Boundary layer resolution in hierarchical models of laminated composites
Boundary value problems in (1.0) approximation of a mathematical model of bars.
Buckling of anisotropic shells. I
The formulation of differential equations of buckling problem of anisotropic cylindrical shell is presented here. The solution for anisotropic cylindrical shells without shear load in case of two way compression is found out from the differential equations formulated. The corresponding results for isotropic case are deduced as a particular case.
Buckling of anisotropic shells. II
The object of this paper is to find the solution of the differential equation of the buckling problem of anisotropic cylindrical shells with shear load in case of torsion of a long tube. The critical values of the shear load and the total torque are also found. The corresponding results for the isotropic case are deduced as a special case.
Buckling of beam-column problem of anisotropic cylindrical shells
The object of this paper is to formulate the differential equations in the beamcolumn problem of the buckling of anisotropic cylindrical shells, placed between the plates of a testing machine subject to an axial load and a radial load of sufficient magnitude to bring the expansion without constraint of the edges produced by to zero deflection. The solution is obtained with necessary boundary conditions and the corresponding results for the isotropic case are deduced.
Characterization and representation of the lower semicontinuous envelope of the elastica functional
Comparaison entre les modèles tridimensionnels et bidimensionnels de plaques en élasticité
Comportement d'une plaque élastique dont une petite région est rigide et animée d'un mouvement vibratoire. Étude asymptotique de la matrice d'impédance
Computation of displacements for nonlinear elastic beam models using monotone iterations.
Computation of Green's matrices for boundary value problems associated with a pair of mixed linear regular ordinary differential operators.
Conditions for periodic vibrations in a symmetric n-string
A symmetric N-string is a network of N ≥ 2 sections of string tied together at one common mobile extremity. In their equilibrium position, the sections of string form N angles of 2π/N at their junction point. Considering the initial and boundary value problem for small-amplitude oscillations perpendicular to the plane of the N-string at rest, we obtain conditions under which the solution will be periodic with an integral period.
Conical differentiability for bone remodeling contact rod models
We prove the conical differentiability of the solution to a bone remodeling contact rod model, for given data (applied loads and rigid obstacle), with respect to small perturbations of the cross section of the rod. The proof is based on the special structure of the model, composed of a variational inequality coupled with an ordinary differential equation with respect to time. This structure enables the verification of the two following fundamental results: the polyhedricity of a modified displacement...
Conical differentiability for bone remodeling contact rod models
We prove the conical differentiability of the solution to a bone remodeling contact rod model, for given data (applied loads and rigid obstacle), with respect to small perturbations of the cross section of the rod. The proof is based on the special structure of the model, composed of a variational inequality coupled with an ordinary differential equation with respect to time. This structure enables the verification of the two following fundamental results: the polyhedricity of a modified displacement constraint...
Control in obstacle-pseudoplate problems with friction on the boundary. optimal design and problems with uncertain data
Four optimal design problems and a weight minimization problem are considered for elastic plates with small bending rigidity, resting on a unilateral elastic foundation, with inner rigid obstacles and a friction condition on a part of the boundary. The state problem is represented by a variational inequality and the design variables influence both the coefficients and the set of admissible state functions. If some input data are allowed to be uncertain a new method of reliable solutions is employed....
Control in obstacle-pseudoplate problems with friction on the boundary. approximate optimal design and worst scenario problems
In addition to the optimal design and worst scenario problems formulated in a previous paper [3], approximate optimization problems are introduced, making use of the finite element method. The solvability of the approximate problems is proved on the basis of a general theorem of [3]. When the mesh size tends to zero, a subsequence of any sequence of approximate solutions converges uniformly to a solution of the continuous problem.
Control of a clamped-free beam by a piezoelectric actuator
We consider a controllability problem for a beam, clamped at one boundary and free at the other boundary, with an attached piezoelectric actuator. By Hilbert Uniqueness Method (HUM) and new results on diophantine approximations, we prove that the space of exactly initial controllable data depends on the location of the actuator. We also illustrate these results with numerical simulations.
Control of networks of Euler-Bernoulli beams
Control of networks of Euler-Bernoulli beams
We consider the exact controllability problem by boundary action of hyperbolic systems of networks of Euler-Bernoulli beams. Using the multiplier method and Ingham's inequality, we give sufficient conditions insuring the exact controllability for all time. These conditions are related to the spectral behaviour of the associated operator and are sufficiently concrete in order to be able to check them on particular networks as illustrated on simple examples.
Control structure in optimization problems of bar systems
Optimal design problems in mechanics can be mathematically formulated as optimal control tasks. The minimum principle is employed in solving such problems. This principle allows us to write down optimal design problems as Multipoint Boundary Value Problems (MPBVPs). The dimension of MPBVPs is an essential restriction that decides on numerical difficulties. Optimal control theory does not give much information about the control structure, i.e., about the sequence of the forms of the right-hand sides...
Control variational method approach to bending and contact problems for Gao beam
This paper deals with a nonlinear beam model which was published by D. Y. Gao in 1996. It is considered either pure bending or a unilateral contact with elastic foundation, where the normal compliance condition is employed. Under additional assumptions on data, higher regularity of solution is proved. It enables us to transform the problem into a control variational problem. For basic types of boundary conditions, suitable transformations of the problem are derived. The control variational problem...