【摘要】：為了找到一種針對任意荷載作用下任意拱軸線彈性支撐拱的非線性穩(wěn)定性研究方法,對集中荷載作用下任意軸線兩端豎向彈性支撐淺拱的面內(nèi)屈曲特性開展研究,推導了量綱一化的非線性平衡方程,并通過算例分析了屈曲路徑和臨界荷載的分布特點,并將其結果與有限元解進行了對比驗證。推導過程中采用具有相同彈性支撐梁的屈曲模態(tài)作為形函數(shù),不截斷地展開拱軸線、外部荷載和結構位移,得到基本平衡狀態(tài)以及極值點屈曲、分岔屈曲的平衡方程;建立了外荷載、結構位移與結構內(nèi)力之間的對應關系,進而得到2種屈曲形式的平衡路徑和臨界荷載;分析了彈性剛度參數(shù)對2種屈曲條件下平衡路徑與極限荷載分布規(guī)律的影響。研究結果表明:采用給出的方法計算的結果與有限元解吻合良好,可以追蹤結構發(fā)生屈曲的全過程;極值點屈曲和分岔屈曲同時存在,當彈性支撐參數(shù)由對稱變?yōu)椴粚ΨQ時,極值點屈曲路徑在特定位置分成基本路徑和獨立的分離路徑,某些位置的分岔屈曲路徑變成極值點屈曲路徑,并伴隨相應臨界荷載點的出現(xiàn)和消失;臨界荷載僅在量綱一的彈性約束參數(shù)較小時隨之發(fā)生變化,當約束剛度增至一定程度時臨界荷載不再隨約束剛度的變化而改變。推導的集中荷載下任意拱軸線形豎向彈性支撐淺拱面內(nèi)屈曲求解公式,可為最終實現(xiàn)任意荷載下任意軸線彈性支撐拱非線性穩(wěn)定性的解析求解提供參考。
[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.
【作者單位】： 長沙理工大學土木與建筑學院;
【基金】：國家自然科學基金項目(51678069,51678071) 長沙理工大學土木工程重點學科基金項目(15ZDXK01);長沙理工大學橋梁工程安全控制省部共建教育部重點實驗室開放基金項目(15KB03)
【分類號】：U441.2

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