Photoelastic plates made of an orthotropic material are used to model the dynamic stress state near free and reinforced circular holes under blast loading. The diffraction of stress waves by holes in a thin-walled plate is studied. Experimental data are used to analyze the dynamic stress concentration in a plate with a hole in which quasilongitudinal and quasitransverse waves propagate Keywords: dynamic photoelasticity, orthotropic plate, blast loading, free and reinforced circular holes, dynamic stress concentration Introduction. The stress concentration near holes of different shapes induced by longitudinal waves of different durations was studied in [12,14,15] using the photoelastic method. In some experiments, the effect of a transverse wave on the hole was also taken into account, but the experiment parameters were such that the stress state around it was determined by both transverse and longitudinal waves. The diffraction of transverse waves by a circular hole was experimentally studied only in [5], which is due to the difficulty of obtaining a pure S-wave. The diffraction of elastic waves in multiply connected bodies is addressed in [2]; and some dynamic problems for structural members are solved in [3,10].Data on the distribution of dynamic stresses around a mine working in a rock mass are of importance for the strength analysis of underground structures subject to blast loads [7,11,13]. Different waves superimposed at the obstacle produce a complicated stress pattern varying in space and time, which gives rise to certain difficulties in solving linear stationary diffraction problems for waves in isotropic and reinforced multiply connected bodies [7,11,13]. To study wave stress fields in bodies of complex geometry, both a general approach and an efficient practical procedure are needed. Note that in modeling a rock mass with a mine working, natural anisotropy should be taken into account [1].The present paper analyzes the dynamic stress concentration around free and reinforced holes in thin anisotropic plates in which plane quasilongitudinal and quasitransverse waves propagate. The wave stress field near the boundary of an anisotropic plate subject to an impulsive load is studied in [6].1. Problem Formulation and Experiment Description. Consider a thin rectangular plate with a circular hole free or reinforced with a ring of certain shape. The plate is made of an orthotropic material with given mechanical characteristics and is subjected to a blast load that generates plane quasilongitudinal P-wave and plane quasitransverse S-wave (Fig. 1); p and q are the principal axes of orthotropy. Considering the available developments and results [5,[16][17][18][19][20], we will study the diffraction of these stress waves by the hole.We used the dynamic photoelastic method [8] to test model plates ( Fig. 1) with the following dimensions (in mm): à = 300, b = 120, h = 3, c 1 90 = , c 2 110 = , where a, b, and h are the length, width, and thickness of the plates; ñ i (³ = 1, 2) is the distance from the center of the h...
The stress wave field around a tunnel in an anisotropic medium subject to shock load is analyzed using the dynamic photoelastic method. The influence of various factors on the distribution and magnitude of boundary stresses around the tunnel are studied by simulating the deformation process. The time dependence of the dynamic stress concentration factor on the tunnel walls is established Introduction. Simulation of refraction, reflection, and scattering of nonstationary waves by rock surfaces with different mechanical properties is especially important for the dynamic analysis of underground structures subject to seismic and blast waves.The photoelastic method was used in [4,5,7] to analyze the dynamic stress concentration around free circular holes in isotropic thin plates and anisotropic rock masses induced by longitudinal waves of different lengths. The blast source is assumed to be at a significant distance from the plate edges; hence, a longitudinal (Ð) wave alone is incident on the hole during diffraction. However, if a rock mass is modeled by a linear elastic medium (as usually done in designing ground support to withstand main types of load) [1] and waves propagate in the cross-sectional plane of a structure, then it is possible to use two-dimensional dynamic contact solutions of elasticity describing the stress concentration around free and reinforced holes of various shapes. Note that the currently available solutions can only be applied to a circular hole in an isotropic medium. If the hole is not circular and the medium is anisotropic, finding such solutions involves severe difficulties [8][9][10][11].1. Problem Formulation. We will use photoelastic models to study the dynamic stress state induced by blast waves around tunnels in an anisotropic rock mass near sloping free surface. The models are plates with the following geometry ( Fig. 1): à = 250 mm, b = 200 mm; h = 3 mm, d = 35 mm, f = 40 mm; and ñ 1 = 105, ñ 2 = 93, ñ 3 = 40 mm (Fig. 1). The plates are made of an optically sensitive orthotropic material with the following characteristics: Å 1 = 7.10⋅10 3 ÌPà, Å 2 = 4.73⋅10 3 ÌPà, ν 12 = 0.26, ν 21 = 0.16, G = 1.51⋅10 3 ÌPà, σ d 90 = 4.89 ÌPà⋅cm/fringe, σ d 0 = 2.81 ÌPà⋅cm/fringe, σ d 45 = 3.69 ÌPà⋅cm/fringe; ε d =
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