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نورس حيدر مصطفى أل سيد حيدر
5/4/2011 2:14:01 PM
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Elastic-Plastic Stress Waves Propagation in One-Dimensional Members Using the Method of Characteristics
H. H. Al-Da ami, A. M. Hosain and N. H. Mostafa
ABSTRACT This research deals with the elastic-plastic dynamic analysis of prismatic and non-prismatic straight members by modeling axial and flexural waves transmission along such structures, using the method of characteristics. The analysis is based on the wave propagation in one-dimensional structural element approach. Timoshenko s beam theory, which includes transverse shear deformation and rotatory inertia effects, is adopted in the analysis. It was found that the interaction between shear and bending waves causes the flexural waves to propagate in prismatic and non-prismatic members in a dispersive manner which is caused by the propagation of waves with different velocities. The dispersive phenomenon will increase when the plastic waves are propagated in these members due to the complex movement of the elastic-plastic interfaces and the changes in member’s geometry. The additional dispersion is caused by the changes in sectional and material properties along the member s length. In addition, the small deformation analysis does not give a reasonable result when high loading conditions are expected because it neglects the effect of geometrical non-linearity.INTRODUCTIONRecently, there has been a marked interest in the dynamic characteristics deformation of many engineering applications such as high-speed machinery, airplane structure, tall building…etc. The rapid expansion in the study of wave propagation was prompted, in part, by the necessity to understand the transient history of such structures that are subjected to rapidly applied loads. The beam is one of the fundamental elements of an engineering structure. It is found in the most structural applications. Moreover, structures like helicopter rotor blades, spacecraft antenna, airplane wings, high-rise building, gun barrels, robot arms and subsystems of more complex structures can be modelled as a beam-like slender member (Malatkar, 2003). Therefore, studying the dynamic response, both elastically and plastically, of this simple structural component under various loading conditions would help in understanding and explaining the behaviour of more complex structures under similar loading. The main objective of this study is to use the method of characteristics to deal with elastic-plastic dynamic analysis of one-dimensional prismatic and non-prismatic straight members, taking into account that these structures are subjected to transient loading. Where this method needs relatively small computer storage with good solution reliability. Thus, the designers can easily overcome the difficulties in the analysis when their designs are subjected to impact and earthquakes loadings. The effect of geometrical and material’s non-linearity (bilinear stress-strain relation) are considered when high loading conditions are expected. A parametric study is presented in order to determine the effect of several influencing parameters on the behaviour of vibrating beam elements.
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وصف الــ Tags لهذا الموضوع
- stress waves, elastic-plastic response, characteristics method, geometrical and material non-linearity
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