Peter A. Djondjorov

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This study is concerned with the determination of the mechanical behaviour of closed fluid lipid bilayer membranes (vesicles) under a uniform hydrostatic pressure, pressed against and adhering onto a flat homogeneous rigid substrate. Assuming that the initial and deformed shapes of the vesicle are axisymmetric, a variational statement of the problem is(More)
Recent results concerning the application of Lie transformation group methods to structural mechanics are presented. Focus is placed on the point Lie symmetries and conservation laws inherent to the Bernoulli–Euler and Timoshenko beam theories as well as to the Marguerrevon Kármán equations describing the large deflection of thin elastic shallow shells(More)
The present study is concerned with thin isotropic shallow shells interacting with inviscid fluid flow of constant velocity. It is assumed that the dynamic behaviour of the shells is governed by the Marguerre–von Kármán equations. The influence of the fluid flow is taken into account by introducing additional differential and external load terms in the(More)
where ∆ is the Laplace operator with respect to x and x, D = Eh/12(1 − ν) is the bending rigidity, E is Young’s modulus, ν is Poisson’s ratio, h is the thickness of the plate, ρ is the mass per unit area of the plate middle-plane, δ is the Kronecker delta symbol and ε is the alternating symbol. Here and throughout the work: Greek (Latin) indices range over(More)
The consideration of some non-standard parametric Lagrangian leads to a fictitious dynamical system which turns out to be equivalent to the Euler problem for finding out all possible shapes of the lamina. Integrating the respective differential equations one arrives at novel explicit parameterizations of the Euler’s elastica curves. The geometry of the(More)
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