Nonlinear Dynamic Analysis Of Structures Research Articles

Development of box-shaped steel slit dampers for seismic retrofit of building structures

In this study a steel slit damper is developed by combining four steel slit plates to be used for seismic retrofit of structures. The proposed damper consists of four slit plates integrated into a box shape, and can produce larger damping force in relatively small size compared with the conventional slit plate dampers composed of single slit plate. Cyclic loading tests of two damper specimens are carried out to evaluate their seismic energy dissipation capability. The slit dampers are applied to seismic retrofit of an existing reinforced concrete structure using the procedure developed based on the capacity spectrum method. Nonlinear dynamic analysis of the model structure shows that the dampers installed using the proposed procedure are effective in restraining the building displacement within a given target performance limit state. The time history of the hysteretic energy dissipation shows that most seismic energy is dissipated by the dampers while the structural elements mostly remain elastic.

New speedup algorithms for nonlinear dynamic time history analysis of supertall building structures under strong earthquakes

SummarySome speedup algorithms oriented to improving computational efficiency of nonlinear dynamic time history analysis of supertall buildings structures excited by strong earthquakes are proposed. In order to minimize Jacobian factorizations, the inexact Newton algorithm combined with the sparse Cholesky matrix factorization (INC) is suggested with an unbalance‐independent relation for the determination of a forcing term in the INC. Further, some shared memory parallel computing techniques are incorporated into the state transformation procedures developed previously (parallel state transformation procedure) and the matrix factorization (parallelized factorization) for full utilization of the resources of an ordinary personal computer. All the algorithms are integrated in a finite element program specialized in time history analysis of aseismic supertall building structures, with some features from OpenSees. Computational efficiency, as well as accuracy, of the proposed speedup algorithms is demonstrated on one 12‐story reinforced concrete frame (K1) and 4 frame‐core‐tube supertall buildings (S1–S4). The results from the demonstration indicate that, as the number of degrees of freedom increases, the proportion of time consumed in Jacobian factorization becomes relatively more dominant. The combination of the INC and the parallelized factorization can achieve better acceleration performance in this case. Factors associated with the forcing term of the INC have much influence on computational efficiency and should be selected based on building scale. Combination of all the algorithms in the biggest model (S4) yields an average of 28.72 of acceleration ratio even with peak ground acceleration equal to 3.2 g. In all cases considered, a desirable agreement in structural response is always reached between conventional time history analysis method and the method using the proposed speedup algorithms.

Local Subdomain Formulation for Structural Nonlinear Dynamic Finite Element Analysis

The local subdomain formulation (LSF) for nonlinear dynamic analysis of large-scale structures is presented using domain decomposition and preconditioned conjugate gradient (PCG) technique. The formulation operates on the local unassembled subdomain matrices and the preconditioner is constructed using the local subdomain information. Newmark- average acceleration technique is employed for time integration. Numerical results indicate that the proposed LSF formulation is superior in performance when compared to the conventional domain decomposition algorithms.

Residual seismic load capacity of fire-damaged rubber bearings of r.c. base-isolated buildings

Abstract Irreversible deterioration in the base-isolation system of framed buildings exposed to high temperatures during a fire has raised concerns about the reliability of elastomeric isolators (e.g. High-Damping-Laminated-Rubber Bearings, HDLRBs, and Lead-Rubber Bearings, LRBs) during seismic aftershocks. The main objective of this research is to evaluate mechanical property loss of HDLRBs and LRBs, based on prediction of their temperature profile. To this aim, transient analysis corresponding to the Eurocode 1 time-temperature fire curves, carried out by means of three-dimensional finite element modelling of HDLRBs and LRBs, is compared with steady response, defined as a heat conduction problem of a constant flux in an infinite circular cylinder. A 200 °C isotherm method is used to evaluate reduction of the mechanical properties of the fire-damaged isolators. To verify the damage in the nonlinear seismic response following fire, a numerical investigation is carried out on six-storey reinforced concrete (r.c.) base-isolated framed buildings comprising a basement and five storeys above ground. Three scenarios are considered, with the fire compartment confined to the area of the base-isolated level (i.e. F0), first level of the superstructure (i.e. F1) and both levels (i.e. F0/1). Base-isolated structures in a no fire situation are compared with those in the event of fire at different durations of resistance. A multi-record nonlinear incremental dynamic analysis of the test structures considers two sets of seven near- and far-fault earthquakes, respectively. Fire loading before earthquake confirms significant reduction of the mechanical and geometrical properties of the HDLRBs and LRBs inducing amplification in the structural response of base-isolated structures.

Fatigue limit state design of fast boats

Typically, the dominant load for the structural design of a planing hull is slamming, while sailing fast at head seas. The slamming is a violent fluid structure interaction, where dynamics, hydro-elasticity, and nonlinear structural effects may be important. Considering these effects in a rational design may reduce the scantlings as compare to design by rules, which assess the scantlings by applying a quasi-static design pressure and linear beam theory. More substantial reduction of the scantlings is expected in a limit state design, where extreme loading conditions and flexible structure increase the importance of hydro-elasticity and non-linearity. While applied rules specify allowable stresses that typically provide a service life of 20 years, without the need to check for fatigue; rational limit state design must incorporate the Fatigue Limit State (FLS). This paper presents a rational limit state design method for planing hulls, which apply hydro-elastic nonlinear dynamic structural analysis, to assess the fatigue service life, based on an operation plan specified by the client. The method integrates design rules with direct analysis of fluid-structure interaction and principles of representation of random sea, to a practical design procedure. Furthermore, a parametric analysis is applied to provide a database of 450 cases that may be used by designers for the assessment of fatigue service life in a practical range of geometrical parameters and service conditions. A design example demonstrates the potential of the method to reduce the scantlings.

Homogenization towards a mechanistic Rigid Body and Spring Model (HRBSM) for the non-linear dynamic analysis of 3D masonry structures

A mechanistic model with rigid elements and interfaces suitable for the non-linear dynamic analysis of full scale 3D masonry buildings is presented. The model relies into two steps: in the first step, a simplified homogenization is performed at the meso-scale to deduce the mechanical properties of a macroscopic material, to be used in structural applications; the second step relies into the implementation of a Rigid Body and Spring Model (RBSM) constituted by rigid elements linked with homogenized interfaces. In the homogenization step, a running bond elementary cell is discretized with 24 three-node plane-stress elastic triangular elements and non-linear interfaces representing mortar joints. It is shown how the mechanical problem in the unit cell is characterized by few displacement variables and how homogenized stress–strain curves can be evaluated by means of a semi-analytical approach. The second step relies on the implementation of the homogenized curves into a RBSM, where an entire masonry structure can be analyzed in the non-linear dynamic range through a discretization with rigid elements and inelastic interfaces. Non-linear structural analyses are conducted on a church facade interconnected with a portion of the perpendicular walls and on a small masonry building, for which experimental and numerical data are available in the literature, in order to show how quite reliable results may be obtained with a limited computational effort.

A 3-NODE PIEZOELECTRIC SHELL ELEMENT FOR LINEAR AND GEOMETRICALLY NONLINEAR DYNAMIC ANALYSIS OF SMART STRUCTURES

Composite laminates consisting of passive and multi-functional materials represent a powerful material system. Passive layers could be made of isotropic materials or fiber-reinforced composites, while piezoelectric ceramics are considered here as a multi-functional material. The paper is focused on linear and geometrically nonlinear dynamic analysis of smart structures made of such a material system. For this purpose, a linear 3-node shell element is used. It employs the Mindlin-Reissner kinematics and the discrete shear gap (DSG) technique to alleviate the transverse shear locking effects. The electric potential is assumed to vary linearly through the thickness for each piezoelectric layer. A co-rotational formulation is used to handle the geometrically nonlinear effects. A number of examples involving actuator and sensor application of piezoelectric layers are considered. For the validation purposes, the results available in the literature and those computed in Abaqus are used as a reference.

Non-Linear Dynamic Analysis of RC-Framed Structure

Non-Linear Dynamic Analysis of RC-Framed Structure

Direct‐Iterative Hybrid Solution in Nonlinear Dynamic Structural Analysis

AbstractAlthough many advanced sparse direct solvers are widely used in structural analysis, these often require longer computing times than iterative solvers for well‐conditioned structural systems. However, iterative solvers cannot efficiently solve an ill‐conditioned system when a structure becomes highly nonlinear. This work proposes a hybrid solution integrating a direct solver and an iterative solver to reduce overall computing time in solving a series of linear equations arising from nonlinear dynamic structural analysis. The hybrid solution selects the iterative solver, which reuses the factorized matrices for preconditioning, and switches to the direct solver in the initial stage or when factorized matrices need updating. The performance of the hybrid solution is tested on the OpenSees platform. The results show that the hybrid solution outperforms the direct solver, even when the structure becomes highly nonlinear during analysis.

Reduced order models for nonlinear dynamic analysis of structures with intermittent contacts

The forced response of structures with complex geometry and intermittent contacts is nonlinear due to contact breathing phenomena that occur during vibration. Therefore, calculation times to predict such responses can be extremely long especially because highly refined finite element models are necessary to properly model geometrically complicated structures. To alleviate this issue, reduced order models can be very beneficial as they can dramatically speed up the analysis process by reducing the size of the system and thus the calculation times. In this paper, a reduced order modeling method for the forced response of structures with intermittent contacts is developed. The proposed approach assumes that the dynamics of the nonlinear system in the frequency range of interest is spatially correlated. The spatial correlation can be dominated by normal modes of the open (or sliding) linear system. Nonetheless, the boundary conditions of a vibrating structure with intermittent frictionless contacts vary in time (i.e. at any time t the contacts are partly open and closed), and the actual extent of the contact area changes over time. Here, this observation is complemented by the assumption that, given the frequency range of the harmonic excitation force, the system dynamics is dominated by one of the modes of either the open or the sliding system, and thus the time evolution of the contact area can be estimated by knowing (a) the normal penetration at the contact node pairs at rest due to pre-stress, and (b) the vector of normal relative displacements at the contact nodes of that dominant mode. As a result, a set of normal modes – referred to as piecewise linear modes – is computed, by imposing special boundary conditions at the nodes lying on the contact surfaces, and a reduction basis is selected and used to reduce the size of the model of the system. Two numerical test cases, specifically a cracked plate and two coaxial cylinders are used for validation. Results show that the proposed method allows to accurately compute the nonlinear forced response of structures with intermittent contacts both in case of zero gap and in case of initial pre-stress at the contacts.

Nonlinear Dynamic Analysis of Base-Isolated Structures Using a Mixed Integration Method: Stability Aspects and Computational Efficiency

Nonlinear Dynamic Analysis of Base-Isolated Structures Using a Mixed Integration Method: Stability Aspects and Computational Efficiency

Nonlinear Dynamic Analysis of Base-Isolated Structures Using a Partitioned Solution Approach and an Exponential Model

Nonlinear Dynamic Analysis of Base-Isolated Structures Using a Partitioned Solution Approach and an Exponential Model

Parallel Algorithm for Structural Nonlinear Dynamic Finite Element Analysis

The parallel algorithm for nonlinear dynamic analysis of large structures is presented using domain decomposition and preconditioned conjugate gradient(PCG) technique. In the formulation called the global interface formulation(GIF), the PCG algorithm is applied on the assembled interface stiffness coefficient matrices of all subdomains. Newmark-β average acceleration technique is employed for time integration. Numerical results indicate that the proposed GIF formulation is superior to the conventional domain decomposition algorithm.

A New Explicit Time Integration Scheme for Nonlinear Dynamic Analysis

An explicit time integration method is presented for the linear and nonlinear dynamic analyses of structures. Using two parameters and employing the Taylor series expansion, a family of second-order accurate methods for the solution of dynamic problems is derived. The proposed scheme includes the central difference method as a special case, while damping is shown to exert no effect on the solution accuracy. The proposed method is featured by the following facts: (i) the relative period error is almost zero for specific values of the parameters; (ii) the numerical dissipation contained can help filter out spurious high-frequency components; and (iii) the crucial lower modes are generally unaffected in the integration. Although the proposed method is conditionally stable, it has an appropriate region of stability, and is self-starting. The numerical tests indicate the improved performance of the proposed technique over the central difference method.

A design method for planing hulls, considering hydro-elasticity and nonlinear dynamic structural response

ABSTRACTTypically, the dominant load for the structural design of a planing hull is slamming, while sailing at high speed in head seas. Applied rules assess the strength of the members of the hull by applying beam theory and a static design pressure, which represents the slamming load. Actually, the slamming is a violent fluid structure interaction, where dynamics, hydro-elasticity, and nonlinear structural effects may be important. This paper presents a design method for planing hulls, which considers hydro-elasticity and nonlinear dynamic structural analysis. The method combines rules calculations with analysis of fluid–structure interaction to a practical design procedure. Furthermore, a parametric analysis is applied to provide a database of 225 cases that may be used by designers for a preliminary assessment in a practical range of geometrical parameters and service conditions. Finally, a design example demonstrates a saving of 20% of the bottom plates thickness, relative to design by rules.

A macro‐model with nonlinear springs for seismic analysis of URM buildings

SummarySeismic assessment of existing unreinforced masonry buildings represents a current challenge in structural engineering. Many historical masonry buildings in earthquake regions were not designed to withstand seismic loading; thus, these structures often do not meet the basic safety requirements recommended by current seismic codes and need to be strengthened considering the results from realistic structural analysis. This paper presents an efficient modelling strategy for representing the nonlinear response of unreinforced masonry components under in‐plane cyclic loading, which can be used for practical and accurate seismic assessment of masonry buildings. According to the proposed strategy, generic masonry perforated walls are modelled using an equivalent frame approach, where each masonry component is described utilising multi‐spring nonlinear elements connected by rigid links. When modelling piers and spandrels, nonlinear springs are placed at the two ends of the masonry element for describing the flexural behaviour and in the middle for representing the response in shear. Specific hysteretic rules allowing for degradation of stiffness and strength are then used for modelling the member response under cyclic loading. The accuracy and the significant potential of the proposed modelling approach are shown in several numerical examples, including comparisons against experimental results and the nonlinear dynamic analysis of a building structure. Copyright © 2016 John Wiley & Sons, Ltd.

PDEM-Based Perspective to Probabilistic Seismic Response Analysis and Design of Earthquake-Resistant Engineering Structures

AbstractA perspective based on the probability density evolution method (PDEM) to the probabilistic seismic response analysis and design of earthquake-resistant engineering structures is provided in this paper. The development of characterization of randomness in seismic ground motions and nonlinear seismic dynamic response analysis of engineering structures are first reviewed and found to be almost independent, which hinders rapid adoption of refined methods for seismic design. The approaches for stochastic dynamics, which is expected to bridge the above gap, in earthquake engineering are revisited, which results in the statement that more physically based methodology is in urgent need for nonlinear stochastic dynamic response analysis of structures. This is the role that the PDEM will play, and thus the theoretical basis and some new advances of PDEM, including the ensemble evolution form of the generalized density evolution equation, ensemble evolution–based dimension reduction of Fokker-Planck-Kolmogo...

Development of diaphragm connector elements for three-dimensional nonlinear dynamic analysis of precast concrete structures

Diaphragm connector elements were developed for three-dimensional finite element models of precast concrete structures used in nonlinear time history analyses. The use of discrete elements for the diaphragm connectors permits the direct evaluation of local force and deformation demands, information needed in calibrating design factors for a new diaphragm seismic design methodology. This article describes the element formulation. The connector elements consist of assemblages of standard elements readily available in most finite element software libraries. The connector element calibration is based on full-scale testing of common precast diaphragm connectors. In these tests, the connector exhibited hysteretic pinching, stiffness/strength degradation, and slip mechanisms. The diaphragm connector elements were constructed to capture these behaviors to an accuracy sufficient for establishing viable design factors, while still appropriate for insertion into large degree-of-freedom models. The models are validated against the results of simulation-driven tests for critical precast diaphragm joints and a half-scale shake table test.

Comparison between Different Shapes of Structure by Response Spectrum Method of Dynamic Analysis

Several procedures for non-linear static and dynamic analysis of structures have been developed in recent years. In this paper, the response spectrum analysis is performed on two different shapes i.e. regular and irregular shape of structure by using STAAD PRO. And the comparison results are studied and compared accounting for the earthquake characteristics and the structure dynamic characteristics. As the results show that the earthquake response peak values and the main response frequencies are very close and comparable. It can be referred to by the engineering applications.

The Analysis of Bearing Capacity of Axially Compressed Cold Formed The Analysis of Bearing Capacity of Axially Compressed Cold Formed Steel Members

This paper presents a calculation method for axially compressed cold formed stainless, high strength and carbon steel profiles. Results of different authors in this field published in international journals depict current trends in this field. Paper also presents author’s numerical and experimental analysis of cold-formed centrally compressed elements. Numerical analysis was carried out by finite element method and program for the nonlinear static and dynamic structural analysis - PAK. The results obtained by experimental and numerical methods included boundary conditions, maximum force, buckling curve etc. Small difference observed in the values obtained by these different methods. Results werw compared to values predicted by international designing code in order to analyze if they are too conservative for cold formed steel sections.