A nonexistence test for biharmonic Green's functions of clamped bodies.
A nonlinear boundary value problem associated with the static equilibrium of an elastic beam supported by sliding clamps.
A nonlinear evolution inclusion in perfect plasticity with friction.
A nonlinear model for inextensible rods as a low energy Γ-limit of three-dimensional nonlinear elasticity
A nonlinear model of a regenerative vibrating machine tool.
A nonlinear model of a turbine blade by asymptotic analysis
In this paper we obtain a limit model for a turbine blade fixed to a 3D solid. This model is a three-dimensional linear elasticity problem in the 3D part of the piece (the rotor) and a two-dimensional problem (the nonlinear shallow shell equations) in the 2D part (the turbine blade), with junction conditions in the part of the turbine blade fixed to the rotor. To obtain this model, we perform an asymptotic analysis, starting with the nonlinear three-dimensional elasticity equations on all the pieces...
A nonlinear plate control without linearization
In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as...
A nonlocal parabolic system with application to a thermoelastic problem.
A Note on Billiard Systems in Finsler Plane with Elliptic Indicatrices
A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry
We prove that the critical points of the 3d nonlinear elasticity functional on shells of small thickness h and around the mid-surface S of arbitrary geometry, converge as h → 0 to the critical points of the von Kármán functional on S, recently proposed in [Lewicka et al., Ann. Scuola Norm. Sup. Pisa Cl. Sci. (to appear)]. This result extends the statement in [Müller and Pakzad, Comm. Part. Differ. Equ.33 (2008) 1018–1032], derived for the case of plates when . The convergence holds provided...
A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry
We prove that the critical points of the 3d nonlinear elasticity functional on shells of small thickness h and around the mid-surface S of arbitrary geometry, converge as h → 0 to the critical points of the von Kármán functional on S, recently proposed in [Lewicka et al., Ann. Scuola Norm. Sup. Pisa Cl. Sci. (to appear)]. This result extends the statement in [Müller and Pakzad, Comm. Part. Differ. Equ.33 (2008) 1018–1032], derived for the case of plates when . The convergence holds provided...
A note on prestressed thermoelastic bodies.
This note is concerned with the ill-posed problem for prestressed thermoelastic bodies. Under suitable hypotheses for the thermoelastic coefficients, the domain and the behavior of solutions at infinity, we prove uniqueness of the solutions. We also obtain some estimates for the solutions related with the initial condition.
A note on resonant frequencies for a system of elastic wave equations.
A note on the Danilovskaia's problem.
A note on the quasi-static problem of periodic linearized thermoviscoelasticity
A note on weak approximation of minors
A Numerical Method for Detecting Singular Minimizers.
A numerical method for detecting singular minimizers of multidimensional problems in nonlinear elasticity.
A numerical method for preserving curve edges in nonlinear anisotropic smoothing.
A numerical method for the solution of plane crack problems in finite media.