Il problema monolaterale di contatto dinamico con attrito di una trave su una fondazione alla Hetényi: un approccio agli elementi finiti

Ascione, Luigi ; Bilotti, Giancarlo

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 82 (1988) no. 1, pp. 61-73

Résumé

The hypotesis of unilateral contact between foundation structure and soil assumes an important meaning in many technical problems, when the area of contact between structure and foundation becomes small, owing either to the soil-structure relative stiffness or to the load condition and consequently the assumption of perfect bonding fails. Much research has been carried out in this area, essentially in the field of statics. However there is very little research concerning the dynamical equilibrium problem with unilateral constraints to be found in literature. In fact this problem presents far more analytical difficulties than statical ones. Neverteless there are some advantagies to be obtained by using simplified models of soil, which allow us to analyse the most significant mechanical features of the problem without too much analytical trouble. In particular, in view of technical applications, Hetényi's model, which simulates the soil by means of bilateral springs connected by an elastic plate seems very useful. In some previous work quoted in References the authors utilized this model to study the frictionless dynamical contact problem relative to beams and circular plates. In the present paper, such analysis is extended to take into account the effects of frictional stresses at the interface between structure and soil. The law of friction that we consider can be seen as a regularization of the classical Coulomb's law. In particular we restrict our analysis to consider a beam case. The problem is formulated and analysed from a numerical point of view via finite elements. Two examples are examined. In the first one the load condition consists in a single force applied at the middle of the beam; in the second only the beam is loaded by vertical and horizontal forces in order to simulate the action on the foundation of a frame subjected to an earthquake. The time integration of the dynamical equilibrium equations is carried out by means of a semi-implicit method. The numerical results obtained show how the most important parameters involved in the analysis influence the solution.