解析型几何非线性圆拱单元

为研究圆拱结构几何非线性内力和位移计算以及平面内稳定分析问题，基于圆拱几何非线性静力分析模型，构造了解析位移形函数，进而利用能量法和势能变分原理，构造了解析型几何非线性圆拱单元，给出了单元列式；同时将该文模型通过理论退化，得到了不考虑轴向变形的无压缩圆拱模型，进一步得到了解析型无压缩几何非线性圆拱单元，并将此单元应用于圆拱的平面内稳定分析。研究结果表明:采用本单元模型进行平面内分岔失稳分析得到的失稳临界荷载系数与经典Timoshenko模型、Dinnik模型及静力法模型计算结果一致，相对误差为0%；平面内分岔失稳的临界荷载与平面内极值点失稳的临界荷载一致。该文单元具有解析型、高精确性以及良好的适用性，可用于任意工况下圆拱结构几何非线性位移、内力和平面内稳定分析。

ANALYTICAL GEOMETRICALLY NONLINEAR ELEMENTS FOR CIRCULAR ARCHES

To study the geometrically nonlinear internal force and displacement calculation and the in-plane stability of circular arch structures, the analytical displacement shape function is established based on the geometrically nonlinear static analysis model of a circular arch. The analytical geometrically nonlinear element for circular arches is constructed by using energy method and potential energy variational principle. The element formulas are obtained. The element model in this paper is theoretically degenerated without the axial deformation. Then the analytical geometrically nonlinear element for circular arches without compression is obtained. The element was used in the in-plane stability analysis of circular arches. The results show that the critical load coefficient of the in-plane bifurcation instability obtained by this element is consistent with the results of classical Timoshenko model, Dinnik model and static method model. The relative error is 0%. The critical load of in-plane bifurcation instability is also in accordance with that of in-plane extreme point instability. The element presented in this paper is of analytical type, high accuracy and good applicability. It can be used for geometrically nonlinear displacement and internal force analysis and in-plane stability analysis of circular arches under any load cases.