Nonlinear Dynamic Analysis Of Structures Research Articles

Seismic demand assessment of self-centering steel plate shear walls

In previous studies, a post-tensioned rocking system has been introduced to steel plate shear wall (SPSW) system as a means for reducing its residual drifts. The success of this method and the performance of self-centering SPSWs (SC-SPSWs) is evaluated, in this study, by nonlinear dynamic analysis of previously-designed structures. For this purpose, a numerical model is developed and validated against experimental results. This model is, then, used for representing five 3- and 9-story SC-SPSWs that reflect various design assumptions. The median and dispersion of various response parameters are then extracted using a set of 20 ground motion records scaled to three different intensity levels. A comparative assessment is next performed between response of the studied structures in presence and absence of the rocking system. This assessment reveals that the rocking system is not effective in reducing the residual deformations of SPSW system. Nevertheless, the rocking behavior is shown to effectively mitigate the ductility demand at the beams' end portion and provide a more uniform distribution of plasticity along beams and within web plates of different stories.

Nonlinear dynamic analysis of shell structures by the formulation based on a discrete shear gap

In this work, a shear locking-free three-node shell element based on Mindlin–Reissner theory is presented for a nonlinear dynamic analysis including sheet metal forming. In the present formulation, only displacement and rotational degrees of freedom are utilized, and the discrete shear gap of each field node is deduced using rotations of all three field nodes in a local coordinate system by the integral from the fictitious central point to the corresponding field node, which makes it alleviate the shear locking phenomenon. In order to validate the availability in solving nonlinear dynamic problems, several benchmark problems and sheet metal forming applications are employed. The results show potentiality in application to practical problems because of the simple implementation.

The fractional derivative expansion method in nonlinear dynamic analysis of structures

The history of formulation of the efficient method for studying the nonlinear dynamic response of structures, damping features of which depend on natural frequencies of vibrations, is presented. This technique is the modified version of the method of multiple scales, the efficiency of which is illustrated by the examples of nonlinear vibrations of suspension bridges and plates subjected to the conditions of the internal resonances.

Sensitivity analysis of the influence of ground motion intensity levels on the seismic behavior of steel frames in assessment of the target displacement considering near-fault effects

Nonlinear time-history analysis conducted as part of a performance-based seismic design approach often require that the ground motion records are selected and then scaled to a specified level of seismic intensity. In such analyses, besides an adequate structural model, a set of acceleration time-series is needed as the most realistic representation of the seismic action. In this paper, the effects of scaling procedure on seismic demands of steel frames are investigated. To this, two special steel moment-resisting frames with considerable higher mode effects, and two sets of ground motions, including near-fault and far-fault motions are considered. Moreover, three scaling procedures are introduced for performing nonlinear dynamic time-history analysis of structures. Among different demands, lateral roof displacement and interstory drift are selected as seismic demands. The height-wise distribution of demands shows that the inelastic seismic demands of the near-fault pulse-like ground motions differ considerably from those of far-fault ones. These results show that the story drifts are mostly larger for far-fault motions in the upper story levels in comparison to near-fault records and in the lower floors, the reverse is true. Thus, the scaling procedures directly affect the results of seismic demands and choosing different methods would result in varying responses. Moreover, a low-cost and fairly effective procedure is proposed to estimate the target displacement demands of buildings from response-spectrum analyses, considering near-fault effects. The precision of this method is verified by nonlinear time-history analysis results, as the benchmark solution, and acceptable improvements have been achieved.

Transient analysis of nonlinear locally resonant metamaterials via computational homogenization

In this paper, the transient computational homogenization scheme is extended to allow for nonlinear elastodynamic phenomena. The framework is used to analyze wave propagation in a locally resonant metamaterial containing hyperelastic rubber-coated inclusions. The ability to properly simulate realistic nonlinearities in elasto-acoustic metamaterials constitutes a step forward in metamaterial design as, so far, the literature has focused only on academic nonlinear material models and simple lattice structures. The accuracy and efficiency of the framework are assessed by comparing the results with direct numerical simulations for transient dynamic analysis. It is found that the band gap features are adequately captured. The ability of the framework to perform accurate nonlinear transient dynamic analyses of finite-size structures is also demonstrated, along with the significant computational time savings achieved.

Co-rotating rigid beam with generalized plastic hinges for the nonlinear dynamic analysis of planar framed structures subjected to impact loading

The purpose of this paper is to model the nonlinear dynamical response of steel frame structures subjected to impact loading. A 2D co-rotational rigid beam element with generalized elasto-plastic hinges is presented. The main idea is to integrate the concept of the generalized elasto-plastic hinge into the standard co-rotational framework by performing a static condensation procedure in order to remove extra internal nodes and their corresponding degrees of freedom. In addition, impact loading is applied through a contact model that is described in the rigorous framework of non-smooth dynamics. In this framework, equations of motion are derived using a set of differential measures and convex analysis tools, whereas Newton's impact law is imposed by means of a restitution coefficient in order to accommodate energy losses. An energy and momentum conserving scheme is adopted to solve the dynamical equations. The main interest of the current model is the ability to evaluate the geometrically nonlinear inelastic behaviour of steel structures with semi-rigid connections subjected to impact in a simple and efficient way, using only a few number of elements. The accuracy of the proposed formulation is assessed in three numerical applications.

Correlation of Ground Motion Intensity Measures and Seismic Damage Indices of Masonry-Infilled Steel Frames

The main aim of this study was to analyze the response of structures with masonry infill walls to the intensity measure (IMs) parameters. Hence, two sets of earthquake ground motions, ordinary seismic records (OSR) and pulse-like seismic records (PLSR), were used for the nonlinear dynamic analysis of multi-story steel structures with masonry infill walls. Seismic performance was evaluated using the general indicators of damage (modified Park–Ang index), maximum inter-story drift ratio (MIDR) and roof drift ratio (RDR). The correlation between the multiple IM parameters with and without pulse-like ground motion and the damage indices of steel moment frames with and without masonry-infilled walls was determined using the Spearman correlation coefficient. Moreover, the correlation between the damage criteria and IMs was investigated. The results revealed that the spectral acceleration and velocity at the primary period of the structure and seismic parameters which are related to velocity have a strong relationship with MIDR and RDR. However, the correlations for PLSR and OSR were differed. The results indicated that the analysis of IMs with ground motion could help predict the parameters for building failure in various systems. The presence of masonry-infilled walls has changed the correlation coefficient for a fully infilled frame when compared with a bare frame.

Numerical model for the non-linear dynamic analysis of multi-storey structures with semi-rigid joints with specific reference to the Algerian code

The current paper aims at investigating the dynamic response of rigid and semi-rigid connections of steel structures built in high seismic areas. A nonlinear dynamic analysis model, which is an extension to the simplified and direct mechanical model used in the static analysis, is proposed and discussed. The novelty of the model consists in the introduction of a bar element with semi-rigid joint as a single element without the need to discretise it (i.e. without a finite element mesh) in the program where non-linearity is considered in the flexibility factor of the stiffness matrix. The model developed is validated through application to examples of steel frames with different types of connections under dynamic forces. The results obtained were very satisfactory. This work is motivated by the need for the revision of the Algerian seismic code (RPA99v2003) which does not yet consider provisions for the design of structures with semi-rigid joints. Based on the results of the study carried out on a multi-storey structure with different types of joints subjected to seismic loading, it can be seen that the safety justifications recommended by Algerian regulations RPA99 in terms of relative displacements as well as the dimension of the seismic joint prove to be too conservative compared to those by Eurocode 8.

Numerical error assessment in nonlinear dynamic analysis of structures

ABSTRACTThe complex nature of exciting forces in earthquake engineering applications mandates employing numerical methods to obtain structural response. Several numerical methods are used in earthquake engineering to solve the ordinary differential equation of motion. Previous studies assumed the appropriate time step as a constant fraction of natural period of the system disregarding period range. This study is concerned with assessing, by numerical experiment; the numerical error of commonly used schemes in nonlinear dynamic analyses and assessing their appropriateness for different excitations with different structural periods. The current investigation involved testing Newmark, HHT and HHT1 methods. The three methods were tested for nonlinear single degree of freedom system representing a typical concrete bridge structure. Three different exciting forces were used to test the schemes; half-sine pulse, harmonic force, and actual ground motion record. Three natural periods were used to conduct the experiment, representing short, medium and long period systems including the resonant condition. Three structural damping ratios, representing lightly, moderately and heavily damped systems, were used to assess the damping effect on the accuracy of the schemes. The results of this investigation indicated that commonly used assumption of time step as a constant fraction of natural period of the system disregarding the period range could result in significant numerical errors. The study also showed the significant effect of damping ratio of the system on the accuracy of the numerical schemes. The study presents a recommendation matrix of the most appropriate time step for each scheme for different applications and structural conditions.

Seismic performance analysis of a bridge-integrated structure based on IDA method

According to the incremental dynamic analysis method (IDA), the intensity amplitude of one or more seismic records is adjusted step by step, and then one or more sets of seismic records with increasing intensity are generated. The seismic records are used to perform nonlinear dynamic time history analysis of the bridge-integrated structure one by one until structural damage. Therefore, a comprehensive and realistic evaluation of the seismic capacity of the bridge-building station structure is made, and the response of the structure under the action of rare earthquakes and multiple earthquakes is deeply understood. This paper provides a reference for practical engineering design.

Complementarity Framework for Nonlinear Analysis of Tensegrity Structures with Slack Cables

A comprehensive complementarity framework is presented for both nonlinear static and dynamic analyses of tensegrity structures with a large number of slack cables. These analyses are characterized by cables switching between taut and slack states and hence exhibit nonsmooth behaviors. The core concept is casting the original computation in each iteration step as a linear complementary problem. To deal with the geometric nonlinearity, the governing equation is formulated based on the positional formulation finite-element method, in which the nodal positions, rather than conventional nodal displacements, are adopted as generalized coordinates. By directly linearizing the governing equation, this complementarity framework is first used to study the static analysis in the small displacement regime and then extended to the large displacement case for both the static and dynamic analyses. Multiple examples are presented to demonstrate performances of the proposed complementarity framework in both the static and dynamic cases.

Seismic Performance Assessment of RC Frame Structures Subjected to Far-Field and Near-Field Ground Motions Considering Strain Rate Effect

This paper investigates the influence of strain rate effect on the seismic performance of Reinforced concrete (RC) frame structures subjected to far-field and near-field ground motions. An approach for the nonlinear dynamic analysis of RC frame structures considering the strain-rate sensitivity of concrete and reinforcing steel materials is proposed and its effectiveness is validated by the experimental data of RC columns under dynamic loadings. A non-dimensional index is put forward to reveal the regularities of strain rate under different types of ground motions with various intensity levels. The influences of strain rate effect and input ground motion on the seismic performance of the exemplar RC frame are studied by comparing the seismic responses and fragilities of rate-dependent structural models with those of rate-independent ones. Numerical results indicate that the strain rates in structural members increase with the ground motion intensity and the strain rates induced by the near-field pulse-like earthquakes are higher than those by the far-field and near-field non-pulse-like earthquakes. The global response, critical member response, local damage and seismic fragility are all influenced by the strain rate effect, especially under the near-field pulse-like ground motions. Neglecting the influences of strain rate effect, variations in strain rates of different structural members and inputs of pulse-like ground motions may lead to erroneous seismic performance assessments of RC frame structures.

Nonlinear structural dynamic analysis by a stabilized central difference method

In this work, a simple stabilized central difference technique is discussed, to analyse nonlinear models. The proposed technique is unconditionally stable for linear systems and it provides enhanced stability features for nonlinear applications. The proposed method stands as a direct single step procedure, avoiding any iterative computations when solving nonlinear models; thus, it is very efficient. In addition, it is extremely accurate, providing much reduced period elongation and amplitude decay errors, compared to standard methods. The present work also introduces a criterion for updating the nonlinear system matrices, significantly reducing the computational complexity of the simulation and enhancing the efficiency of the technique. Numerical results are presented along the manuscript, illustrating the performance and accuracy of the proposed methodology.

Adaptive numerical method algorithms for nonlinear viscous and bilinear oil damper models subjected to dynamic loading

Adaptive numerical method algorithms are presented for the numerical simulation of the hysteretic behaviour of nonlinear viscous and bilinear oil dampers within a finite element program for nonlinear dynamic analysis of frame structures under earthquake excitations. The adaptive algorithms are applicable for computing high-precision solutions for nonlinear viscous and bilinear oil dampers with valve relief that are typically represented mathematically with a nonlinear Maxwell model. The algorithms presented possess excellent convergence characteristics for viscous dampers with a wide range of velocity exponents and axial stiffness properties. The algorithms are implemented in an open source finite element software, and their applicability and computational efficiency is demonstrated through a number of validation examples with data that involve component experimentation as well as the utilization of full-scale shake table tests of a 5-story steel building equipped with nonlinear viscous and bilinear oil dampers.

Development of a high-order compact finite-difference total Lagrangian method for nonlinear structural dynamic analysis

• A compact finite-difference total Lagrangian method (CFDTLM) is developed for nonlinear structural dynamics analysis. • The large deformation of elastic structures for Hookean and neo-Hookean materials is accurately simulated using the CFDTLM. • The CFDTLM is extended and assessed for simulating thermo-elastodynamic problems. • The numerical solution procedure adopted is simpler than high-order finite volume and finite element formulations . • The solution methodology proposed is accurate for simulating nonlinear structural dynamics problems. A high-order compact finite-difference total Lagrangian method (CFDTLM) is developed and applied to nonlinear structural dynamic analysis. The two-dimensional simulation of thermo-elastodynamics is numerically performed in generalized curvilinear coordinates by taking into account the geometric and material nonlinearities. The spatial discretization is carried out by a fourth-order compact finite-difference scheme and an implicit second-order accurate dual time-stepping method is applied for the time integration. The accuracy and capability of the proposed solution methodology for the nonlinear structural analysis is investigated through simulating different static and dynamic benchmark problems including large deformations, large displacements and Hookean/neo-Hookean materials. The solution method is demonstrated to be free of shear-locking behavior. The results obtained by the present solution algorithm are compared with the analytical solution and the numerical results of the finite element and finite volume methods to examine the accuracy and robustness of the solution method proposed. A grid study is also performed to investigate the grid size effect on the accuracy and performance of the solution. Indications are that the solution methodology proposed is accurate for simulating nonlinear structural dynamics problems.

Non-linear dynamic analysis to assess the seismic performance of cross-laminated timber structures

Timber structures are widely recognized to perform very well under strong ground motions. A non-linear dynamic analysis can be carried out to assess their seismic performance for design purposes, as allowed by the current regulations. When dealing with timber structures, however, the difficulties typically involved by this very powerful method of analysis may increase and sometimes become even overwhelming. The reasons are mainly due to insufficient experimental data, lack of standard constitutive models for timber connections and inadequate support provided by the current seismic codes. The key aspects related to modelling the non-linear behaviour of modern timber structures with particular focus to the crucial role of connections are analyzed in this paper. By referring to a case-study building made by solid cross-laminated (X-Lam) timber panels and designed according to the Eurocodes, the path that the designer has to undertake when carrying out a time-history non-linear analysis of a X-Lam timber structure is put in evidence, while some simplified assumptions are suggested and justified. A concentrated plasticity three-dimensional model is adopted where the hysteretic behaviour of connections is implemented by exploiting experimental data available from the literature. Three suites of earthquake records are considered in the investigation. The paper aims to give structural engineers some useful hints to carry out non-linear dynamic analyses of cross-laminated timber structures for design purposes.

A lumped parameter model for time‐domain inertial soil‐structure interaction analysis of structures on pile foundations

SummaryThe paper presents a lumped parameter model for the approximation of the frequency‐dependent dynamic stiffness of pile group foundations. The model can be implemented in commercial software to perform linear or nonlinear dynamic analyses of structures founded on piles taking into account the frequency‐dependent coupled roto‐translational, vertical, and torsional behaviour of the soil‐foundation system. Closed‐form formulas for estimating parameters of the model are proposed with reference to pile groups embedded in homogeneous soil deposits. These are calibrated with a nonlinear least square procedure, based on data provided by an extensive non‐dimensional parametric analysis performed with a model previously developed by the authors. Pile groups with square layout and different number of piles embedded in soft and stiff soils are considered. Formulas are overall well capable to reproduce parameters of the proposed lumped system that can be straightforwardly incorporated into inertial structural analyses to account for the dynamic behaviour of the soil‐foundation system. Some applications on typical bridge piers are finally presented to show examples of practical use of the proposed model. Results demonstrate the capability of the proposed lumped system as well as the formulas efficiency in approximating impedances of pile groups and the relevant effect on the response of the superstructure.

Nonlinear dynamic and deployment analysis of clustered tensegrity structures using a positional formulation FEM

This paper addresses the dynamic analysis of the clustered tensegrity structures via the framework of the positional formulation finite element method (FEM). The nodal coordinates are chosen as the generalized coordinates. The rod element and multi-nodes clustered cable element are first formulated. A comprehensive dynamic model for investigating the dynamic properties of the clustered tensegrity is then developed. The dynamic model is subsequently modified for the structural vibration analysis and modal analysis. The results of the modal analysis show that each order of natural frequency of a clustered tensegrity is lower than that of its corresponding classical tensegrity, indicating that the structure tends to be more flexible if a classical tensegrity is transformed into a clustered tensegrity. The results of the nonlinear deployment analysis show that the motion characteristics differ from those of the quasi-static analysis as the actuation speed increases. To pursuit a fast actuation speed to actuate the structure, mere quasi-static analysis in the existing literature is inadequate, and dynamic effects must be taken into account. The proposed method provides an effective tool to capture the dynamic properties, such as the determination of an appropriate actuation speed, and to actuate the clustered tensegrity.

Linear shell elements for active piezoelectric laminates

Piezoelectric composite laminates are a powerful material system that offers vast options to improve structural behavior. Successful design of piezoelectric adaptive structures and testing of control laws call for highly accurate, reliable and numerically efficient numerical tools. This paper puts focus onto linear and geometrically nonlinear static and dynamic analysis of smart structures made of such a material system. For this purpose, highly efficient linear 3-node and 4-node finite shell elements are proposed. Both elements employ the Mindlin-Reissner kinematics. The shear locking effect is treated by the discrete shear gap (DSG) technique with the 3-node element and by the assumed natural strain (ANS) approach with the 4-node element. Geometrically nonlinear effects are considered using the co-rotational approach. Static and dynamic examples involving actuator and sensor function of piezoelectric layers are considered.

Adaptive superelement modeling for progressive collapse analysis of reinforced concrete frames

A new adaptive superelement procedure for progressive collapse analysis of 2D reinforced concrete frames under column removal scenario is proposed. Superelement formulation is employed to reduce the computational cost. In addition, a new procedure for rigid body rotation correction is proposed to improve the accuracy of the superelement formulation. An error indicator is developed to monitor the propagation of the nonlinear zone during analysis. The adaptive analysis procedure is then formed by combining the error indicator with a reliable member and substructure collapse identification algorithm. Numerical examples are given to demonstrate the accuracy, robustness and efficiency of the modeling procedure. As the work involves establishing a novel concept to reduce computational effort when simulating the whole process of collapse, the authors only consider the impact energy of falling objects in a quasi-static manner through the use of dynamic increase factors, thereby obviating the need for time-consuming nonlinear structural dynamic analysis.