Abstract

Structural elements, in many situations, are supported by other surfaces, such as soil, which may offer movement constraints in some directions. Therefore, the static and dynamic analysis of these elements considering their interaction with the soil becomes important in the design of a structural design. This paper presents the nonlinear dynamic analysis of structural systems considering such interaction through the Finite Element Method. A geometrically nonlinear beam-column element is used to model the structure, while the soil can be idealized as a continuum foundation, through the Winkler and Pasternak models. It is assumed that the foundation reacts to tension and compression stresses, so during the deformation process the structural elements are subjected to bilateral contact constraints. The analysis is based on the modeling of the structural system using the finite element method, where the Newmark integration method and Newton-Raphson iterative strategy are used in the process of solving the nonlinear dynamic equations in the time domain. Practical situations involving the interaction between soil and structure were evaluated during the study, showing the influence of contact in the natural vibration frequency and transient response of these structures.

Abstract

A fully geometric and constitutive nonlinear model for the description of the dynamic behavior of beam structures is developed. The
proposed formulation is based on the geometrically exact formulation for beams due to Simo but, in this article an intermediate curved
reference configuration is considered. The resulting deformation map belongs to a nonlinear differential manifold and, therefore, an
appropriated version of Newmark’s scheme is used in updating the kinematics variables. Each material point of the cross-section is
assumed to be composed of several simple materials with their own constitutive laws. The mixing rule is used to describe the resulting
composite. An explicit expression for the objective measure of the strain rate acting on each material point is deduced in this article.
Details about its numerical implementation in the time-stepping scheme are also addressed. Viscosity is included at the constitutive level by means of a thermodynamically consistent visco damage model developed in terms of the material description of the First Piola Kirchhoff stress vector. The constitutive part of the tangent tensor is deduced including the effect of rate dependent inelasticity. Finally, several numerical examples, validating the proposed formulation, are given.

Abstract

In this article, the nonlinear constitutive behavior is considered in the geometrically nonlinear formulation for beams proposed by
Simo and Vu-Quoc. The displacement based method is employed in solving the resulting nonlinear problem in the static case. Thermodynamically consistent three-dimensional constitutive laws are used in describing the material behavior, leading to a more precise estimation of the energy dissipated by the structures. The simple mixing rule is also applied in modeling materials which are composed by several simple components. An appropriated cross sectional analysis is implemented under the assumption and limitations of the planarity
of the beam cross sections. Special attention is paid to the development of a method for defining the global damage state of a structure
based on a scalar damage index capable of describing the residual strength and the load carrying capacity. Several numerical examples,
including composite materials and strain localization, are presented and discussed.

Abstract

In this work, a formulation for rod structures, able to consider coupled geometric and constitutive sources of nonlinearity in both the static and the dynamic range, is developed. It is extended for allowing the inclusion of passive energy dissipating elements as a special rod element and geometric irregularities as a full three-dimensional body connected to the framed structure by means of a two-scale model. The proposed formulation is based on the Reissner-Simo geometrically exact formulation for rods considering an initially curved reference configuration and extended to include arbitrary distribution of composite materials in the cross sections. Each material point of the cross section is assumed to be composed of several simple materials with their own thermodynamically consistent constitutive laws. The simple mixing rule is used for treating the resulting composite. Cross sections are meshed into a grid of quadrilaterals, each of them corresponding to a fiber directed along the axis of the beam. A mesh independent response is obtained by means of the regularization of the energy dissipated at constitutive level considering the characteristic length of the mesh and the fracture energy of the materials. Local and global damage indices have been developed based on the ratio between the visco-elastic and nonlinear stresses. The consistent linearization of the weak form of the momentum balance equations is performed considering the effects of rate dependent inelasticity. Due to the fact that the deformation map belongs to a nonlinear manifold, an appropriated version of Newmark's scheme and of the iterative updating procedure of the involved variables is developed. The space discretization of the linearized problem is performed using the standard Galerkin finite element approach. A Newton-Raphson type of iterative scheme is used for the step-by-step solution of the discrete problem. A specific element for energy dissipating devices is developed, based on the rod model but releasing the rotational degrees of freedom. Appropriated constitutive relations are given for a wide variety of possible dissipative mechanisms. Several numerical examples have been included for the validation of the proposed formulation. The examples include elastic and inelastic finite deformation response of framed structures with initially straight and curved beams. Comparisons with existing literature is performed for the case of plasticity and new results are presented for degrading and composite materials. Those examples show how the present formulation is able to capture different complex mechanical phenomena such as the uncoupling of the dynamic response from resonance due to inelastic incursions and suppression of the high frequency content. The study of realistic flexible pre-cast and cast in place reinforced concrete framed structures subjected to static and dynamic actions is also carried out. Detailed studies regarding to the evolution of local damage indices, energy dissipation and ductility demands are presented. The studies include the seismic response of concrete structures with energy dissipating devices. Advantages of the use of passive control are verified.

Abstract

This paper presents a continuum model for the simulation of the viscous effects and the long-term damage accumulation in masonry structures. The rheological model is based on a generalized Maxwell chain representation with a constitutive law utilizing a limited number of internal variables. Thanks to its computational efficiency, this approach is suitable for the analysis of large and complex structures. In the paper, the viscous and damage models are presented and their coupling is discussed. The FE simulation of the construction process of the representative bay of Mallorca Cathedral is presented, together with the analysis of the long-term effects. The parameters of the model are tentatively calibrated on the basis of the time-dependent viscous deformations detected during the cathedral monitoring.

Abstract

From the theoretical point of view, systems composed by masonry arches or vaults would require, during construction, the simultaneous activation of all structural elements in order to reach the optimum balance of thrusts. This is not obviously the case of complex ancient masonry constructions, whose long and gradual building process may have contributed to their deformed condition and even to damage.In this paper, the possible influence of the construction process as well as that of later long-term deformation on the final condition of the building is investigated in the case of a complex and large historical structure, namely Mallorca Cathedral. A FE code has been specifically developed for the present study. The code is able to account for construction processes through sequential-evolutionary analyses, with the description of masonry mechanical damage and long-term deformation. The representative bay of the cathedral is analyzed taking into account different construction phases, as emerged from historical research. The response of such substructure to transverse earthquake equivalent forces is then investigated. In this case, the damage model is improved with a local crack-tracking algorithm. This numerical strategy models the tensile damage as distinct cracks, leading to a better prediction of realistic collapsing mechanisms.

Abstract

This article presents the analysis of the structure of Mallorca Cathedral taking into account the influence on the structural behavior of auxiliary iron ties used during the construction process. Recent studies (Roca et al. 2012, 2013) presented some hypotheses about the construction process of the cathedral. This article complements the previous results by considering the use of auxiliary ties as temporary stabilizing device during the construction. Evidence of the use of ties during the construction has been recognized after a comprehensive survey. The study of the role of such ties and the effect of their later removal are studied by a FE analysis carried out on a representative bay of the structure. The study includes a time-dependent FE analysis after the removal of the ties to assess the long-term structural behavior. The results of the numerical analysis are compared with the deformation trends identified by means of a recent monitoring campaign.