On the existence of infinitely many periodic solutions for an equation of a rectangular thin plate
On the flexural and extensional thermoelastic waves in orthotropic plates with two thermal relaxation times.
On the minimum of the work of interaction forces between a pseudoplate and a rigid obstacle
An optimization problem for the unilateral contact between a pseudoplate and a rigid obstacle is considered. The variable thickness of the pseudoplate plays the role of a control variable. The cost functional is a regular functional only in the smooth case. The existence of an optimal thickness is verified. The penalized optimal control problem is considered in the general case.
On the nonlinear behaviour of bimodular multilayer ed plates.
In an earlier study [16] the nonlinear behaviour of unimodular laminated plates was studied. This paper, following the previous study, concerns a large deflection analysis of moderately thick rectangular plates having arbitrary boundary conditions and finite thickness shear moduli. The plates are manufactured in bimodular materials and constructed in a cross-ply fashion or in a single layer with arbitrary fibre direction angle. Numerical results are obtained by a finite element technique in which...
On the Numerical Analysis of the Von Karman Equations : Mixed Finite Element Approximation and Continuation Techniques.
On the numerical solution of plate bending problems by hybrid methods
On the optimal control problem governed by the equations of von Kármán. I. The homogeneous Dirichlet boundary conditions
A control of the system of nonlinear Kármán's equations for a thin elastic plate with clamped edge is considered. The transversal loading plays the role of the control variable. The set of admissible controls is chosen in a way guaranteeing the unique solvability of the state function with respect to the control variable is proved. A disscussion of uniqueness of the optimal control and some necessary conditions of optimality are presented.
On the optimal control problem governed by the equations of von Kármán. II. Mixed boundary conditions
A control of the system of Kármán's equations for a thin elastic plate is considered. Existence of an optimal transversal load and optimal stress function, respectively, is proven. The set of admissible functions is chosen in a way guaranteeing the unique solvability of the state problem. The differentiability of the state function with respect to the control variable, uniqueness of the optimal control and some necessary conditions of optimality are discussed.
On the optimal control problem governed by the equations of von Kármán. III. The case of an arbitrary large perpendicular load
We shall deal with an optimal control problem for the deffection of a thin elastic plate. We consider the perpendicular load on the plate as the control variable. In contrast to the papers [1], [2], arbitrarily large loads are edmitted. As the unicity of a solution of the state equation is not guaranteed, we consider the cost functional defined on the set of admissible controls and states, and the state equation plays the role of the constraint. The existence of an optimal couple (i.e., control...
On the solution of a finite element approximation of a linear obstacle plate problem
In this paper the solution of a finite element approximation of a linear obstacle plate problem is investigated. A simple version of an interior point method and a block pivoting algorithm have been proposed for the solution of this problem. Special purpose implementations of these procedures are included and have been used in the solution of a set of test problems. The results of these experiences indicate that these procedures are quite efficient to deal with these instances and compare favourably...
On the solution of a generalized system of von Kármán equations
A nonlinear system of equations generalizing von Kármán equations is studied. The existence of a solution is proved and the relation between the solutions of the considered system and the solutions of von Kármán system is studied. The system considered is derived in a former paper by Lepig under the assumption of a nonlinear relation between the intensity of stresses and deformations in the constitutive law.
On the solution of a plate with ribs
On the solution of boundary value problems for sandwich plates
A mathematical model of the equilibrium problem of elastic sandwich plates is established. Using the theory of inequalities of Korn's type for a general class of elliptic systems the existence and uniqueness of a variational solution is proved.
On the solution of one problem of the plate with ribs
In the present paper the convergence of the finite element method to the solution of the problem of a plate with ribs which are stiff against torsion in the sense of Vlasov is studied. According to the conclusions of a paper by the author and J. Haslinger it suffices to prove a density theorem (Theorem 2.1).
On the stationary vibrations of a rectangular plate subjected to stress prescribed partially at the circumference.
Operator of thin plate reinforced with thin-walled ribs
Optimal control for elasto-orthotropic plate
Optimal control problems for variational inequalities with controls in coefficients and in unilateral constraints
We deal with an optimal control problem for variational inequalities, where the monotone operators as well as the convex sets of possible states depend on the control parameter. The existence theorem for the optimal control will be applied to the optimal design problems for an elasto-plastic beam and an elastic plate, where a variable thickness appears as a control variable.
Optimal design of laminated plate with obstacle
The aim of the present paper is to study problems of optimal design in mechanics, whose variational form is given by inequalities expressing the principle of virtual power in its inequality form. The elliptic, linear symmetric operators as well as convex sets of possible states depend on the control parameter. The existence theorem for the optimal control is applied to design problems for an elastic laminated plate whose variable thickness appears as a control variable.