On the Dynamic Response of Rigid-Plastic Beams

Abstract

The stability of the motion of a simply supported rigid-plastic beam subjected to an initial velocity distribution is discussed for the case of the second modal response. This problem is solved with the aid of the method of quasimode form solutions. It is shown that the second mode is unstable and the response of the beam tends toward the fundamental mode form solution. Nevertheless, when the real initial velocity field does not differ much from the velocity distribution corresponding to the second mode, this mode form solution gives a good approximation for permanent deflections.     

Solving fractional integral equations by the Haar wavelet method

Haar wavelets for the solution of fractional integral equations are applied. Fractional Volterra and Fredholm integral equations are considered. The proposed method also is used for analysing fractional harmonic vibrations. The efficiency of the method is demonstrated by three numerical examples.     

Postcritical stage of plates buckling beyond the elastic limit

The theory of small elastoplastic deformations is used to construct differential equations for investigating the behavior of plates in the postcritical stage. The problem of the cylindrical bending of a rectangular plate compressed in one direction is solved by way of example.Tartu State University. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 881–886, September–October, 1968.     

Optimal design of beams with minimum compliance

An optimization problem of non-linear elastic or viscous beams is discussed. To the beam an additional support is introduced whose location must be selected so as to minimize the compliance of the beam. The problem is solved with the aid of optimal control theory. Both rigid and flexible supports are considered. Some new optimization conditions, which are valid for arbitral compliance criterions, are deduced. A few illustrating examples are given.     

Intracellular Breakable and Ultrasound‐Responsive Hybrid Microsized Containers for Selective Drug Release into Cancerous Cells

This work reports an efficient and straightforward strategy to fabricate hybrid microsized containers with reduction‐sensitive and ultrasound‐responsive properties. The ultrasound and reductive sensitivity are visualized using scanning electron microscopy, with the results showing structural decomposition upon ultrasound irradiation and in the presence of reducing agent. The ultrasound‐responsive functionalities of hybrid carriers can be used as external trigger for rapid controlled release, while prolonged drug release can be achieved in the presence of reducing agent. To evaluate the potential for targeted drug delivery, hybrid microsized containers are loaded with the anticancer drug doxorubicin (Dox). Such hybrid capsules can undergo structural intracellular degradation after cellular uptake by human cervical cancer cell line (HeLa), resulting in Dox release into cancer cells. In contrast, there is no Dox release when hybrid capsules are incubated with human mesenchymal stem cells (MSCs) as an example of normal human cells. The cell viability results indicate that Dox‐loaded capsules effectively killed HeLa cells, while they have lower cytotoxicity against MSCs as an example of healthy cells. Thus, the newly developed intracellular‐ and ultrasound‐responsive microcarriers obtained via sol‐gel method and layer‐by‐layer technique provide a high therapeutic efficacy for cancer, while minimizing adverse side effect.     

Optimal design of plastic structures under impulsive and dynamic pressure loading

Optimal design of a rigid-plastic stepped beam and circular plate is considered in the first part of the paper assuming the mode form of motion. The form of optimal mode is sought for which a structure of constant volume attains a minimum of local or mean deflection. It is assumed that the constant kinetic energy Ko is attained by the structure through impulsive loading. Differences between optimal static and dynamic solutions are discussed. Non-uniqueness of modes is demonstrated and significance of stable mode motions is emphasized. In the second part of the paper, an optimal design of a rigid-plastic stepped beam loaded by a uniform pressure over a time interval 0 ? t ? t₁ is considered assuming constant beam volume and looking for a design corresponding to minimum of local deflection. The solution presented is valid for moderate dynamic pressures when mode motion occurs during consecutive time intervals and no travelling plastic hinges exist.