集中荷载作用下弹性支撑浅拱屈曲特性求解
发布时间：2019-04-20 13:55
【摘要】：为了找到一种针对任意荷载作用下任意拱轴线弹性支撑拱的非线性稳定性研究方法,对集中荷载作用下任意轴线两端竖向弹性支撑浅拱的面内屈曲特性开展研究,推导了量纲一化的非线性平衡方程,并通过算例分析了屈曲路径和临界荷载的分布特点,并将其结果与有限元解进行了对比验证。推导过程中采用具有相同弹性支撑梁的屈曲模态作为形函数,不截断地展开拱轴线、外部荷载和结构位移,得到基本平衡状态以及极值点屈曲、分岔屈曲的平衡方程;建立了外荷载、结构位移与结构内力之间的对应关系,进而得到2种屈曲形式的平衡路径和临界荷载;分析了弹性刚度参数对2种屈曲条件下平衡路径与极限荷载分布规律的影响。研究结果表明:采用给出的方法计算的结果与有限元解吻合良好,可以追踪结构发生屈曲的全过程;极值点屈曲和分岔屈曲同时存在,当弹性支撑参数由对称变为不对称时,极值点屈曲路径在特定位置分成基本路径和独立的分离路径,某些位置的分岔屈曲路径变成极值点屈曲路径,并伴随相应临界荷载点的出现和消失;临界荷载仅在量纲一的弹性约束参数较小时随之发生变化,当约束刚度增至一定程度时临界荷载不再随约束刚度的变化而改变。推导的集中荷载下任意拱轴线形竖向弹性支撑浅拱面内屈曲求解公式,可为最终实现任意荷载下任意轴线弹性支撑拱非线性稳定性的解析求解提供参考。
[Abstract]:In order to find a nonlinear stability research method for elastic braced arch with arbitrary axis under arbitrary load, the in-plane buckling characteristics of shallow arch with vertical elastic braced at both ends of arbitrary axis under concentrated load are studied. The dimensional nonlinear equilibrium equation is derived, and the distribution characteristics of buckling path and critical load are analyzed by numerical examples, and the results are verified by comparison with the finite element solution. The buckling mode of the beam with the same elastic support is used as the shape function to unfold the arch axis, external load and structural displacement without truncation. The equilibrium equations of the basic equilibrium state, the extreme point buckling and the bifurcation buckling are obtained. The corresponding relationship between external load, structural displacement and structural internal force is established, and then the equilibrium path and critical load of two buckling forms are obtained. The influence of elastic stiffness parameters on the distribution of equilibrium path and ultimate load under two buckling conditions is analyzed. The results show that the calculated results are in good agreement with the finite element solution, and the whole buckling process of the structure can be traced. The extreme point buckling and bifurcation buckling exist at the same time. When the elastic bracing parameter is changed from symmetry to asymmetry, the extreme point buckling path is divided into the basic path and the independent separation path in a particular position. The bifurcation buckling path at some positions becomes the extreme point buckling path, accompanied by the emergence and disappearance of the corresponding critical load point. The critical load changes only when the elastic constraint parameter of dimension-one is small, and when the constraint stiffness increases to a certain extent, the critical load no longer changes with the change of constraint stiffness. The derived formula for calculating the in-plane buckling of shallow arch with vertical elastic bracing of arbitrary arch axis under concentrated load can provide a reference for the analytical solution of nonlinear stability of elastic braced arch with arbitrary axis under arbitrary load.
【作者单位】： 长沙理工大学土木与建筑学院;
【基金】：国家自然科学基金项目(51678069,51678071) 长沙理工大学土木工程重点学科基金项目(15ZDXK01);长沙理工大学桥梁工程安全控制省部共建教育部重点实验室开放基金项目(15KB03)
【分类号】：U441.2
本文编号：2461660
[Abstract]:In order to find a nonlinear stability research method for elastic braced arch with arbitrary axis under arbitrary load, the in-plane buckling characteristics of shallow arch with vertical elastic braced at both ends of arbitrary axis under concentrated load are studied. The dimensional nonlinear equilibrium equation is derived, and the distribution characteristics of buckling path and critical load are analyzed by numerical examples, and the results are verified by comparison with the finite element solution. The buckling mode of the beam with the same elastic support is used as the shape function to unfold the arch axis, external load and structural displacement without truncation. The equilibrium equations of the basic equilibrium state, the extreme point buckling and the bifurcation buckling are obtained. The corresponding relationship between external load, structural displacement and structural internal force is established, and then the equilibrium path and critical load of two buckling forms are obtained. The influence of elastic stiffness parameters on the distribution of equilibrium path and ultimate load under two buckling conditions is analyzed. The results show that the calculated results are in good agreement with the finite element solution, and the whole buckling process of the structure can be traced. The extreme point buckling and bifurcation buckling exist at the same time. When the elastic bracing parameter is changed from symmetry to asymmetry, the extreme point buckling path is divided into the basic path and the independent separation path in a particular position. The bifurcation buckling path at some positions becomes the extreme point buckling path, accompanied by the emergence and disappearance of the corresponding critical load point. The critical load changes only when the elastic constraint parameter of dimension-one is small, and when the constraint stiffness increases to a certain extent, the critical load no longer changes with the change of constraint stiffness. The derived formula for calculating the in-plane buckling of shallow arch with vertical elastic bracing of arbitrary arch axis under concentrated load can provide a reference for the analytical solution of nonlinear stability of elastic braced arch with arbitrary axis under arbitrary load.
【作者单位】： 长沙理工大学土木与建筑学院;
【基金】：国家自然科学基金项目(51678069,51678071) 长沙理工大学土木工程重点学科基金项目(15ZDXK01);长沙理工大学桥梁工程安全控制省部共建教育部重点实验室开放基金项目(15KB03)
【分类号】：U441.2
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