Dynamic Analysis Of Structural Systems Research Articles

Analysis of Ground Motion Intensity Measures and Selection Techniques for Estimating Building Response

The structural response of buildings to earthquake shaking is of critical importance for seismic design purposes. Research on the relationship between earthquake ground motion intensity, building response, and seismic risk is ongoing, but not yet fully conclusive. Often, probability demand models rely on one ground motion intensity measure (IM) to predict the engineering demand parameter (EDP). The engineering community has suggested several IMs to account for different ground motion characteristics, but there is no single optimal IM. For this study, we compile a comprehensive list of IMs and their characteristics to assist engineers in making an informed decision. We discuss the ground motion selection process used for dynamic analysis of structural systems. For illustration, we compute building responses of 2D frames with different natural period subjected to more than 3500 recorded earthquake ground motions. Using our analysis, we examine the effects of different structural characteristics and seismological parameters on EDP-IM relationships by applying multi-regression models and statistical inter-model comparisons. As such, our results support and augment previous studies and suggest further improvements on the relationship between EDP and IM in terms of efficiency and sufficiency. Finally, we provide guidance on future approaches to the selection of both optimal intensity measures and ground motions using newer techniques.

Homotopy Perturbation–Based Dynamic Analysis of Structural Systems

AbstractThis paper presents the dynamic analysis of structural systems using the homotopy perturbation method (HPM). HPM was applied to the first-order differential equations of motion defined by t...

Análise dinâmica não linear de estruturas em contato com o solo

Structural elements, in many situations, are supported by other surfaces, such as soil, which may offer movement constraints in some directions. Therefore, the static and dynamic analysis of these elements considering their interaction with the soil becomes important in the design of a structural design. This paper presents the nonlinear dynamic analysis of structural systems considering such interaction through the Finite Element Method. A geometrically nonlinear beam-column element is used to model the structure, while the soil can be idealized as a continuum foundation, through the Winkler and Pasternak models. It is assumed that the foundation reacts to tension and compression stresses, so during the deformation process the structural elements are subjected to bilateral contact constraints. The analysis is based on the modeling of the structural system using the finite element method, where the Newmark integration method and Newton-Raphson iterative strategy are used in the process of solving the nonlinear dynamic equations in the time domain. Practical situations involving the interaction between soil and structure were evaluated during the study, showing the influence of contact in the natural vibration frequency and transient response of these structures.

Comparison of spectral density models to simulate wind records

Due to the lack of real wind records to perform dynamic analysis of structural systems, civil and structural engineers commonly use simplified and conservative approaches to consider the dynamic effects of wind. With the aim to provide wind records, several studies suggest that the use of spectral density models and configuration of basic wind speed and terrain roughness are adequate to simulate the velocity field of the turbulent wind; however, nowadays there is no enough information to conclude which is the best spectral density model to simulate wind records for various configurations of basic wind speed and terrain roughness. For this reason, in this paper different scenarios are simulated in order to study the behavior of six spectral density functions which are frequently used in wind engineering. It is observed that the models proposed by von Karman, von Karman-Harris and Solari are the best alternative to simulate wind records.

Dynamic Finite Element analysis of fractionally damped structural systems in the time domain

Visco-elastic material models with fractional characteristics have been used for several decades. This paper provides a simple methodology for Finite-Element-based dynamic analysis of structural systems with viscosity characterized by fractional derivatives of the strains. In particular, a re-formulation of the well-known Newmark method taking into account fractional derivatives discretized via the Grunwald–Letnikov summation allows the analysis of structural systems using standard Finite Element technology.

Estimating the annual probability of failure using improved progressive incremental dynamic analysis of structural systems

SUMMARYA methodology based on the progressive incremental dynamic analysis has been introduced in this paper to estimate the structural response and the corresponding annual probability of failure. The proposed methodology employs the genetic algorithm optimisation technique and an equivalent single‐degree‐of‐freedom system corresponding to the first‐mode period of a considered structure. The proposed methodology can significantly reduce the number of ground motion records needed for estimating the annual probability of failure. The numerical results indicate that the proposed method can effectively reduce the computational effort needed for computation of probability of failure for the first‐mode dominated structures, which is advantageous as the structure becomes larger. A relatively huge set of single‐degree‐of‐freedom systems as well as three multi‐degree‐of‐freedom systems including 3, 8 and 12 storeyed reinforced concrete structures was taken into account to test the proposed methodology. It has been shown that the probability of failure can be estimated within ±15% error with 95% confidence. The proposed method can speed up the decision‐making process in the probability‐based seismic performance assessment of structures, and it also incorporates the randomness of strong ground motions explicitly. Copyright © 2012 John Wiley & Sons, Ltd.

Selection of earthquake ground motion records: A state-of-the-art review from a structural engineering perspective

This paper reviews alternative selection procedures based on established methods for incorporating strong ground motion records within the framework of seismic design of structures. Given the fact that time history signals recorded at a given site constitute a random process which is practically impossible to reproduce, considerable effort has been expended in recent years on processing actual records so as to become ‘representative’ of future input histories to existing as well as planned construction in earthquake-prone regions. Moreover, considerable effort has been expended to ensure that dispersion in the structural response due to usage of different earthquake records is minimized. Along these lines, the aim of this paper is to present the most recent methods developed for selecting an ‘appropriate’ set of records that can be used for dynamic analysis of structural systems in the context of performance-based design. A comparative evaluation of the various alternatives available indicates that the current seismic code framework is rather simplified compared to what has actually been observed, thus highlighting both the uncertainties and challenges related to the selection of earthquake records.

Homogenised finite element for transient dynamic analysis of unconstrained layer damping beams involving fractional derivative models

This paper presents a homogenised finite element formulation for the transient dynamic analysis of asymmetric and symmetric unconstrained layer damping beams in which the viscoelastic material is characterised by a five-parameter fractional derivative model. This formulation is based on the weighted residual method (Galerkin’s approach) providing a fractional matrix equation of motion. The application of Grunwald-Letnikov’s definition of the fractional derivatives allows to solve numerically the fractional equation by means of two different implicit formulations. Numerical examples for a cantilever beam with viscoelastic treatment are presented comparing the response provided by the proposed homogenised formulation with that of Padovan, based on the principle of virtual work. Different damping levels and load cases are analysed, as well as the influence of the truncation and time-step. From the numerical applications it can be concluded that the presented formulation allows to reduce significantly the degrees of freedom and consequently the computational time and storage needs for the transient dynamic analysis of structural systems in which damping treatments have been applied by means of viscoelastic materials characterised by fractional derivative models.

Superelement method for transient dynamic analysis of structural systems

AbstractA superelement algorithm for the transient dynamic analysis of structural systems is presented. The method represents a generalization of existing static and dynamic superelement (substructure) algorithms. Natural frequencies and modal shapes of a fixed boundary substructure are used to obtain equations of motion of a superelement. An implicit time‐stepping algorithm is presented for the numerical solution of a resulting superelement system of equations of motion. Numerical examples are given to illustrate the presented approach. The method is believed to be effective for large‐scale problems of structural analysis.

EFFICIENT SOLUTION PROCEDURES FOR SYSTEMS WITH LOCAL NON‐LINEARITIES

This paper presents several methods for enhancing computational efficiency in both static and dynamic analysis of structural systems with localized non‐linear behaviour. A significant reduction of computational effort with respect to brute‐force non‐linear analysis is achieved in all cases at the insignificant (or no) loss of accuracy. The presented methodologies are easily incorporated into a standard computer program for linear analysis.

A modal superposition pseudo‐force method for dynamic analysis of structural systems with non‐proportional damping

AbstractA modal superposition pseudo‐force method for the dynamic analysis of structural systems with non‐proportional damping is presented. The method combines the advantages of the classical modal superposition method and the pseudo‐force method. When the system damping is non‐proportional, the dynamic equilibrium equations in generalized coordinates are coupled through the damping terms. In the present method, these coupled equations are solved by an iterative process in which the coupling terms are treated as pseudo‐forces. A proof of the convergence of the iterative process is given. Numerical examples show the good convergence characteristics of the process and the good accuracy of the obtained results.

CAL-GRAF—a computer-graphics supplement for CAL

The computer analysis language CAL developed by Wilson[1] has proven to be a valuable tool in the teaching of modern methods of static and dynamic analysis of structural systems. The language has now been extended to cover the fundamental operations involved in composing graphic displays of various computational aspects of these methods on a screen and on paper. The computer graphics supplement CAL-GRAF covers the graphical representation of GRids And Functions. The purpose of the supplement is to allow students to graphically check the geometry and topology of their models, and to help them to interpret the results of their computations, such as, for example, displacements and stress resultants. CAL-GRAF consists of four types of operations: service operations, geometry processing, plotting of grids, and plotting of functions. Operations for extracting element topology tables and node and element related results have been added to CAL. Following the underlying philosophy of CAL, the composition of a graphical frame is subdivided into a logical sequence of separated CAL and CAL-GRAF operations. The new operations are formulated in the general form of the CAL operations and are embedded in the data management system of CAL. Examples are presented of applications to membrane/plate models with a plate element[2] which has recently been added to CAL.

A Generalized Coupling Technique for the Dynamic Analysis of Structural Systems

A Generalized Coupling Technique for the Dynamic Analysis of Structural Systems

Direct dynamic analysis of shells of revolution using high-precision finite elements

For the transient dynamic analysis of structural systems, the direct numerical integration of the equations of motion may be regarded as an alternative to the mode superposition method for linear problems and a necessity for nonlinear problems. When compared to a modal superposition solution, the direct integration approach is attractive in that the eigenvalue problem is avoided. Depending on the amount of information required from the dynamic analysis, e.g. frequencies, frequencies and mode shapes, and/or a complete time history, a direct integration scheme may prove to be more efficient than a modal superposition solution for some linear problems as well. The purpose of this study is to develop and demonstrate a direct integration algorithm which is compatible with an existing high-precision rotational shell finite element. Excellent comparative efficiency for static problems was achieved with this element by the incorporation of the exact geometry, the utilization of high-order interpolation polynomials and, yet, the retention of only a minimum number of nodal variables in the global formulation. Likewise, accurate and efficient results for the free vibration analysis of rotational shells were facilitated by the inclusion of a consistent mass matrix and the utilization of a rationally justified kinematic condensation procedure. The approach to the direct integration stage is strongly tempered by the established characteristics of this element which enable a given shell to be modeled accurately in the spatial domain with a comparatively coarse discretization. The equations of motion for a shell of revolution under conservative loading are derived from Hamilton's variational principle and specialized for the discretization of a rotational shell into curved shell elements. Degrees of freedom in excess of those required to establish minimum (C°) continuity at the nodal circles are eliminated through kinematic condensation. Some guidance as to the proper order of the polynominal approximations for a dynamic analysis is provided by earlier free vibration studies. Whereas the condensation is exact for static problems, it is only approximate for dynamic response and it was found that the accuracy of the eigenvalues obtained for the reduced problem decreases with increasing order of the condensed functions. This tendency is counted by the desirability of using sufficiently high-order interpolations so as to permit accurate stress computations, both at the nodal circles and between nodes since a coarse discretization is necessary to realize maximum efficiency. It was found that cubic polynomials were generally satisfactory from both standpoints, except in localized regions of high stress gradients where quintic polynomials were employed. The finite element discretizations for the direct integration studies were selected on this basis. For the high-precision finite element at hand, the efficiencies achieved in the space domain are demonstrated by the ability to achieve precise solutions with relatively coarse discretization patterns. The resulting comparatively large elements are not subject to accurate representation by diagonal mass matrices so that an implicit, consistent mass approach is followed. Efficiency in the time domain as well rests on the successful modeling of rotational shells subject to dynamic loading using coarse discretitations in space and large increments in time. Computational efficiency and accuracy are demonstrated for various problems documented in the literature, including a shallow spherical cap subject to a step pulse and a hyperboloidal shell under a simulated dynamic wind pressure.

Dynamic analysis of structural systems using component modes

A method is developed for analyzing complex structural systems that can be divided into interconnected components. Displacements of the separate components are expressed in generalized coordinates that are defined by displacement modes. These are generated in three categories: rigid-body, constraint, and normal modes. Rigid-body modes are convenient where displacements are denned in inertial space for dynamic analysis. Constraint modes are included to treat redundancies in the interconnection system. Normal modes define displacements relative to the connections. Generalized mass, stiffness, and damping matrices are determined for each component, as are generalized forces. The requirement of system continuity gives rise to equations of displacement compatibility at the connections. These serve as equations of constraint among the component coordinates and are used to construct a transformation relating component coordinates to system coordinates. This transformation is used to derive system properties and forces from component properties and forces. System equations of motion are formulated and solved to determine system response. Component responses are found using the transformation. Connection forces are computed from the component equations. Each component can then be isolated and treated separately.