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- P. DJONDJOROV
- 2008

In the present paper, a class of partial differential equations related to various plate and rod problems is studied by Lie transformation group methods. A system of equations determining the generators of the admitted point Lie groups (symmetries) is derived. A general statement of the associated groupclassification problem is given. A simple intrinsic… (More)

- Peter A. Djondjorov, Vassil M. Vassilev, Ivaïlo M. Mladenov
- Computers & Mathematics with Applications
- 2012

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)

- V Vassilev, P Djondjorov
- 2000

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)

- Ivaïlo M. Mladenov, PETER A. DJONDJOROV, +6 authors Vassil Vassilev
- 2013

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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