An attempt is made in this research to analyse the nonlinear response of functionally graded material shallow arches with both edges clamped. The arch is resting on a three parameter nonlinear elastic foundation during deformation and is subjected to uniform lateral pressure and uniform temperature rise. Material properties are expressed according to a power law function and are assumed to be temperature dependent. The governing equilibrium equations of the arch are established with the aid of third order shear deformation curved beam theory of Reddy and von Kármán type of strain–displacement relations. The obtained equations contain three coupled and nonlinear equations in terms of circumferential displacement, lateral displacement and cross section rotation. Considering the immovable type of edge supports, the equations are reduced to two new coupled and nonlinear equations. These equations are solved using the two step perturbation technique for the case of clamped boundary conditions. Explicit expressions are resulted which yield the deflected shape of the arch as a function of temperature elevation and uniform pressure. It is shown that the arch reveals the snap-through type of instability under certain conditions. The response of the arch is highly affected by the power law index, thermal environment, side to thickness ratio and stiffnesses of the foundation.

本研究尝试分析功能梯度材料的浅拱形，其两个边都被夹紧。拱在变形过程中放置​​在三参数非线性弹性基础上，并承受均匀的侧向压力和均匀的温度升高。材料特性根据幂律函数表示，并假定为温度相关。拱的支配平衡方程是根据Reddy和vonKármán类型的应变-位移关系的三阶剪切变形弯曲梁理论建立的。所获得的方程式在周向位移，横向位移和横截面旋转方面包含三个耦合和非线性方程式。考虑到边缘支撑的固定类型，该方程被简化为两个新的耦合方程和非线性方程。对于约束边界条件，使用两步摄动技术求解这些方程。得出了明确的表达式，这些表达式根据温度升高和均匀压力的变化得出了弓形的挠曲形状。结果表明，在某些情况下，拱形结构显示出不稳定的卡扣型。拱的响应受幂律指数，热环境，边厚比和基础刚度的很大影响。结果表明，在某些情况下，拱形结构显示出不稳定的卡扣型。拱的响应受幂律指数，热环境，边厚比和基础刚度的很大影响。结果表明，在某些情况下，拱形结构显示出不稳定的卡扣型。拱的响应受幂律指数，热环境，边厚比和基础刚度的很大影响。