Scattering of anti-plane waves by scalene trapezoidal boundary with embedded cavity in anisotropic material based on mapping space

Both surface motion and hole stress concentration have always been concerned in anisotropic medium. In this paper, a theoretical approach is used to study the scattering problem of circular holes under a scalene trapezoid on the surface. The mapping function that anisotropic medium to homogeneous medium is established, and the relationship between the free boundary of anisotropic medium and the mapping of homogeneous medium boundary is proved. In the space of homogeneous medium mapping, the wave displacement function is obtained by solving the equation of motion that meets the zero-stress boundary conditions by separating the variable method and the symmetric method. Based on the complex function, multi-polar coordinate method and region-matching technique, algebraic equations are established at auxiliary boundary and free boundary conditions in complex domain. Then according to sample statistics, least square method is used instead of the Fourier expansion method to solve the undetermined coefficient of the algebraic equations by discrete boundary. Numerical results shows that the continuity of the auxiliary boundary and the accuracy of the zero-stress boundary are nice, and the displacement of the free surface and the stress of the circular hole are related to the parameters of material medium, the position of the circular hole, the direction of the incident wave and the frequency content of the excitation. Finally the process of the wave propagation and scattering around trapezoid and shallow circle are shown in time domain through the inverse fourier transform.

Modeling of stress states in intact layered rock massifs

Предложена структурная модель анизотропной среды для расчета напряженнодеформированного состояния в нетронутых массивах горных пород, которая учитывает ряд горнотехнических и горно-геологических факторов. Результаты аналитического решения позволили объяснить известные из практики натурных наблюдений факты (возможность превосходства горизонтальных напряжений над вертикальными, кусочно-линейный характер напряжений и т.д.), которые находились в противоречии с широко распространенными гипотезами о распределении напряжений в породных массивах. A structural model of an anisotropic medium is proposed for calculating the stressstrain state in intact rock massifs, which takes into account a number of mining and geological factors. The results of the analytical solution allowed us to explain the facts known from the practice of field observations (the possibility of the superiority of horizontal stresses over vertical ones, the piecewise linear nature of stresses, etc.), which were in contradiction with the widespread hypotheses about the distribution of stresses in rock massifs.

Modeling and Imaging of Ultrasonic Array Inspection of Side Drilled Holes in Layered Anisotropic Media

There has been an increase in the use of ultrasonic arrays for the detection of defects in composite structures used in the aerospace industry. The response of a defect embedded in such a medium is influenced by the inherent anisotropy of the bounding medium and the layering of the bounding medium and hence poses challenges for the interpretation of the full matrix capture (FMC) results. Modeling techniques can be used to understand and simulate the effect of the structure and the defect on the received signals. Existing modeling techniques, such as finite element methods (FEM), finite difference time domain (FDTD), and analytical solutions, are computationally inefficient or are singularly used for structures with complex geometries. In this paper, we develop a novel model based on the Gaussian-based recursive stiffness matrix approach to model the scattering from a side-drilled hole embedded in an anisotropic layered medium. The paper provides a novel method to calculate the transmission and reflection coefficients of plane waves traveling from a layered anisotropic medium into a semi-infinite anisotropic medium by combining the transfer matrix and stiffness matrix methods. The novelty of the paper is the developed model using Gaussian beams to simulate the scattering from a Side Drilled Hole (SDH) embedded in a multilayered composite laminate, which can be used in both immersion and contact setups. We describe a method to combine the scattering from defects with the model to simulate the response of a layered structure and to simulate the full matrix capture (FMC) signals that are received from an SDH embedded in a layered medium. The model-assisted correction total focusing method (MAC-TFM) imaging is used to image both the simulated and experimental results. The proposed method has been validated for both isotropic and anisotropic media by a qualitative and quantitative comparison with experimentally determined signals. The method proposed in this paper is modular, computationally inexpensive, and is in good agreement with experimentally determined signals, and it enables us to understand the effects of various parameters on the scattering of a defect embedded in a layered anisotropic medium.