Mecanica, projecto e controle dos sistemas de corpos multiplos

Abstract

Global and incremental in reference configuration and in control volume boundary-value problems are obtained from the conservation principles of Mechanics: of mass, of linear and rotational momentum and of energy. Variational equations and inequalities, constraint conditions, weak form of differential equations, global and incremental, and equations for iterative approximation are derived from Hamilton's, HU-Washizu's and potential energy principles. The incremental problem arises from a perturbation of design and control, i.e., of the global problem's data, the multiple-body system and the time interval of analysis included. Rigid and hyper elastic bodies with internal constraints and material discontinuities are considered. The reference configuration is time-varying and can be identified with the current configuration. Material properties are defined by means of a second configuration, the problem is described in both and relations for the change of reference configuration are stated. The following decompositions of deformation are considered: rigid-body motion overlying deformation proper; rigid-body motion with overlying deformation, and the motion for which the latter is a minimum is evaluated. Virtual work of stress is represented by means of differential operators and corresponding transformation laws for change of reference configuration and decomposition of deformation are stated. Interaction of the system's bodies, among themselves and with the ground, is materialized by contact conditions, holonomic constraints, internal energy and dissipation functionals and kinematic boundary condition. In dynamics three sorts of problems are accounted for: fixed end points; initial conditions; periodicAvailable from Fundacao para a Ciencia e a Tecnologia, Servico de Informacao e Documentacao, Av. D. Carlos I, 126, 1249-074 Lisboa, Portugal / FCT - Fundação para o Ciência e a TecnologiaSIGLEPTPortuga