Nonlinear Dynamic Response Analysis Research Articles

Damage Analysis of Hanshin Expressway Viaducts during 1995 Kobe Earthquake. III: Three-Span Continuous Girder Bridges

Almost all the single reinforced concrete (RC) piers from P35 to P350 received consistently severe damage, considering the large residual inclination of piers included in earthquake-induced severe damage. However, some of the piers in the section from P35 to P350 remained lightly damaged, and this phenomenon is observed especially in many piers under fixed bearings in continuous girder bridges. In this study, using experimentally based models for metal bearings and installing them to an existing FEM code, a nonlinear dynamic response analysis of a continuous girder bridge system is conducted. It is shown that the results depend on the ground motion, but the fuse effect of the breaking of the bearings could have been a reason for the phenomenon.

A method for nonlinear dynamic response analysis of semi-infinite foundation using mapping

A method for nonlinear dynamic response analysis of semi-infinite foundation using mapping

Non-standard, explicit integration algorithms based on linearization for nonlinear dynamic response analysis

Non-standard finite difference methods for initial-value problems of second-order ordinary differential equations based on piecewise linearization are developed. Linearization methods provide piecewise analytical solutions which are globally differentiable, result in explicit finite difference algorithms, and are exact for constant coefficients equations with a right-hand side which depends linearly on time. The accuracy of these methods is assessed by obtaining the solutions of several conservative and dissipative, stiff and non-stiff, regular and chaotic problems, and comparing them with those of the MATLAB ode45 solver, state transition matrix algorithms and non-standard Euler techniques.

Nonlinear elastoplastic dynamic analysis of single-layer reticulated shells subjected to earthquake excitation

A nonlinear dynamic finite element technique is developed to analyze the elastoplastic dynamic response of single-layer reticulated shells under strong earthquake excitation, in which the nonlinear three-dimensional beam elements are employed. An elastoplastic tangent stiffness matrix of three-dimensional beam element is derived by using the updated Lagrangian formulation, in which the isotropic hardening model, the Von-Mises yield criterion and the Prandtl–Reuss flow relations are applied to this study. This procedure considers both geometric and material nonlinearities. In this paper, several condensation and reduction techniques in matrices and degrees of freedom are used to simplify the analysis. An incremental-iterative technique based on the Newmark direct integration method and the modified Newton–Raphson method is employed for obtaining the solutions of the nonlinear dynamic equilibrium equations. Moreover, an accurate method is developed to compute the large rotations of space structures. As a numerical example, the elastoplastic dynamic response of a single-layer reticulated shell under strong seismic excitation is investigated. It is shown through the numerical example that the method developed in this paper is efficient for the nonlinear dynamic response analysis and plastic design of space structures.

Two-step seismic limit state design procedure based on non-linear LRFD and dynamic response analyses

Recently, the limit state design (LSD) or performance-based design have got popularity in the field of building design in Japan as well as in other countries. In the two design methods the structural reliability theory plays an essential role in setting design criteria as well as demonstrating the target reliability level to society. However, the conventional load and resistance factor design (LRFD) has been basically formulated supposing that safety checking is done on the basis of linear assumption of member forces and displacement. Therefore, when applying the LRFD for seismic design, for more accurate treatment of the non-linearity, a new procedure has to be explored especially for the ultimate limit state. Although several procedures for the structural reliability evaluation, treating non-linear displacement responses, have been proposed, they require complex procedures that may not be used in the practical design process. Accordingly, for applying it to a seismic LSD format based on the probabilistic concept, it is essential to manage two important requirements at the same time, accuracy and simplicity of procedure. In the present study, a new design format using the following two-step procedure is proposed to maintain both accuracy and simplicity; (1) a non-linear LRFD formulation, and (2) a formulation based on non-linear dynamic response analysis. Also, two design examples are presented.

Effect of earthquake ground motions on fragility curves of highway bridge piers based on numerical simulation

AbstractFragility curves express the probability of structural damage due to earthquakes as a function of ground motion indices, e.g., PGA, PGV. Based on the actual damage data of highway bridges from the 1995 Hyogoken‐Nanbu (Kobe) earthquake, a set of empirical fragility curves was constructed. However, the type of structure, structural performance (static and dynamic) and variation of input ground motion were not considered to construct the empirical fragility curves. In this study, an analytical approach was adopted to construct fragility curves for highway bridge piers of specific bridges. A typical bridge structure was considered and its piers were designed according to the seismic design codes in Japan. Using the strong motion records from Japan and the United States, non‐linear dynamic response analyses were performed, and the damage indices for the bridge piers were obtained. Using the damage indices and ground motion indices, fragility curves for the bridge piers were constructed assuming a lognormal distribution. The analytical fragility curves were compared with the empirical ones. The proposed approach may be used in constructing the fragility curves for highway bridge structures. Copyright © 2001 John Wiley & Sons, Ltd.

橋梁全体系の地震時損傷評価のシステム化

This paper describes a newly developed probabilistic evaluation system of seismic damage states for bridge structures. At first, non-linear dynamic response analyses for the reinforced concrete bridge pier system were performed and the response values were calculated. And also, the probability of the first excursion for the threshold that corresponds to multiple damage states was calculated for each response value by the application of threshold-crossing in random vibration theory. Next, the damage transition probability matrix was constructed on the basis of probability of the first excursion. Then, the damage transition probability matrix conducted the damage transition model that included the damage interaction between elements. Finally, based on resulting probabilities of multiple damage states of structure elements, both functional and social damage states of the bridge structures damaged by earthquakes were evaluated. In addition, the development of a program for visualizing damage transition over time with graphical user interface made it possible to check the transition of structural damage easily in the behavior of the entire bridge structure during an earthquake. Then, by comparing cases with and without seismic retrofits, the effects of different seismic retrofit measures on seismic performance were evaluated.

Comparison of Analytical Fragility Curves for RC Bridge Piers Designed by Using Japanese Old and Recent Seismic Design Codes

To estimate damage levels (slight, moderate, extensive and complete) of highway bridge piers due to earthquakes, we need a set of fragility curves, which predict the damage level for a given level of ground motion indices (e.g., PGA, PGV and SI). Based on the actual damage data of highway bridges from the 1995 Hyogoken-Nanbu (Kobe) earthquake, a set of empirical fragility curvst) were developed. However, these fragility curves do not consider structural parameters and sffuctural responses. Considering structural parameters and variation of input ground motion, an analytical approach') wus adopted to construct such kind of fragility cufves. In this study, a hypothetical bridge is considered. Then its pier is modeled using the old (1964) and recent (1998) seismic design codes') for highway bridges in Japan' From a static analysis the yield force and yield displacement of the pier is obtained for the both cases. Then the damage analysis of the RC bridge pier is performed using the sffong ground motion records that were chosen from the Hyogoken-Nanbu earthquake. The damage indices are obtained from a nonlinear dynamic response analysis and finally using these damage indices and ground motion indices, the analytical fragility curves are constructed for the both cases. Then the fragility curves are compared to see the damage behavior of the piers due to seismic actlon.

Simplified Seismic Design Procedure for Geosynthetic-Lined, Solid-Waste Landfills

This paper critically reviews seismic design practices in light of the observed performance of landfills during recent earthquakes. Developments in these areas are summarized as follows: earthquake ground motions, dynamic waste fill properties, dynamic responses of geomembranes and their interfaces, nonlinear dynamic response analysis, and seismic stability evaluation. A newly developed simplified seismic analysis procedure that requires the most critical factors be addressed during a seismic performance evaluation is presented. The underlying seismic analysis procedure has been validated against observed performance of landfills shaken by the 1989 Loma Prieta and 1994 Northridge, California earthquakes. The procedure is comprehensive in that it requires: (i) characterization of the design bedrock motions in terms of intensity, frequency content, and duration; (ii) estimation of the seismic loading at the base and cover of the landfill; (iii) e valuation of performance in terms of seismically induced permanent deformations; and (iv) appropriate engineering judgment.

Stick-Slip Motion of Frictionally Damped Turbine Airfoils: A Finite Element in Time (FET) Approach

A method is proposed for analyzing the periodic stick-slip motion of a single degree of freedom model of frictionally damped turbine blades. The method of finite elements in the time domain (FET) is based on a Hamilton’s weak principle, paralleling the variational methods in elastostatics. It permits a complete determination of the hysteretic friction force, and results in a set of highly structured system equations. The method has a number of unique features, which are utilized to provide a simple yet efficient approach for predicting the steady-state response. When applied to a number of example problems, including systems with static friction and the excitation of multiple discrete frequencies, the FET method is demonstrated to be an efficient and reliable alternative technique for nonlinear dynamic response analysis.

Nonlinear analysis of a reinforced concrete building with a soft first story collapsed by the 1995 Hyogoken-Nanbu earthquake

A very new reinforced concrete (RC) building with a soft first story was collapsed by the 1995 Hyogoken-Nanbu earthquake. Nonlinear dynamic response analysis, where strength deterioration was considered in representing member nonlinearity, was conducted to simulate how the building behaved and eventually collapsed during the earthquake. The analysis was found to reproduce the observed damages well, such as residual displacement, mechanism and damages to members. It was also revealed that if first story mechanism might occur, the collapse could be unavoidable even for buildings with a base shear strength of as much as 60% of the total weight.

SEISMIC DESIGN AND RESPONSE OF BARE AND MASONRY-INFILLED REINFORCED CONCRETE BUILDINGS. PART I: BARE STRUCTURES

Eurocode 8 is applied for the complete design of 26 multi-storey reinforced concrete buildings to study its operationally and compare the implications of trading strength for ductility through designing the same structure for a different Ductility Class. The difference between the conventional full Capacity Design of columns in bending and the relaxed one allowed by Eurocode 8 is quantified, and the implications on the column capacities are examined. About half of the designed buildings, representative of the class of regular frames, are subjected to nonlinear dynamic response analyses to spectrum-compatible motions with intensities up to twice that of the design motion. Nonlinear modeling is very simple, but gives satisfactory agreement with available quasistatic or pseudodynamic test results on full scale structures. Results show that the three Ductility Classes of Eurocode 8 are essentially equivalent in terms of material quantities and seismic performance. Within the limitations of the nonlinear modelling, the response results suggest very satisfactory performance of structures designed to Eurocode 8, even under twice the design motion intensity. Softening of the structure due to concrete cracking and steel yielding significantly reduces the seismic force demands and contributes to the satisfactory performance, despite the increased P — 6 effects. Another important contributor to the good performance is the significant overstrength of the members considered in the analyses with their average as-built properties. Beam overstrength due to the contribution of the slab to flexural capacity is large enough to overcome the effects of the application of the relaxed Capacity Design rule to columns in bending. However, the resulting column plastic hinging does not lead to drift concentrations suggesting formation of storey-sway mechanisms.

Finite element analysis of nonlinear dynamic response of articulated towers

In the analysis of articulated towers, being a compliant structure, the nonlinear effects due to large displacement, large rotation and wave force are very important. The structural velocity and acceleration have also been included in computing the wave force. A three-dimensional nonlinear dynamic finite element analysis of articulated towers has been developed adopting a beam element. Updated Lagrangian formulation, which is computationally more effective, has been used in the formulation of stiffness matrices. The Wilson-θ method, Newmark-β method and Newton-Raphson method are used for the solution of nonlinear equations. The details of the program formulation have been highlighted. The results of the analyses have been presented, along with a comparison of the response of the structure with available results.

Design sensitivity analysis and optimization of nonlinear dynamic response for a motorcycle driving on a half-sine bump road

This paper analyses the design sensitivity of a suspension system with material and geometric nonlinearities for a motorcycle structure. The main procedures include nonlinear structural analysis, formulation of the problem with nonlinear dynamic response, design sensitivity analysis, and optimization. The incremental finite element method is used in structural analysis. The stiffness and damping parameters of the suspension system are considered as design variables. The maximum amplitude of nonlinear transient response at the seat is taken as the objective function during the optimization simulation. A more realistic finite element model for the motorcycle structure with elasto-damping elements of different material models is presented. A comparison is made of the optimum designs with and without geometric nonlinear response and is discussed.

Dynamics of unsymmetric piecewise-linear/non-linear systems using finite elements in time

The dynamic response and stability of a single-degree-of-freedom system with unsymmetric piecewise-linear/non-linear stiffness are analyzed using the finite element method in the time domain. Based on a Hamilton’s weak principle, this method provides a simple and efficient approach for predicting all possible fundamental and sub-periodic responses. The stability of the steady state response is determined by using Floquet’s theory without any special effort for calculating transition matrices. This method is applied to a number of examples, demonstrating its effectiveness even for a strongly non-linear problem involving both clearance and continuous stiffness non-linearities. Close agreement is found between available published findings and the predictions of the finite element in time approach, which appears to be an efficient and reliable alternative technique for non-linear dynamic response and stability analysis of periodic systems.

Direct integration method for stochastic finite element analysis of nonlinear dynamic response

Stochastic response of systems to random excitation can be estimated by direct integration methods in the time domain such as the stochastic central difference method (SCDM). In this paper, the SCDM is applied to compute the variance and covariance in response of linear and nonlinear structures subjected to random excitation. The accuracy of the SCDM is assessed using two-DOF systems with both deterministic and random material properties excited by white noise. For the former case, closed-form solutions can be obtained. Numerical results also are presented for a simply supported geometrically nonlinear beam. The stiffness of this beam is modeled as a random field, and the beam is idealized by the stochastic finite element method. A perturbation technique is applied to formulate the equations of motion of the system, and the dynamic structural response statistics are obtained in a time domain analysis. The effect of variations in structural parameters and the numerical stability of the SCDM also are examined.

Nonlinear dynamic response analysis of soil and soil-structure interacting systems : J.H. Prevost, Soil dynamics and geotechnical earthquake engineering. Proc. seminar, Lisboa, 1992, ed P. Seco e Pinto, (Balkema), 1993, pp 49–74

Nonlinear dynamic response analysis of soil and soil-structure interacting systems : J.H. Prevost, Soil dynamics and geotechnical earthquake engineering. Proc. seminar, Lisboa, 1992, ed P. Seco e Pinto, (Balkema), 1993, pp 49–74

Chaos, solitons & fractals—sample layout

The dynamic response and stability of a single-degree-of-freedom system with unsymmetric piecewise-linear/non-linear stiffness are analyzed using the finite element method in the time domain. Based on a Hamilton’s weak principle, this method provides a simple and efficient approach for predicting all possible fundamental and sub-periodic responses. The stability of the steady state response is determined by using Floquet’s theory without any special effort for calculating transition matrices. This method is applied to a number of examples, demonstrating its effectiveness even for a strongly non-linear problem involving both clearance and continuous stiffness non-linearities. Close agreement is found between available published findings and the predictions of the finite element in time approach, which appears to be an efficient and reliable alternative technique for non-linear dynamic response and stability analysis of periodic systems.

Nonlinear static and dynamic damped response of a composite rectangular plate resting on a two-parameter elastic foundation

Nonlinear static and dynamic response analyses of a clamped, rectangular composite plate resting on a two-parameter elastic foundation have been studied using von Karman's relations. Incorporating the material damping, the governing coupled, nonlinear partial differential equations are obtained for the plate under step pressure pulse load excitation. These equations have been solved by a one-term solution and by applying Galerkin's technique to the deflection equation. This yields an ordinary nonlinear differential equation in time. The nonlinear static solution is obtained by neglecting the time-dependent variables. The nonlinear dynamic damped response is obtained by applying the ultraspherical polynomial approximation (UPA) technique. The influences of foundation modulus, shear modulus, orthotropy, etc. upon the nonlinear static and dynamic responses have been presented.

A STUDY ON THE CYPRESS VIADUCT COLLAPSE AND SEISMIC PERFORMANCE OF A RETROFITTED BENT

This paper describes numerical simulation studies on the bent collapse of the Cypress Viaduct during the Loma Prieta Earthquake and on the seismic performance of the same type bent retrofitted. The purpose of the 1st simulation is to identify bent damage due to ground conditions and structural types and that of the 2nd simulation is to estimate seismic performance of the retrofitted bent. Systematized analyses provided following conclusions: 1) Amplified ground motion was appropriately predicted based on the multiple reflection theory, 2) Finite element nonlinear analyses provided good agreement with test results both of pre-retrofitted and retrofitted bents, 3) Nonlinear dynamic response analyses provided quantitative explanation on the relationship between ground conditions, bent types and bent collapses and also ensured sufficient seismic safety of the retrofitted bent.