Abstract

This paper presents a new algorithm for solving the equations of motion of multi-storey buildings that incorporate frictional energy dissipators as seismic protection. The behavior of the dissipators is represented by Coulomb dry friction models, they introduce severe nonlinearities in the dynamic behavior of the structure every time that the contact conditions (stick or slip) change in the dissipators. These nonlinearities complicate the resolution of the equations of motion as it usually is described by lumped masses models whose degrees of freedom are the displacements of the floors and, as the stick or slip conditions change, the degrees of freedom must be modified: for blocking conditions they are only the displacements of the storeys while under sliding conditions the displacements of the dissipators have to be also considered. In previous articles the accuracy of the proposed algorithm has been verified by comparison with experimental results, as well, the computational efficiency of the algorithm has been confirmed by comparing the required resources (in terms of computation time and of memory allocation) with those of other algorithms. The objectives of this paper are to describe in detail the numerical solution of the equations of motion and present representative examples confirming the ability of the algorithm to reproduce the dynamic behavior of buildings with friction dissipators and reporting preliminarily about the usefulness of such devices to reduce the oscillations of the structure to be protected.

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

The conventional form of solving the equations of motion governing the seismic response of building structures with nonlinear base isolation consists of using monolithic step by step integrationmethods. As an alternative, the application of a block iterative scheme is examined in this paper. After describing the particularities of the equations of motion of the structure with base isolation, different block
iterative schemes are described. Their effectiveness is discussed and compared with that of monolithic step by step integration methods. Adequate examples are used with the aim of performing numerical comparisons.

Abstract

Structures subjected to cyclic loads show alternative tension–compression stress states; in such a case,  even if certain damage (fracture) is reached during the tension cycle, the computational model of the structure should maintain its capacity to withstand subsequent compression based only on the contact effect in the damaged area (opening, closing and reopening of cracks). In order to control this behavior, a phenomenological constitutive model able to consider the contact as a structural limitation is required. From the constitutive point of view, geomaterials have different damage thresholds for tension and compression and, from the structural point of view, it must be ensured that the material damaged in tension still resist compression. In this case, it is accepted that cracks behave as a contact surface at the structural level. To meet the above mentioned phenomenology, a modification of the damage model
differentiated in tension and compression proposed by Faria et al. [Faria R, Oliver J, Cervera M. A strainbased plastic viscous-damage model for massive concrete structures. Int J Solids Struct 1998; 35:1533–58] is performed in this paper, considering independent strength thresholds in each of these processes, controlled with two independent discontinuity threshold functions. Also, in this work an elasto-plastic constitutive model is used to represent the behaviour of the steel bars.

Abstract

A new damage model, based on continuum damage mechanics and simulating the opening, closing, and reopening of cracks in
concrete using only one surface of discontinuity, is proposed in this article. The model complies with the thermodynamics principles of nonreversible, isothermal, and adiabatic processes. Two scalar internal variables have been defined: a tensile damage variable d+ and a compressive damage variable d−; the threshold of damage is controlled by only one surface of discontinuity and a new parameter controlling the damage variable that should be activated. This new parameter represents the ratio of tensile stress to compressive stress in the damaged material. The continuity of response under complex loads, which is one of the aims of this work, is ensured. An adequate response under different types of loads leads to the conclusion that the proposed model provides a powerful tool to numerically analyze reinforced concrete structures. Validation and illustrative examples are included in the article.

Abstract

The objectives of the seismic design of buildings can be achieved by applying techniques of conventional design that consider the that the ground motion is transmitted to the structure through its fixed base. As an alternative to this traditional design, base isolation systems were developed consisting of mechanisms that partially uncouple the structure of the foundation ground to reduce, in this way, the damages of the structure and of its content. Decoupling is carried out by placing support devices between the base of the structure and its foundation that increase the flexibility of the overall structure-base system and that produce, at the same time, an appropriate damping. Despite the large number of studies on different base isolation systems, there are few comparative analyzes between these systems. In this monograph, structures isolated with different systems are compared with structures with conventional design. To this end, criteria for evaluating the behavior of the different systems have been defined. In the numerical studies, models with linear behavior for the structure and nonlinear behavior of the base isolation system have been considered. The type of nonlinearity of the isolation is formulated by means of differential equations, capable of describing both hysteretic and frictional systems.

Abstract

In this monograph, we study a type of hybrid system that combines a base isolation system with an active control system that applies forces on the base. The control forces are calculated by means of a control law that guarantees an adequate behavior, both of the structure and of the base, considering a wide class of non-linearities of the base isolator and uncertainties in the dynamic model and in the excitation. In order to simulate properly the proposed hybrid system, algorithms are used able to analyze the effect of the base isolation with non-linear behavior. At the same time, it is necessary to have a control law that generates the active control force, whose objective is examined from the point of view of the behavior of the system composed by the structure and the base isolation in purely passive conditions. The control law is formulated for the two subsystems coupled through their boundary conditions. The active control forces are applied upon one of the subsystems in order to guarantee a form of practical stability. In this case, the subsystem over which the control acts is the base and the other subsystem is the structure. In the monograph the equations that describe the two systems of seismic base isolation considered in this monograph are developed (one hysteretic and the other frictional), the use of the hybrid system is justified, the different components are described and a critical analysis of the different existing hybrid systems is performed. The law of adaptive control is developed, the hypotheses are stated and the stability of said law is analyzed. The developed strategy is applied to different buildings with base isolation systems and numerical simulation results of their seismic response are shown.

Abstract

The paper introduces a new global damage evaluation method which leads to a meaningful global damage index. A numerical procedure for the prediction of local and global damage in civil engineering structures using the finite element method and a continuum damage model, is presented. The method is adequate for the computation of the limit load in reinforced concrete (RC) structures and for the prediction of the failure mechanisms. Details of the applied damage model are given together with a description of the finite element implementation and the procedure for computing the global damage parameters. Examples of applications of the methodology to the nonlinear analysis of a range of RC structures, are presented.

Abstract