A mathematical model of suspension bridges
We prove the existence of weak T-periodic solutions for a nonlinear mathematical model associated with suspension bridges. Under further assumptions a regularity result is also given.
A mixed finite element method for plate bending with a unilateral inner obstacle
A unilateral problem of an elastic plate above a rigid interior obstacle is solved on the basis of a mixed variational inequality formulation. Using the saddle point theory and the Herrmann-Johnson scheme for a simultaneous computation of deflections and moments, an iterative procedure is proposed, each step of which consists in a linear plate problem. The existence, uniqueness and some convergence analysis is presented.
A mixed finite element method for the biharmonic problem
A mixed system of differential equations as a mathematical model of vibrations of continuum-discrete mechanical systems.
A model for passive damping of a membrane
A model of neck formation on a rod under tension.
A model problem for boundary layers of thin elastic shells
A model problem for boundary layers of thin elastic shells
We consider a model problem (with constant coefficients and simplified geometry) for the boundary layer phenomena which appear in thin shell theory as the relative thickness ε of the shell tends to zero. For ε = 0 our problem is parabolic, then it is a model of developpable surfaces. Boundary layers along and across the characteristic have very different structure. It also appears internal layers associated with propagations of singularities along the characteristics. The special structure of...
A mountain pass method for the numerical solution of semilinear wave equations.
A Multigrid Method for a Parameter Dependent Problem in Solid Mechanics.
A multigrid method for Reissner-Mindlin plates.
A new approach for estimating the friction in thin film lubrication.
A new approach of Timoshenko's beam theory by asymptotic expansion method
A new mixed finite element method for the Timoshenko beam problem
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 model for inextensible rods as a low energy Γ-limit of three-dimensional nonlinear elasticity
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 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...