Fuzzy-Affine Approach in Dynamic Analysis of Uncertain Structural Systems

A 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.

Hysteresis is a non-linear phenomenon exhibited by the mechanical systems. Beyond elastic limit the loading and unloading path of most of the system will differ and that nonlinear path is indicated by hysteresis. The reason for shape of hysteretic cure may due to either changes in material properties beyond the elastic range or due to the changes in structural geometry because of subjected load. This response is a function of both immediate deformation and the previous residual deformation acted on it since it represents the dissipated energy of structure. The hysteretic characteristics or degrading characteristics includes pinching, stiffness degradation, load deterioration, and sliding. A study of four commonly available hysteresis models, which are Bouc Wen Model, Mostaghel Model, Menegotto Pinto Model and Preisach Model were briefly reviewed and discussed in this section and the outcome of this study is the best fitted model for the nonlinear analysis. The scope of the work is to simulate nonlinear response of the building frame subjected to earthquake excitation in a most effective way.

DYNOR is a computer program that was developed to analyze the response of structural systems to the vibratory ground motion of earthquakes as well as sinusoidal motion.This program can be applied to structural systems that can be mathematically idealized with beam-type elements which have no more than three degrees of freedom per joint.The input for the earthquake vibratory motion may be either timehistory or response-spectrum data.The program is written in Fortran IV language, and it is operable on the IBM 360/91 computer at Oak Ridge National Laboratory.The supporting theory and procedures are described and detailed instructions for the use of DYNOR are presented herein.

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.

An equivalent stiffness approach for modelling the behaviour of compression members according to Eurocode 3

A meshless Chebyshev collocation method for eigenvalue problems of the Helmholtz equation

The hyperbolic quadratic eigenvalue problem (HQEP) was shown to admit Courant–Fischer type min–max principles in 1955 by Duffin and Cauchy type interlacing inequalities in 2010 by Veselić. It can be regarded as the closest analog (among all kinds of quadratic eigenvalue problem) to the standard Hermitian eigenvalue problem (among all kinds of standard eigenvalue problem). In this paper, we conduct a systematic study on the HQEP both theoretically and numerically. On the theoretical front, we generalize Wielandt–Lidskii type min–max principles and, as a special case, Fan type trace min/max principles and establish Weyl type and Wielandt–Lidskii–Mirsky type perturbation results when an HQEP is perturbed to another HQEP. On the numerical front, we justify the natural generalization of the Rayleigh–Ritz procedure with existing principles and our new optimization principles, and, as consequences of these principles, we extend various current optimization approaches—steepest descent/ascent and nonlinear conjugate gradient type methods for the Hermitian eigenvalue problem—to calculate a few extreme eigenvalues (of both positive and negative type). A detailed convergence analysis is given for the steepest descent/ascent methods. The analysis reveals the intrinsic quantities that control convergence rates and consequently yields ways of constructing effective preconditioners. Numerical examples are presented to demonstrate the proposed theory and algorithms.

The selection of representative ground motions (GMs) for dynamic analysis of soil and structural systems considering soil–structure interaction (SSI) is critical for accurately predicting their performance under seismic loads. Site-specific GMs are typically generated first by selecting a set of seed time histories and then modifying them by matching to the target spectrum using either Time-Domain (TD) or Frequency-Domain (FD) techniques. While previous studies have recommended TD over FD techniques based on 1D site response analysis and engineering judgment, their effects on predicting soil and structural performance, considering SSI, are poorly understood in a 3D nonlinear domain. In this study, a set of seed ground motions corresponding to 3% and 50% in 75 years hazard conditions specific to Charleston, SC, was selected and modified using TD and FD techniques. Then, sixteen dynamic nonlinear 3D finite element simulations of a bridge bent supported by a 2 × 2 pile group were performed using the general-purpose finite element software ABAQUS by applying the motions generated using the FD and TD techniques. The geotechnical properties specific to Charleston were obtained from published documents, and the stress–strain behavior of the soil was represented by the Drucker-Prager model. The soil domain was spatially discretized with 3D brick elements. The structural components were represented by linear elastic beam elements. Results indicate that FD matching tends to distort nonstationary waveform components, particularly in displacement time histories. In contrast, TD matching preserves waveform features, including phase and frequency content, more effectively. Despite this, these distortions in FD-matched motions did not lead to substantial differences in structural response in most cases. However, noticeable response variations were observed in the 1 to 2.5-s period range. Overall, TD matching exhibited greater consistency and reliability in preserving input motion characteristics and is recommended for use in nonlinear SSI analyses.

Linear modal analysis has provided a robust and eminently useful framework for the analysis of structural dynamic systems. Considerable attention has been directed towards the development of a nonlinear variant of modal analysis that is effective in the presence of nonlinearities. Thus far, essentially two approaches to constructing nonlinear normal modes (NNM) have gained traction. The first was that of Rosenberg, whereby the modes are defined in terms of synchronous motions of the structure. The second is the geometrically more general approach of Shaw and Pierre, wherein modes are defined on invariant manifolds of the phase space of the system. A recent third approach from Worden and Green proposes a statistical definition of a nonlinear normal mode. Under this framework, the modal coordinates are defined by latent directions in the configuration space that result in statistically uncorrelated time series. This paper examines the properties of the NNMs generated by this framework, by applying techniques from nonlinear system identification (NLSI). Both linear and nonlinear time domain models are fitted to the physical and modal coordinates of a two degree-of-freedom simulated system with a cubic nonlinearity. It is demonstrated in this work, that the NNMs generated are able to decompose the system into independent functionals, and that the modal transformation generalises to lower excitation levels, while maintaining excellent reconstruction of the physical displacements.

The [formula omitted]-compound of a difference–algebraic system

Modified subset simulation method for reliability analysis of structural systems

In this chapter, the functionality of the proposed Octave- and MATLAB-compatible network-based observability and controllability analysis of dynamical systems (NOCAD) toolbox is introduced. This toolbox provides a set of methods, which enables the structural controllability and observability analysis of dynamical systems presented in the earlier chapters. The implemented functions are also demonstrated.

18 - Expression Programming Techniques for Formulation of Structural Engineering Systems

Dielectric waveguide formulations usually result in generalized eigenvalue problems which are non-Hermitian in nature. We solve this class of problems by a two stage process. In the first stage, a standard lumped eigenvalue problem is solved for a few eigenpairs of interest (usually the guided modes) by Arnoldi's method accelerated by Chebyshev polynomials. The solution is then refined for the actual unlumped generalised eigenvalue problem by using inflated inverse iteration. After the eigenvalues and eigenvectors have been calculated at the first point (preferably the highest frequency), the eigenpairs for the rest of the frequencies of interest are calculated for progressively smaller frequencies by inflated inverse iteration alone, using the eigenvectors of the last step as the initial guess. To demonstrate the efficacy of this method, we use a variational formulation for anisotropic, dielectric waveguides based only on the E/sub s/ components or only on the H/sub s/ components of the electromagnetic fields that was presented by Chew and Nasir (1989). In this formulation it was shown that due of the imposition of the divergence condition the spurious waveguide modes were eliminated.

Integrated structural analysis system with on-line coordinate-measuring machines for car body panels