Shape optimization in contact problems. Approximation and numerical realization
Shape optimization in contact problems based on penalization of the state inequality
The paper deals with the approximation of optimal shape of elastic bodies, unilaterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established.
Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method
A problem of unilateral contact between an elasto-plastic body and a rigid frictionless foundation is solved within the range of the so called deformation theory of plasticity. The weak solution is defined by means of a variational inequality. Then the so called secant module (Kačanov's) iterative method is introduced, each step of which corresponds to a Signorini's problem of elastoplastics. The convergence of the method is proved on an abstract level.
Special curved elements and theitr application [Abstract of thesis]
Special exact curved finite elements
Special exact curved finite elements useful for solving contact problems of the second order in domains boundaries of which consist of a finite number of circular ares and a finite number of line segments are introduced and the interpolation estimates are proved.
Sul problema di contatto tra piastre
Si studia il problema di contatto tra due piastre sottili linearmente elastiche, incastrate al bordo, poste inizialmente a distanza e trasversalmente caricate. Si fa l'ipotesi che il contatto tra le due piastre, a deformazione avvenuta, sia privo di attrito. Il problema dell'equilibrio elastico è formulato per via variazionale in termini di lavori virtuali o, equivalentemente, di minimo del funzionale dell'energia. Il quadro analitico di riferimento è quello della teoria delle disequazioni variazionali...
Sur les fréquences de diffusion (scattering) d'un corps élastique couplé avec l'air