Design of tension structures and shells using the Airy stress function

Discontinuities in the Airy stress function for in-plane stress analysis represent forces and moments in connected one-dimensional elements. We expand this representation to curved membrane-action structures, such as shells and cable nets, and graphically visualise the internal stresses and section forces at the boundary necessary for equilibrium. The approach enhances understanding of the interplay between form and forces and can support design decisions related to form-finding and force efficiency. As illustrative examples, the prestressing needed for three existing cable nets is determined, and its influence on the edge-beam bending moment is explored.

Membrane Action of Cladding Subjected to Blast Loading and Effects on the Supporting Structure

A recent blast design trend is to properly select cladding characteristics in order to limit blast consequences on its supporting structure. In this context, it is worth noting that cladding components may exhibit significant membrane action, and its effects may be decisive for the supporting structure. The main focus of the present study was to examine these effects through two-step dimensionless SDOF analyses, aimed at reaching conclusions that would be applicable to a large variety of cladding/supporting structure arrangements. The results of these analyses are presented by employing the dynamic load factor, representing the maximum supporting structure displacement. It was found that cladding membrane action has adverse effects over its supporting structure, as it does not allow for extensive plastic dissipation and leads to higher support reactions. On the contrary, insignificant membrane action leads to lower dynamic load factor for the supporting structure. Thus, membrane behavior should be activated only as a safety backup action in order to prevent cladding failure. A case study of a typical cladding/supporting structure is presented to demonstrate and verify the proposed two-step SDOF analyses and the obtained results.

The exponential tracking and disturbance rejection of the propagated membrane action potential with conductance coefficient feedforward controllers

In the early 1950's, using their experimental data, Hodgkin and Huxley constructed the sodium and potassium conductance feedback controllers for their mathematical model of the flow of electric current through the surface membrane of a giant nerve fibre. In this paper, we re-formulate the construction as a problem of exponential tracking and disturbance rejection and then re-construct new conductance feedforward controllers in the more complicated case of a propagated action potential. The dynamics of the potential is governed by the Hodgkin-Huxley's partial differential equation (PDE) model. The problem is solved for any current disturbances and potential references and conductance coefficient feedforward controllers are designed by using the method of variable transform. It is proved that, under the designed feedforward controllers, the potential tracks exponentially a desired potential reference uniformly on an interval of one unit and the reference satisfies the controlled PDE model except an initial condition. A numerical example shows that the simulated action potential and sodium and potassium conductances are close to the experimental observations.

The exponential tracking and disturbance rejection of the propagated membrane action potential with conductance coefficient feedforward controllers

In the early 1950's, using their experimental data, Hodgkin and Huxley constructed the sodium and potassium conductance feedback controllers for their mathematical model of the flow of electric current through the surface membrane of a giant nerve fibre. In this paper, we re-formulate the construction as a problem of exponential tracking and disturbance rejection and then re-construct new conductance feedforward controllers in the more complicated case of a propagated action potential. The dynamics of the potential is governed by the Hodgkin-Huxley's partial differential equation (PDE) model. The problem is solved for any current disturbances and potential references and conductance coefficient feedforward controllers are designed by using the method of variable transform. It is proved that, under the designed feedforward controllers, the potential tracks exponentially a desired potential reference uniformly on an interval of one unit and the reference satisfies the controlled PDE model except an initial condition. A numerical example shows that the simulated action potential and sodium and potassium conductances are close to the experimental observations.