Although wings of insects show a large variation in morphology, they are all made from a network of irregular veins interconnected through membranous areas. Depending on their shape, size, and position, wing veins are usually divided into three different groups: longitudinal veins, cross-veins and ambient veins. The veins together with the membrane and some other elements such as spines, nodus and pterostigma can be considered as the wing’s “constructional elements”. In spite of rather extensive literature on dragonfly wing structure, the role of each of these elements in determining the wing’s function remains mostly unknown. As this question is difficult to answer in vivo using biomechanical experiments on actual wings, this study was undertaken to reveal the effects of the constructional elements on the mechanical behaviour of dragonfly wings by applying numerical simulations. An image processing technique was used to develop 12 finite element models of the insect wings with different constructional elements. The mechanical behaviour of these models was then simulated under normal and shear stresses due to tension, bending and torsion. A free vibration analysis was also performed to determine the resonant frequencies and the mode shapes of the models. For the first time, a quantitative comparison was carried out between the mechanical effects selectively caused by different elements. Our results suggest that the complex interactions of veins, membranes and corrugations may considerably affect the dynamic deformation of the insect wings during flight
This paper studies the dynamic plastic response of thin quadrangular mild steel plates subjected to uniform and localized impulsive loading. For this, two new dimensionless numbers based on dimensionless governing equation of plates have been suggested. Four different effective parameters such as plate geometry, inertia of applied load, mechanical properties of material and strain rate sensitivity have been considered in suggested dimensionless numbers. The unknown coefficients of these numbers have been calculated by using singular value decomposition method. In order to illustrate the ability of empirical constitutive equations for predicting the maximum deflection, these equations are compared with different sets of experimental results that have been performed by various researchers. The comparison between the results of present empirical equations and the other theoretical and experimental ones shows that these models are more accurate than the other ones and are suitable to use for predicting the maximum deflection of all quadrangular mild steel plates subjected to uniform and localized loading.
This study introduces an empirical analysis approach to assess mechanical behavior of thin circular mild steel plates subjected to uniform and localized impulsive loading. The empirical models have been derived by singular values decomposition procedure to predict midpoint deflection of circular plates. The essence of empirical analysis is based on dimensionless numbers. For this, Jones’s dimensionless number λ is considered as a dimensionless number for both uniform and localized loading. This number has some features such as considering plate geometries, mechanical properties of material, and loading conditions. The well-known Cowper–Symonds constitutive equation has been used to investigate the potential influence of material strain rate sensitivity where the constant parameters in this equation are considered as a function of plate thickness. In localized impulsive loading, two other dimensionless numbers are appended to investigate the effects of changing load ratio and standoff distance. The results of empirical models are compared to the other experimental and theoretical studies which have been performed by different researchers. Also, the obtained results show that the presented models have much less root mean square error than the other ones. Hence, these models are suitable to predict midpoint deflection of thin circular plates subjected to both uniform and localized impulsive loading.
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