Duality based a posteriori error estimates for higher order variational inequalities with power growth functionals.
Duality in the obstacle and unilateral problem for the biharmonic operator
The paper presents a problem of duality for the obstacle and unilateral biharmonic problem (the equilibrium of a thin plate with an obstacle inside the domain or on the boundary). The dual variational inequality is derived by introducing polar functions.
Dynamic crack propagation between two bonded orthotropic plates.
Dynamic stability of functionally graded plate under in-plane compression.
Dynamic von Kármán equations involving nonlinear damping: Time-periodic solutions
In the paper, time-periodic solutions to dynamic von Kármán equations are investigated. Assuming that there is a damping term in the equations we are able to show the existence of at least one solution to the problem. The Faedo-Galerkin method is used together with some basic ideas concerning monotone operators on Orlicz spaces.
Effect of imperfections and damping on the type of nonlinearity of circular plates and shallow spherical shells.
Engergy decay for the quasilinear wave equation with viscosity.
Equivalent formulations of generalized von Kármán equations for circular viscoelastic plates
The paper deals with the analysis of generalized von Kármán equations which desribe stability of a thin circular viscoelastic clamped plate of constant thickness under a uniform compressible load which is applied along its edge and depends on a real parameter. The meaning of a solution of the mathematical problem is extended and various equivalent reformulations of the problem are considered. The structural pattern of the generalized von Kármán equations is analyzed from the point of view of nonlinear...
Error estimates for the Coupled Cluster method
The Coupled Cluster (CC) method is a widely used and highly successful high precision method for the solution of the stationary electronic Schrödinger equation, with its practical convergence properties being similar to that of a corresponding Galerkin (CI) scheme. This behaviour has for the discrete CC method been analyzed with respect to the discrete Galerkin solution (the “full-CI-limit”) in [Schneider, 2009]. Recently, we globalized the CC formulation to the full continuous space, giving a root...
Estimates for second order derivatives of eigenvectors in thin anisotropic plates with variable thickness.
Étude dans d’un modèle de plaques élastoplastiques comportant une non-linéarité géométrique
Exact controllability of a multilayer Rao-Nakra plate with clamped boundary conditions
Exact controllability results for a multilayer plate system are obtained from the method of Carleman estimates. The multilayer plate system is a natural multilayer generalization of a classical three-layer “sandwich plate” system due to Rao and Nakra. The multilayer version involves a number of Lamé systems for plane elasticity coupled with a scalar Kirchhoff plate equation. The plate is assumed to be either clamped or hinged and controls are assumed to be locally distributed in a neighborhood...
Exact controllability of a multilayer Rao-Nakra plate with clamped boundary conditions
Exact controllability results for a multilayer plate system are obtained from the method of Carleman estimates. The multilayer plate system is a natural multilayer generalization of a classical three-layer “sandwich plate” system due to Rao and Nakra. The multilayer version involves a number of Lamé systems for plane elasticity coupled with a scalar Kirchhoff plate equation. The plate is assumed to be either clamped or hinged and controls are assumed to be locally distributed in a neighborhood...
Exact controllability of vibrations of thin bodies.
Existence and convergence of the expansion in the asymptotic theory of elastic thin plates
Existence and uniform decay of solutions for a class of generalized plate-membrane-like systems.
Existence, uniqueness and stabilization for a nonlinear plate system with nonlinear damping
Exponential stability of a von Kármán model with thermal effects.
External approximation of first order variational problems via W-1,p estimates
Here we present an approximation method for a rather broad class of first order variational problems in spaces of piece-wise constant functions over triangulations of the base domain. The convergence of the method is based on an inequality involving norms obtained by Nečas and on the general framework of Γ-convergence theory.
Finite Dimensional Approximation of Nonlinear Problems. Part I. Branches of Nonsingular Solutions.