Padovani C., Pasquinelli G., Silhavy M. Processes in masonry bodies and the dynamical significance of collapse. In: Mathematics and Mechanics of Solids, vol. 13 (7) pp. 573 - 710. Sage Publications, 2008. |

Abstract (English) |
We consider masonry bodies with dissipation of the rate type. Global in time existence and uniqueness of weak solutions for arbitrary loads and initial conditions is established; this includes the loads for which the masonry structure collapses. "Safe" and "collapse" loads are distinguished by different behaviors of solutions (= processes) at large times. Three situations can arise according to the properties of the equilibrium problem. (1): The equilibrium problem has a (typically nonunique) solution in the Sobolev space W1,2 of displacements; then each process stabilizes inasmuch as the kinetic energy tends to 0 and the L2 distance of the displacement from the set of all equilibrium displacements tends to 0 (2): The equilibrium problem has no solution in W1,2 but the infimum of the energy functional on the space of admissible displacements is finite. Then the kinetic energy tends to 0 but the W1,2 norm of the displacement tends to infinity. This may correspond either to a collapse or to a situation when the process approaches an equilibrium solution in a larger function space. (3): The infimum of the energy functional on the space of admissible displacements is - infinity. Then the total energy approaches - infinity in any process and the W1,1 norm of the displacement tends to infinity ; the structure collapses. | |

URL: | http://mms.sagepub.com/archive/ | |

DOI: | 10.1177/1081286507078307 | |

Subject | Dynamics of masonry structures Collapse J.2 74H20, 74H25, 74H35, 74H40 |

1) Download Document PDF |

Open access Restricted Private