A comparative experimental and numerical study of the impact behaviour of carbon-fiber-reinforced thermoplastic (TP) and thermoset (TS) composites has been carried out. On the one hand, low velocity impact (LVI) tests were performed on TP and TS composites with different lay-up sequences at different energy levels, and the damage modes and microscopic damage mechanisms after impact were investigated using macroscale inspection, C-scan inspection, and X-ray-computed tomography. The comparative results show that the initial damage valve force under LVI depends not only on the material, but also on the layup sequence. The initial valve force of the P2 soft layer with lower stiffness is about 11% lower than that of the P1 quasi-isotropic layer under the same material, while the initial valve force of thermoplastic composites is about 28% lower than that of thermoset composites under the same stacking order. Under the same stacking order and impact energy level, the damage area and depth of TP composites are smaller than those of TS composites; while under the same material and impact energy level, the indentation depth of P2 plies is greater than that of P1 plies, and the damage area of P2 plies is smaller than that of P1 plies, but the change of thermoplastic composites is not as obvious as that of thermoset composites. This indicates that TP composites have a higher initial damage threshold energy and impact resistance at the same lay-up order, while increasing the lay-up ratio of the same material by 45° improves the impact resistance of the structure. In addition, a damage model based on continuum damage mechanics (CDM) was developed to predict different damage modes of thermoplastic composites during low velocity impact, and the analytical results were compared with the experimental results. At an impact energy of 4.45 J/mm, the error of the initial damage valve force is 5.26% and the error of the maximum impact force is 4.36%. The simulated impact energy and impact velocity curves agree with the experimental results, indicating that the finite element model has good reliability.

The existence of local terrain has a great influence on the scattering and diffraction of seismic waves. The wave function expansion method is a commonly used method for studying terrain effects, because it can reveal the physical process of wave scattering and verify the accuracy of numerical methods. An exact, analytical solution of two-dimensional scattering of plane SH (shear-horizontal) waves by an elliptical-arc canyon on the surface of the elastic half-space is proposed by using the wave function expansion method. The problem of transforming wave functions in multi-ellipse coordinate systems was solved by using the extra-domain Mathieu function addition theorem, and the steady-state solution of the SH wave scattering problem of elliptical-arc depression terrain was reduced to the solution of simple infinite algebra equations. The numerical results of the solution are obtained by truncating the infinite equation. The accuracy of the proposed solution is verified by comparing the results obtained when the elliptical arc-shaped depression is degraded into a semi-ellipsoidal depression or even a semi-circular depression with previous results. Complicated effects of the canyon depth-to-span ratio, elliptical axis ratio, and incident angle on ground motion are shown by the numerical results for typical cases.

Wave diffusion in the composite soil layer with the lined tunnel structure is often encountered in the field of seismic engineering. The wave function expansion method is an effective method for solving the wave diffusion problem. In this paper, the wave function expansion method is used to present a semi-analytical solution to the shear horizontal (SH) wave scattering problem of a circular lined tunnel under the covering soil layer. Considering the existence of the covering soil layer, the great arc assumption (that is, the curved boundary instead of the straight-line boundary) is used to construct the wavefield in the composite soil layer. Based on the wave field and boundary conditions, an infinite linear equation system is established by adding the application of complex variable functions. The finite term is intercepted and solved, and the accuracy of the solution is analyzed. Although truncation is inevitable, due to the Bessel function has better convergence, a smaller truncation coefficient can achieve mechanical accuracy. Based on numerical examples, the influence of SH wave incident frequency, soil parameters, and lining thickness on the dynamic stress concentration factor of lining is analyzed. Compared with the SH wave scattering problem by lining in a single medium half-space, due to the existence of the cover layer and the influence of its stiffness, the dynamic stress of the lining can be increased or inhibited. In addition, the lining thickness has obvious different effects on the dynamic stress concentration coefficient of the inner and outer walls of different materials.

It is necessary to study the problem of seismic wave scattering in composite stratum for tunnel engineering because the existence of composite strata will make the stress of tunnels more complicated during earthquakes. In this thesis, a series solution of the scattering wave field of the composite strata and lining is obtained using the complex function method. According to the stress and displacement boundary conditions between the composite stratum and the lining, a series of equations are established and are solved by means of Fourier transformation and finite term truncation, and the calculation errors are also discussed. Through programming calculations, the dynamic stress concentration factor (DSCF) of circular tunnels in the two types of composite strata, “hard‐over‐soft” and “soft‐over‐hard,” is analyzed when SH waves propagate, and certain conclusions on the scattering of SH waves that are distinguished from the case of single homogeneous layers are reached. The research in this article reveals some phenomena. For the Q345 steel lining in the calculation examples, it is found in this paper that increasing the thickness of the lining is effective to reduce the influence of the DSCF. But, for C30 concrete, increasing the thickness of the lining reduces the DSCF of the outer surface while increasing the DSCF of the inner surface.

Materials and structures in practical engineering inevitably subject to dynamic loads. Surface and internal discontinuities have signification effects on wave propagation and may cause dynamic stress concentration in the vicinity of them. Thus, it is of great significance to determine the dynamic response of materials and structures with surface and internal features under elastic waves. In this article, based on the wave function expansion method, the image method and the complex function method, an analytical solution is presented for the scattering of anti-plane (SH) waves by multiple cylindrical elastic inclusions and semi-cylindrical depressions in an elastic infinite plate. The series expressions of the displacement fields, stress fields, and dynamic stress concentration factors around the inclusion and the depression are derived. Numerical calculations show that the incident wavenumber, shear modulus of the inclusion, plate thickness, and relative position between the inclusion and the depression express great effects on the dynamic stress concentration. The theoretical solutions of this article can provide a reference for the results of numerical methods. And the findings are useful for structural design and nondestructive testing of the plate.

An analysis of the scattering of steady-state SH waves by a shallow buried unlined elliptical tunnel is presented. For the horizontal boundary, a mirror method in elliptic coordinates is proposed, which is implemented using the Mathieu function addition theorem. Taking into account the stress-free condition of the tunnel, an infinite equation system was created and solved after truncating it. The orientation of the tunnel is arbitrary, and typical calculations are performed for tunnels arranged horizontally and vertically in the long axis. The effects of depth, the ellipse’s axis ratio, and wavenumber on the dynamic stresses around the tunnel are investigated.