A large number of non-circular tunnels are widely used in engineering practice. The application of these geometric structures not only makes the boundary conditions of mechanical problems more complex, but also makes the theoretical solution more difficult. The introduction of curvilinear coordinate system can easily transform the elliptical region into a circular region, and the physical relationship can also be adjusted accordingly. In the state space, the transformed problem can be solved by using the dual variables of Hamiltonian mechanics, and the special solution equation can be obtained. With regard to the non-homogeneous boundary conditions of general engineering problems, Fourier expansion is used to transform them into algebraic sums. According to the special solution equation, the relationship between the direction eigenvalues and the angle coefficients of each order of the expansion term is found. Then the analytical solution of the non-homogeneous problem is obtained by superposing the special solutions of the expansion terms of each order. By comparing the calculation results of the boundary stress around the elliptical tunnel, it can be seen that the results are completely consistent with the finite element calculation results, which verifies the correctness and reliability of the method in this paper. This paper analyzes the influence of internal pressure, lateral pressure coefficient and elliptical shape coefficient on the circumferential stress around the elliptical hole, and obtains the following conclusions: increasing the internal pressure of the elliptical hole can effectively reduce the circumferential compressive stress at the hole edge; when the lateral pressure coefficient approaches 1, the circumferential stress distribution around the elliptical hole tends to be uniform; the minimum value of the circumferential stress around the elliptical hole is independent of the shape coefficient, while the maximum value is closely related to the shape coefficient. The research results can not only provide specific theoretical guidance for the construction and construction of elliptical tunnel, but also expand the application scope of the symplectic elasticity method.

大量的非圆形隧道在工程实践中被广泛使用。这些几何结构的应用不仅使力学问题的边界条件更加复杂，而且使理论解变得更加困难。引入曲线坐标系可以很容易地将椭圆区域转换成圆形区域，并且可以相应地调整物理关系。在状态空间中，可以通过使用哈密顿力学的对偶变量来解决变换后的问题，并且可以获得特殊的求解方程。对于一般工程问题的非均匀边界条件，使用傅立叶展开将其转换为代数和。根据特殊解方程，找到方向特征值和每个扩展项阶数的角度系数之间的关系。然后，通过叠加各阶展开项的特殊解来获得非齐次问题的解析解。通过比较椭圆隧道周围边界应力的计算结果，可以看出该结果与有限元计算结果完全吻合，验证了本文方法的正确性和可靠性。分析了内部压力，侧向压力系数和椭圆形状系数对椭圆孔周围圆周应力的影响，得出以下结论：增加椭圆孔的内压可以有效减小孔边缘的周向压应力。当侧向压力系数接近1时，椭圆孔周围的周向应力分布趋于均匀。椭圆孔周围的圆周应力的最小值与形状系数无关，而最大值与形状系数紧密相关。研究结果不仅可以为椭圆隧道的施工提供具体的理论指导，而且可以扩展辛弹性法的应用范围。椭圆孔周围的圆周应力的最小值与形状系数无关，而最大值与形状系数紧密相关。研究结果不仅可以为椭圆隧道的施工提供具体的理论指导，而且可以扩展辛弹性法的应用范围。椭圆孔周围的圆周应力的最小值与形状系数无关，而最大值与形状系数紧密相关。研究结果不仅可以为椭圆隧道的施工提供具体的理论指导，而且可以扩展辛弹性法的应用范围。