# Transient Response of Dynamic Stress Concentration around a Circular Opening: Incident SH Wave
## 1 Introduction
The experimental model and numerical model established by then have a certain practicability for a thermal stress analysis of functionally graded plates. [PERSON] et al. [11] investigated dynamic stress concentration in an infinite exponential-graded material with two openings using complex variable and conformal mapping methods combined with local coordinates and elastic wave scattering. [PERSON] et al. [12] investigated the effect of porosity distribution on the nonlinear free vibration and transient analysis of a porous functionally graded skew plate with multiple holes. They adopted a modified power law equation to describe the effective material properties of the porous functionally graded skew plate and applied the first-order shear deformation theory and [PERSON]'s nonlinear strain-displacement relationship to derive a nonlinear finite element calculation formula for the overall porous functionally graded skew plate. The research mentioned above primarily focuses on cases involving infinite planes and circular apertures, while studying non-circular apertures and semi-infinite planes is more practical. [PERSON] et al. [13] evaluated stress concentration near an eccentric elliptical opening with a penetrable interface crack tip in a piezoelectric material under anti-plane shear loading. They utilized methods such as Green's function and conformal mapping methods to solve the boundary condition problem and analyze the stress concentration near the crack tip. This study provides valuable insights into the behavior of piezoelectric materials under shear loading conditions and the effects of crack geometry on stress concentration. [PERSON] et al. [14] investigated the influence of different geometric and physical parameters on the dynamic stress intensity factor at the crack tip using methods such as Green's function, complex variables, and multipolar coordinates. They conducted theoretical research on the dynamic debonding of cylindrical inclusions near the interface of a semi-infinite piezoelectric material. [PERSON] et al. [15] applied the method of complex variables and multipolar coordinate systems to study the dynamic stress concentration coefficient (DSCC) around a cylindrical cavity in a vertically non-uniform half-space. Their study considered a density variation in the half-space while the shear modulus remained constant. [PERSON] et al. [16] studied the dynamic response of shallow circular inclusions in a radially non-uniform half-space under SH wave incidence. They considered that the mass density of the half-space varies with the radii, and the governing equation can be expressed as a variable-coefficient Helmholtz equation. It can be observed that methods such as complex variables, Green's function, and multipolar coordinates play a significant role in the study of non-circular apertures. Although significant research achievements have been made in stress concentration around openings, most of the studies found in the existing literature focuses on the steady-state response of dynamic stress [3; 4; 5; 6; 7; 8; 9; 10; 11; 17; 18]. Currently, few studies provide analytical solutions for the transient response of materials with openings. [PERSON] et al. [19; 20] developed a direct time-domain boundary element method for half-planes, which was successfully applied to analyze the transient response of arbitrarily shaped lined tunnels on the ground surface. This model is simple and highly accurate through an analysis and comparison of the existing literature and then applied to alluvial valleys of arbitrary shape propagated by obliquely incident plane SH waves. [PERSON] and [PERSON] [21] theoretically analyzed the propagation of transient waves in the piezoelectric and magnetic half-space under the action of dynamic anti-plane concentrated linear forces, and obtained explicit closed solutions of transverse displacement, shearing stress, magnetic potential, and induction via Laplace transform and Cagniard de-Hoop method. Experimentally, [PERSON] et al.