Diffraction of stress waves by a free or reinforced hole in an orthotropic plate

Abstract

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...

Stress state around cracks on the boundary of a hole in a photoelastic orthotropic plate under creep

“…The major results in the field have been obtained in the static case. Solutions to dynamic problems for anisotropic bodies with stress concentrators obtained by the photoelastic method can be found in [12][13][14][15].…”

“…The major results in the field have been obtained in the static case. Solutions to dynamic problems for anisotropic bodies with stress concentrators obtained by the photoelastic method can be found in [12][13][14][15].We will use photoelastic measurements to study the stress distribution around cracks on the boundary of a hole in linear elastic fiber-reinforced composite plates under a tensile force normal to the cracks. Use will be made of a procedure that produces more accurate results than in [16].…”

Viscoplastic deformation of reinforced plates with varying thickness under explosive loads

“…The majority of solutions is based on a perfect rigid-plastic model [4, 10, etc.]. As a rule, such solutions are approximate, based on extreme principles of the dynamics of a rigid-plastic body [6], and describe the behavior of homogeneous isotropic plates of constant thickness, with the dependence of the yield stress on the strain rate being neglected [22][23][24][25].For the last decades, slabs reinforced with high-strength bars (fibers) have been used in engineering as effective protective elements. The study into the inelastic dynamic deformation of such structures is in its initial stage [12].…”

Behavior of rigid-plastic polygonal plates with a rigid insert under blast loads

“…Up to now, such a problem has only been solved for a circular plate with a rigid circle at the center under axisymmetric fixation and loading conditions [3]. The viscoelastic state of plates with elastic inclusions was analyzed in [4], and dynamic problems for plates with stress concentrators under a wave load were addressed in the experimental studies [17,18,20].The present paper gives a method based on the perfect rigid-plastic body model to calculate arbitrarily fixed polygonal plates with a perfectly rigid insert subjected to short-term intensive dynamic loads and resting on a resisting viscoelastic foundation. The method can widely be used for engineering calculations.…”

“…Up to now, such a problem has only been solved for a circular plate with a rigid circle at the center under axisymmetric fixation and loading conditions [3]. The viscoelastic state of plates with elastic inclusions was analyzed in [4], and dynamic problems for plates with stress concentrators under a wave load were addressed in the experimental studies [17,18,20].…”