The Equation of Motion of a Chain.
The existence of a solution and a numerical method for the Timoshenko nonlinear wave system
The initial boundary value problem for a beam is considered in the Timoshenko model. Assuming the analyticity of the initial conditions, it is proved that the problem is solvable throughout the time interval. After that, a numerical algorithm, consisting of three steps, is constructed. The solution is approximated with respect to the spatial and time variables using the Galerkin method and a Crank–Nicholson type scheme. The system of equations obtained by discretization is solved by a version of...
The existence of a solution and a numerical method for the Timoshenko nonlinear wave system
The initial boundary value problem for a beam is considered in the Timoshenko model. Assuming the analyticity of the initial conditions, it is proved that the problem is solvable throughout the time interval. After that, a numerical algorithm, consisting of three steps, is constructed. The solution is approximated with respect to the spatial and time variables using the Galerkin method and a Crank–Nicholson type scheme. The system of equations obtained by discretization is solved by a version...
The exponential stability of a coupled hyperbolic/parabolic system arising in structural acoustics.
The extended adjoint method
Searching for the optimal partitioning of a domain leads to the use of the adjoint method in topological asymptotic expansions to know the influence of a domain perturbation on a cost function. Our approach works by restricting to local subproblems containing the perturbation and outperforms the adjoint method by providing approximations of higher order. It is a universal tool, easily adapted to different kinds of real problems and does not need the fundamental solution of the problem; furthermore...
The extended adjoint method
Searching for the optimal partitioning of a domain leads to the use of the adjoint method in topological asymptotic expansions to know the influence of a domain perturbation on a cost function. Our approach works by restricting to local subproblems containing the perturbation and outperforms the adjoint method by providing approximations of higher order. It is a universal tool, easily adapted to different kinds of real problems and does not need...
The Fourier method in three-dimensional boundary-contact dynamic problems of elasticity.
The fundamental solution for a consistent complex model of the shallow shell equations.
The global solubility of problems of nonlinear vibrations of plates on nonlinear foundations.
The version of the finite element method with quasiuniform meshes
The h-p Version of the Finite Element Method for Elliptic Equations of Order 2m.
The impact of uncertain parameters on ratchetting trends in hypoplasticity
Perturbed parameters are considered in a hypoplastic model of granular materials. For fixed parameters, the model response to a periodic stress loading and unloading converges to a limit state of strain. The focus of this contribution is the assessment of the change in the limit strain caused by varying model parameters.
The Indicatrix Method in Free Boundary Problems.
The inf-sup condition and error estimates for the Arnold-Falk plate bending element.
The interface crack with Coulomb friction between two bonded dissimilar elastic media
We study a model of interfacial crack between two bonded dissimilar linearized elastic media. The Coulomb friction law and non-penetration condition are assumed to hold on the whole crack surface. We define a weak formulation of the problem in the primal form and get the equivalent primal-dual formulation. Then we state the existence theorem of the solution. Further, by means of Goursat-Kolosov-Muskhelishvili stress functions we derive convergent expansions of the solution near the crack tip.
The kinematic and dynamic properties of seismic waves in the neighbourhood of caustics
The Korn inequality for Jones domains.
The large deformation of nonlinearly elastic shells in axisymmetric flows
The Laws Of Conservation Of One Dimensional Motion Of Nonlinear Continuum
The laws of conservation of one dimensional motion of nonlinear continuum.