The objective of this study is to investigate the effect of the flexible connections on the dynamic behavior of structures. To take into account the uncertainties in their values, the stiffness of the connections are regarded as random variables. In the first part of the report the problem is studied from a deterministic point of view in order to develop the analytical models and expressions required for a stochastic analysis. A bibliographic review of the deterministic analysis of structures with non-rigid joints and analysis of structures with random parameters is presented. A finite element model that includes the effect of the flexibility and finite size of the connections is formulated. By using a variational approach it is shown that the mass matrix is also affected by the flexible connections A sensitivity analysis is carried out to assess how the natural frequencies and modal shapes are affected by the variation in the stiffness of the joints. Closed from expressions to calculate the derivatives of the eigenvalues and eigenvectors are provided. Flexible connections, Finite element models, Sensitivity analysis, Perturbation Methods.

The objective of this study is to quantify the effect of flexible connections with random stiffness on the modal properties and dynamic response of structures. Since the mass and stiffness matrices contain random parameters, the modal decomposition solution of the equations of motion lead to a random eigenvalue problem. A second order perturbation technique is used for the solution the random eigenproblem. Closed form expressions for the mean and variance of the natural frequencies and vibration modes are provided. The response of systems with random parameters subjected to deterministic loads is examined next beginning with single degree of freedom systems. When standard perturbation methods are applied to calculate the statistics of the response, the expressions obtained become non uniform as time grows. A detailed discussion about the cause of the problem is presented. A new formulation based on the method of multiple scales used for nonlinear systems is proposed to overcome the problem. The response analysis is extended to multi degree of freedom systems. Conclusions and recommendations for further research are presented ... Flexible connections, Random eigenvalue problems, Perturbation techniques, Stochastic finite elements.

The purpose of this monograph is threefold. First, mathematical models of the transient behavior of some or all of the state variables describing the motion of multiple-link flexible structures will be developed. The structures which we have in mind consist of finitely many interconnected flexible ele ments such as strings, beams, plates and shells or combinations thereof and are representative of trusses, frames, robot arms, solar panels, antennae, deformable mirrors, etc. , currently in use. For example, a typical subsys tem found in almost all aircraft and space vehicles consists of beam, plate and/or shell elements attached to each other in a rigid or flexible manner. Due to limitations on their weights, the elements themselves must be highly flexible, and due to limitations on their initial configuration (i. e. , before de ployment), those aggregates often have to contain several links so that the substructure may be unfolded or telescoped once it is deployed. The point of view we wish to adopt is that in order to understand completely the dynamic response of a complex elastic structure it is not sufficient to con to take into account the sider only its global motion but also necessary flexibility of individual elements and the interaction and transmission of elastic effects such as bending, torsion and axial deformations at junctions where members are connected to each other. The second object of this book is to provide rigorous mathematical analyses of the resulting models.

This important, self-contained reference deals with structural life assessment (SLA) and structural health monitoring (SHM) in a combined form. SLA periodically evaluates the state and condition of a structural system and provides recommendations for possible maintenance actions or the end of structural service life. It is a diversified field and relies on the theories of fracture mechanics, fatigue damage process, and reliability theory. For common structures, their life assessment is not only governed by the theory of fracture mechanics and fatigue damage process, but by other factors such as corrosion, grounding, and sudden collision. On the other hand, SHM deals with the detection, prediction, and location of crack development online. Both SLA and SHM are combined in a unified and coherent treatment.