Articles written in Sadhana

    • A simplified approach to solve quasi-statically moving load problems of elastica using end loaded elastica solution


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      Elastica problems with non-conservative moving forces are more complicated as compared to end loaded elastica problems. Established methods exist to solve an end loaded elastica problem. For solving a moving boundary problem, such methods need considerable modification or re-formulation. In this article,results of an end loaded elastica problem which is readily obtainable are used to solve two relatively involved moving boundary cases. The solution methodology involves a unique normalization procedure for the available elastic solution followed by few simple steps. One of the problems considered is three point bending of elastica with finite roller dimension. The other one being cantilever elastica under the action of wedge contact. Structural stiffening is observed in both the cases as a result of moving boundary condition as compared to when roller dimension is negligible or wedge makes only point contact. A structured approach may potentially originate from this kind of procedure to tackle more complicated moving boundary problems of elastica.

    • On numerical moment-curvature relationship of a beam


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      In complex bending problems involving material and geometric non-linearity, quite often moment curvature based approach is preferred over stress-strain based methods. For such an approach, available uniaxial stress-strain test data or models are required to be converted into moment-curvature relationship. The process of con-version of uniaxial stress-strain relationship into a moment-curvature relationship is non-unique. And hence, complete moment-curvature law can be modelled suiting any of the several hardening laws. Such modelling will be very important when abeam is under cyclic load producing reverse plastic deformation. In this paper, an approach is presented to obtain a unique moment-curvature relationship from any given stress-strain law. Standard elasto-plastic models viz.elastic-perfectly plastic, isotropic and kinematic hardening are considered to produce corresponding unique moment-curvature relationships. The results indicate that an isotropic curvature hardening model, corresponding to an elastic perfectly plastic stress-strain model, would be erroneous. Additionally, step by step procedure of using the approach in solving a large deflection elasto-plastic beam problem, is demonstrated here.

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