Using Refined Theory to Studied Elastic Wave Scattering and Dynamic Stress Concentrations in Plates with Two Cutouts

In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.

Dynamic stress concentrations in thick plates with two holes based on refined theory

Based on complex variables and conformal mapping, the elastic wave scat- tering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonM function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concen- tration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese.

Dynamic Mechanical Characteristics and Damage Evolution Model of Granite

By using the technique of the split Hopkinson pressure bar（ SHPB）,impact tests at different stress wavelengths（ 0. 8-2. 0 m） and strain rates（ 20-120 s^（-1）） were conducted to study the dynamic mechanical properties and damage accumulation evolution lawof granite. Test results showthat the dynamic compressive strength and strain rate of granite have a significantly exponential correlation;the relationship between peak strain and strain rate is approximately linear,and the increase of wavelengths generally makes the level of peak strain uplift. The multiple-impacts test at a lowstrain rate indicates that at the same wavelength,the cumulative damage of granite shows an exponential increasing form with the increase of strain rate; when keeping the increase of strain rate constant and increasing the stress wavelength,the damage accumulation effect of granite is intensified and still shows an exponential increasing form; under the effect of multiple impacts,the damage development trend of granite is similar overall,but the increase rate is accelerating. Therefore the damage evolution model was established on the basis of the exponential function while the physical meaning of parameters in the model was determined. The model can reflect the effect of the wave parameters and multiple impacts. The validity of the model and the physical meaning of the parameters were verified by the test,which further offer a reference for correlational research and engineering application for the granite.

Influence of the connecting condition on the dynamic buckling of longitudinal impact for an elastic rod

The stress wave propagation law and dynamic buckling critical velocity are formulated and solved by considering a general axial connecting boundary for a slender elastic straight rod impacted by a rigid body. The influence of connecting stiffness on the critical velocity is investigated with varied impactor mass and buckling time. The influences of rod length and rod mass on the critical velocity are also discussed. It is found that greater connecting stiffness leads to larger stress amplitude, and further results in lower critical velocity. It is particularly noteworthy that when the connecting stiffness is less than a certain value, dynamic buckling only occurs before stress wave reflects off the connecting end. It is also shown that longer rod with larger slenderness ratio is easier to buckle, and the critical velocity for a larger-mass rod is higher than that for a lighter rod with the same geometry.