unstressed state amounts were determined by geometrical analysis for quadrilateral isoparametric plane stress element.The starting point of the total elastic potential energy calculation was set in the unstress state,and the total elastic potential energy was founded.Equilibrium equation for structures comprised of iso-parametric quadrilateral plane stress elements formed by stages was derived based on principle of minimum potential energy.Meanwhile,unstressed state amounts of quadrilateral iso-parametric plane stress element were defined.A computational program was developed based on theoretical derivation,and was applied to a plane structure formed by stages.Numerical calculation showed that when the structural system,external loads and unstressed state amounts of all elements were definite,ultimate state of structures comprised of quadrilateral plane stress elements was independent with forming process.

关 键 词：无应力状态量 成形状态 平衡方程 等参四边形平面应力单元 分阶段成形 

分 类 号：U445.1[建筑科学—桥梁与隧道工程]