Inelastic analysis of geometrically exact rods

Postprint (published version

Operational modal analysis and FE model updating of the Metropolitan Cathedral of Santiago, Chile

Heritage buildings in Latin American countries possess high architectural value. Studying these constructions under extreme loads, particularly earthquakes, requires representative models for simulating expected response. At present, the non-invasive Operational Modal Analysis (OMA) tests offer interesting possibilities for obtaining modal parameters to update and validate a structural model for this type of structure. In this context, this article focuses on the calibration and adjustment process for a finite element model of the Metropolitan Cathedral of Santiago Chile, based on experimentally identified modal and mechanical material properties. Accordingly, an in situ experimental campaign, aimed at obtaining the response of the structure due to ambient vibrations is presented and discussed. Six high-sensitivity synchronous triaxial accelerometers were employed in this campaign. Enhanced Frequency Domain Decomposition (EFDD) and Stochastic Subspace Identification (SSI), system identification methods, were applied. Mechanical tests were performed on the Cathedral's stone blocks. The experimental data and derived modal properties were used to generate and update a finite element model. Several considerations were made in the model updating process: the most relevant was the homogeneous treatment of the stone masonry with their mortar interface, and the boundary elements restraining effect caused by adjacent structures. A preliminary model updating process was applied to define the boundary conditions and initial material properties. This optimization was based on minimizing an error function given by the difference between the experimental and analytical frequencies. A second step was then applied, in which models with different material properties were evaluated within a physically possible range. The final model selection was based on the distance between the experimental and analytical frequencies, and the mode shapes. The updated model allows an assessment to be made of the structure behavior in its current condition and models to be prepared for a wide range of possible future research scenarios

Numerical simulation of the inelastic seismic response of RC structures with energy dissipators

The nonlinear dynamic response of RC buildings with dissipators is studied using advanced computational techniques. A fully 3D geometric and constitutive nonlinear model is used for the description of the dynamic behavior of structures. Each material point of the cross section is assumed to be composed of several simple materials with their own constitutive laws. A specific element based on the beam theory is proposed for the dissipators. Several numerical tests are carried out to validate the proposed model.Peer Reviewe

Nonlinear constitutive formulation for a finite deformation beam model based on the mixing rule for composites

Constitutive nonlinearity for beam models has been traditionally described by means of concentrated and distributed models, in the most cases, formulated assuming infinitesimal deformation. The concentrated models consider elastic elements equipped with plastic hinges at the ends. In the case of distributed plasticity models, inelasticity is evaluated at a fixed number of points on the cross sections and along the beam axis. These points corresponds to of fibers directed along the axis. Therefore, this approach is referred as fiber approach. Additionally, two versions of the models can be defined: the displacement based method, which is based on the interpolation of the strain field along the elements and force based method which obtains the sectional forces and moments interpolating the nodal values and satisfying the equilibrium equations even in the inelastic range. Both approaches are affected by the strain localization phenomenon when materials with softening behavior are employed and, therefore, the whole structural response becomes mesh dependent if no appropriate corrections are considered. On the another hand, one of the most invoked geometrically exact formulations for beams in finite deformation is that of Simo which generalize to the 3–D dynamic case the formulation developed by Reissner. Only a few works have developed fully geometrical and constitutive nonlinear formulations for beams, but they have been mainly focused on plasticity. Recently, Mata et.al. [14, 15] have extended the formulation due to Reissner-Simo for considering and arbitrary distribution of composite materials on the cross sections for the static and dynamic cases. The displacement based method is used for solving the resulting nonlinear problem. Thermodynamically consistent constitutive laws are used in describing the material behavior of simple materials and the parallel version of the mixing rule is used for composites. In this work a detailed presentation of the implementation of the mixing rule for the treatment of constitutive nonlinearity in the Reissner–Simo formulation for beams is presented. Finally, several numerical examples validating the proposed formulation are given.Peer ReviewedPostprint (published version

Numerical code for seismic analysis of structures incorporating energy dissipating devices

The nonlinear dynamic response of civil structures with energy dissipating devices is studied. The structure is modeled using the Vu Quoc–Simo formulation for beams in finite deformation. The effects of shear stresses are considered, allowing rotating the local system of each beam independently of the position of the beam axis. The material nolinearity is treated at material point level with an appropriated constitutive law for concrete and fiber behavior for steel reinforcements and stirrups. The simple mixing theory is used to treat the resulting composite. The equation of motion of the system as well as the conservation laws are expressed in terms of sectional forces and generalized strains and the dynamic problem is solved in the finite element framework. A specific kind of finite element is proposed for modeling the energy dissipating devices. Several tests were conducted to validate the ability of the model to reproduce the nonlinear response of concrete structures subjected to earthquake loading.Peer ReviewedPostprint (published version

Numerical code for seismic analysis of structures incorporating energy dissipating devices

The nonlinear dynamic response of civil structures with energy dissipating devices is studied. The structure is modeled using the Vu Quoc–Simo formulation for beams in finite deformation. The effects of shear stresses are considered, allowing rotating the local system of each beam independently of the position of the beam axis. The material nolinearity is treated at material point level with an appropriated constitutive law for concrete and fiber behavior for steel reinforcements and stirrups. The simple mixing theory is used to treat the resulting composite. The equation of motion of the system as well as the conservation laws are expressed in terms of sectional forces and generalized strains and the dynamic problem is solved in the finite element framework. A specific kind of finite element is proposed for modeling the energy dissipating devices. Several tests were conducted to validate the ability of the model to reproduce the nonlinear response of concrete structures subjected to earthquake loading.Peer Reviewe

Evaluation of the seismic behavior of precast concrete buildings with energy dissipating devices

The poor performance of some precast structures have limited their use in seismic zones due to their low level of structural damping, P-Δ effects and low ductility of de structural joints. These characteristics allow proposing the use of passive dissipating devices for improving their behavior. The seismic response of two precast buildings is studied in this work. The response of the structures equipped with energy dissipators is compared with the non-controlled case. The first structure is a low damped industrial precast concrete building with low ductility connecting joints. The second one is a 3D frame typically built in urban areas. The structures are simulated using the Simo’s formulation for beams. Each beam section is meshed in a secondary grid of fibers along the beam axis. The materials of each fiber can be composed of several components having appropriated constitutive laws. The simple mixing theory is used to treat the resulting composite. A special kind of element is developed for modeling the dissipating devices. The results obtained in this work allow validating the use of passive control for improving the seismic performance of precast structures.Peer ReviewedPostprint (published version

Nonlinear constitutive formulation for a finite deformation beam model based on the mixing rule for composites

Constitutive nonlinearity for beam models has been traditionally described by means of concentrated and distributed models, in the most cases, formulated assuming infinitesimal deformation. The concentrated models consider elastic elements equipped with plastic hinges at the ends. In the case of distributed plasticity models, inelasticity is evaluated at a fixed number of points on the cross sections and along the beam axis. These points corresponds to of fibers directed along the axis. Therefore, this approach is referred as fiber approach. Additionally, two versions of the models can be defined: the displacement based method, which is based on the interpolation of the strain field along the elements and force based method which obtains the sectional forces and moments interpolating the nodal values and satisfying the equilibrium equations even in the inelastic range. Both approaches are affected by the strain localization phenomenon when materials with softening behavior are employed and, therefore, the whole structural response becomes mesh dependent if no appropriate corrections are considered. On the another hand, one of the most invoked geometrically exact formulations for beams in finite deformation is that of Simo which generalize to the 3–D dynamic case the formulation developed by Reissner. Only a few works have developed fully geometrical and constitutive nonlinear formulations for beams, but they have been mainly focused on plasticity. Recently, Mata et.al. [14, 15] have extended the formulation due to Reissner-Simo for considering and arbitrary distribution of composite materials on the cross sections for the static and dynamic cases. The displacement based method is used for solving the resulting nonlinear problem. Thermodynamically consistent constitutive laws are used in describing the material behavior of simple materials and the parallel version of the mixing rule is used for composites. In this work a detailed presentation of the implementation of the mixing rule for the treatment of constitutive nonlinearity in the Reissner–Simo formulation for beams is presented. Finally, several numerical examples validating the proposed formulation are given.Peer Reviewe

Numerical-experimental study of high damping elastomers for energy dissipating devices

In work the results of a study carried out to characterize the mechanical response of a high damping rubber to be used to design and construct energy dissipating devices and base isolators for controlling strong vibrations in civil engineering structures is presented. A new parametric constitutive model of the rubber is proposed to be employed in the design procedure and structural analysis of passive controlled structures. The parameters of the model are calibrated using experimental results obtained from tests on rubber specimens subjected to different loading paths. The new model is able to reproduce the main dissipative mechanisms as well as axial hardening. The response predicted for the proposed model is compared with these obtained from experimental tests.Peer ReviewedPostprint (published version