Ground Displacements due to the Deformations of Shallow Tunnels with Arbitrary Cross Sections in Soft Ground

Nowadays, a huge number of shield-driven tunnels with noncircular cross sections are constructed in urban areas all around the world. However, the ground displacements associated with tunneling still form a difficult issue, especially for noncircular tunnels. In this study, an analytical solution is derived to estimate the ground displacements induced by the deformations of shallow noncircular tunnels in soft ground. First, a solution for the stresses and displacements around a deep tunnel in a full plane is formulated by imposing a specified convergence pattern over the cavity boundary. Subsequently, this solution is validated using finite element simulations in a case study of an elliptical tunnel with four different convergence patterns. Afterward, the solution in the full plane is extended to a half plane using the virtual image technique to estimate the ground displacements around shallow tunnels. The solution is also validated using finite element simulations.

The anti-plane shear elasto-static fields near a crack terminating at an isotropic hyperelastic bi-material interface

In the framework of hyperelasticity, we treat the configuration of a terminated crack at the interface of an incompressible full plane composite. Considering the traction-free boundary conditions, three particular cases are discussed when a cylinder is subjected to an anti-plane shear transformation. Taking all these conditions into account, an asymptotic analysis is performed to identify the sufficient orders contributing to the singular form of the Cauchy stress static fields. Adding to that, an inquiry about the presence of logarithmic singularities was achieved using the approach of Dempsey and Sinclair.

Wind tunnel experiments on wind turbine wakes in yaw: Redefining the wake width

This paper presents an investigation of wakes behind model wind turbines, including cases of yaw misalignment. Two different turbines were used and their wakes are compared, isolating effects of boundary conditions and turbine specifications. Laser Doppler Anemometry was used to scan a full plane of a wake normal to the main fow direction, 6 rotor diameters downstream of the respective turbine. The wakes of both turbines are compared in terms of the time averaged main flow component, the turbulent kinetic energy and the distribution of velocity increments. The shape of the velocity increments' distributions is quantified by the shape parameter λ2. The results show that areas of strongly heavy-tailed distributed velocity increments are surrounding the velocity deficit in all cases examined. Thus, a wake is significantly wider when two-point statistics are included as opposed to a description limited to one-point quantities. As non-Gaussian distributions of velocity increments affect loads of downstream rotors, our findings impact the application of active wake steering through yaw misalignment as well as wind farm layout optimizations and should therefore be considered in future wake studies, wind farm layout and farm control approaches. Further, the velocity deficits behind both turbines are deformed to a kidney-like curled shape during yaw misalignment, for which parameterization methods are introduced. Moreover, the lateral wake deflection during yaw misalignment is investigated.

Eshelby's problem of polygonal inclusions with polynomial eigenstrains in an anisotropic magneto-electro-elastic full plane

This paper presents a closed-form solution for the arbitrary polygonal inclusion problem with polynomial eigenstrains of arbitrary order in an anisotropic magneto-electro-elastic full plane. The additional displacements or eigendisplacements, instead of the eigenstrains, are assumed to be a polynomial with general terms of order M + N . By virtue of the extended Stroh formulism, the induced fields are expressed in terms of a group of basic functions which involve boundary integrals of the inclusion domain. For the special case of polygonal inclusions, the boundary integrals are carried out explicitly, and their averages over the inclusion are also obtained. The induced fields under quadratic eigenstrains are mostly analysed in terms of figures and tables, as well as those under the linear and cubic eigenstrains. The connection between the present solution and the solution via the Green's function method is established and numerically verified. The singularity at the vertices of the arbitrary polygon is further analysed via the basic functions. The general solution and the numerical results for the constant, linear, quadratic and cubic eigenstrains presented in this paper enable us to investigate the features of the inclusion and inhomogeneity problem concerning polynomial eigenstrains in semiconductors and advanced composites, while the results can further serve as benchmarks for future analyses of Eshelby's inclusion problem.

The Generalized Two Dimensional Thermal-Electro-Elastic Solution for the Cracked-Half-Elliptical-Hole Problem in a Half Plane

The half elliptical hole with an edge crack in a thermopiezoelectric material is studied by using the complex variable method. First, the mapping function which maps the outside of the elliptical hole and the crack in the right half plane into the outside of a circular hole in a full plane is given by the method of conformal mapping. Then, the complex potential functions and the field intensity factors (FIF) are presented according to the boundary conditions, respectively. Some useful results can be found by numerical analysis: 1) The influence of the heat flux on FIF depends on the model of the crack; 2) The shape and the size of the hole possess a significant effect on the field distribution at the crack tip.

Electromagnetic diffraction and scattering of a complex-source beam by a semi-infinite circular cone

A complex-source beam (CSB) is used to investigate the electromagnetic scattering and diffraction by the tip of a perfectly conducting semi-infinite circular cone. The boundary value problem is defined by assigning a complex-valued source coordinate in the spherical-multipole expansion of the field due to a Hertzian dipole in the presence of the PEC circular cone. Since the incident CSB field can be interpreted as a localized plane wave illuminating the tip, the classical exact tip scattering problem can be analysed by an eigenfunction expansion without having the convergence problems in case of a full plane wave incident field. The numerical evaluation includes corresponding near- and far-fields.

Irregular Inhomogeneities in an Anisotropic Piezoelectric Plane

This paper presents an analytical solution for the Eshelby problem of polygonal inhomogeneity in an anisotropic piezoelectric plane. By virtue of the equivalent body-force concept of eigenstrain, the induced elastic and piezoelectric fields in the corresponding inclusion are first expressed in terms of the line integral along its boundary with the integrand being the Green’s functions, which is carried out analytically. The Eshelby inhomogeneity relation for the elliptical shape is then extended to the polygonal inhomogeneity, with the final induced field involving only elementary functions with small steps of iteration. Numerical solutions are compared to the results obtained from other methods, which verified the accuracy of the proposed method. Finally, the solution is applied to a triangular and a rectangular quantum wire made of InAs within the semiconductor GaAs full-plane substrate.

Mixture of Particles' Influence in Computer Simulations of a Spouted Bed

This article aims to assess the influence of the way of simulating monoparticles as just monoparticles or as a mixture of particles, the latter, unlike the first, considering the effect of particle-particle interaction. The Eulerian–Eulerian multiphase model is used in the computational simulation of fluid dynamics of spouted beds and compared with experimental data. A half column of cylindrical spouted bed with a full plane glass attached to the front open surface of the bed as the transparent window was used for observation and photographing. Images of solid flows were recorded using a high speed camera (2000 frames per second). Glass beads with a diameter of 0.00368, 0.005 and 0.00252 mm are used as bed material. The simulated characteristic fluid dynamic curves of spouted bed for 0.15 m static bed heights (Ho) were obtained with good agreement with experimental data when the monoparticles was simulated as a mixture of particles with mixture’s percentage of 50%. The same occurred for the simulation of vertical velocities of particles profile, that is, when the monoparticles was simulated as a mixture of particles with mixture’s percentage of 50% we observed a more approach to the experimental data. It was also observed that the air concentration distribution seem to be independent of the changing of the composition.

Analytical Solution for the Stress Field of Eshelby’s Inclusion of Polygonal Shape

Recently, we developed a closed-form solution to the stress field due to a point eigenstrain in an elastic full plane. This solution can be employed as a Green’s function to compute the stress field caused by an arbitrary-shaped Eshelby’s inclusion subjected to any distributed eigenstrain. In this study, analytical expressions are derived when uniform eigenstrain is distributed in a planar inclusion bounded by line elements. Here it is demonstrated that both the interior and exterior stress fields of a polygonal inclusion subjected to uniform eigenstrain can be represented in a unified expression, which consists of only elementary functions. Singular stress components are identified at all the vertices of the polygon. These distinctive properties contrast to the well-known Eshelby’s solution for an elliptical inclusion, where the interior stress field is uniform but the formulae for the exterior field are remarkably complicated. The elementary solution of a polygonal inclusion has valuable application in the numerical implementation of the equivalent inclusion method.