Static Structural Response Research Articles

Finite element method based Monte Carlo filters for structural system identification

The paper proposes a strategy for combining two powerful computational procedures, namely, the finite element method (FEM) for structural analysis and particle filtering for dynamic state estimation, to tackle the problem of structural system parameter identification based on a set of noisy measurements on static and (or) dynamic structural responses. The proposed identification method automatically inherits the wide ranging capabilities of both FEM and particle filtering procedures thereby enabling the treatment of many complicated features of system identification problems, namely, imperfections in mathematical models for structural behavior, noisy and spatially incomplete measurements, nonlinear models for process and measurement equations, possible non-Gaussian nature of system and measurement noises, and dynamic and (or) static behaviors of the structure. Additionally, the authors propose a method that permits assimilation of measurements from multiple static and (or) dynamic tests and from multiple sensors in the system identification procedure in a unified manner. The paper describes how finite element models residing in commercially available softwares can be made to communicate with a database of measurements via a particle filtering algorithm developed on the Matlab platform. This leads to a probabilistic description of system parameters to be identified. Illustrative examples consider measurements from computational models, laboratory and field tests. These illustrations include studies on a rubber sheet with a hole undergoing large deformations, laboratory investigations on a single span beam and field investigations on an existing multi-span masonry arch bridge subjected to diagnostic moving loads.

Visualisation, modelling and parametric analysis of an elevated guideway structure for condition assessment

Several studies on analytical and experimental evaluation of various types of highway bridges are available in the literature. However, there are very few studies on the modelling and analysis of transit guideways, which are unique structures in terms of their geometric and structural details. This study explores the condition of an existing transit guideway system that has been in service for 35 years. The structural system is composed of six-span continuous prestressed concrete bridge segments. The overall guideway system incorporates a number of continuous bridges that share common design details, geometries and loading conditions. The original design analysis of the structure was based on certain simplifying assumptions of complicated mechanisms such as rigid behaviour over supports and simplified tendon–concrete–steel plate interactions. The current objective is to conduct a representative study for a more accurate understanding of the structural system and its behaviour for decision making. Due to the unique and complex structural details, it is shown that visualisation is the first step for conceptualising the system behaviour. Then, the structural behaviour is described using finite element models, and static and dynamic parameter sensitivity studies are conducted for characterising the performance under service loads. Parameter sensitivity studies consider the effect of changing critical parameters, including material properties, prestress loss, and boundary and continuity conditions, on the static and dynamic structural response. This study provides information about critical components of the guideway. It serves as a benchmark, presenting a procedure and methodology for modelling a guideway structure for future evaluations, to help make better decisions for operations, maintenance and safety requirements.

Static response and reliability analysis of structural systems with random and interval properties

This paper presents the displacement, stress and reliability analysis of structures with a mixture of random and interval parameters under uncertain static loads. The structural displacement and stress responses are random interval variables when some structural parameters/loads are modelled as random variables and others are considered as intervals. The random interval perturbation method and random interval moment method are employed to predict the random interval structural response. The structural reliability is not a deterministic value but an interval as the structural responses are random interval variables. The expressions for lower and upper bounds of reliability index, probability of failure and reliability of structural elements and systems are then developed by using the combination of the structural reliability theory and interval approach. Truss and frame structures are used as examples to demonstrate the validity and feasibility of the presented methods. The probabilistic and interval characteristics of structural static response and reliability are investigated and some useful conclusions are given.

Effect of Bimodularity on Dynamic Response of Cross-ply Conical Panels

The effect of bimodularity ratio on free vibration characteristics of cross-ply conical panels of various geometry and lamination scheme is studied. Forced vibration response is also studied for a typical case. The formulation is based on first order shear deformation theory and Bert’s constitutive model. An iterative eigenvalue approach is employed to obtain the positive and negative half cycle free vibration frequencies. Galerkin’s approach in time domain is used to obtain the frequency response. It is interesting to note that there is a significant difference between positive and negative half cycle frequencies depending on panel parameters. Also, there is a significant difference in positive and negative half cycle forced response amplitudes due to bimodularity. Bimodularity, the different behavior of material in tension and compression, affects the static and dynamic response of structures. Few studies on static analysis of bimodulus laminated cross-ply composite shells and dynamic analysis of cross-ply panels have been presented [1-4]. To the best of the authors’ knowledge, the work on the analysis of bimodular laminated cross-ply conical shell panels is not dealt in the literature. The effect of bimodularity ratio on free and forced vibration characteristics of cross-ply conical panel is important for design of such structures under dynamic loading condition. Here, the dynamic analysis of cross-ply laminated conical panels of bimodulus material is carried out using finite element method and Bert’s constitutive model. The effect of semi-cone angle, number of layers and bimodularity ratio (E 2t /E 2c ) on free vibration frequencies and frequency response is investigated. 2. FORMULATION The geometry and dimensions of a conical panel is shown in Fig. 1 with total thickness h, small end radius r 1 , large end radius r 2 , meridional length L, circumferential length b at small end, sector angle y, and semi-cone angle a. Displacements u, v, w at a point (s, q, z) are expressed as functions of middle surface displacements u 0 , v 0 , w 0 and independent rotation b s , b q of the meridional and hoop sections, respectively, as: u (s, q, z, t) = u 0 (s, q, t) + z b s (s, q, t) v (s, q, z, t) = v 0 (s, q, t) + z b q (s, q, t) (1) w (s, q, z, t) = w 0 (s, q, t)

Investigation on the Static Response and Failure Process of Metallic Open Lattice Cellular Structures

Abstract: The response of three different cellular core types, suitable for manufacturing crashworthiness sandwich cellular structures, is investigated in this paper. A methodology is developed, comprising linear static and eigenvalue buckling analysis, as well as nonlinear material elastoplastic analysis. The methodology is used to study the structural response and failure process of open lattice metallic cellular cores and derive the most important structural properties of the cellular core, i.e. elasticity modulus, plateau stress and compaction strain. The critical elastoplastic buckling stress of the metallic struts is approximated by analytical solutions, while a simple engineering approach is applied for the estimation of the compaction strain. The influence of core basic design parameters, i.e. strut aspect ratio (radius/length), unit‐cell spatial configuration and unit‐cell size on the structural behaviour is assessed.

A reduced-order stochastic finite element approach for design optimization under uncertainty

This paper presents a computational framework for structural design optimization under uncertainty. The stochastic static response of linear elastic structures is predicted by a spectral stochastic finite element method (SSFEM) based on a polynomial chaos expansion (PCE). Traditional SSFEM approaches lead to large-scale numerical problems and computational costs rendering these methods impractical for design optimization purposes. To mitigate the computational burden, a Galerkin-based multi-point reduced-order model (ROM) is integrated into SSFEM. The ROM basis is spanned by displacements and derivatives of displacements with respect to design and random variables evaluated at adaptively selected calibration points in the design space. The design sensitivity equations are derived and a formal analysis of the computational costs in terms of floating-point operations is presented. The efficiency of the ROM based approach versus traditional SSFEM is studied with the shape optimization of a shell structure. For this example, the results show that the proposed reduced-order modeling scheme can lower the total turnaround time by more than a factor of 30.

Structural assessment and reliability analysis for existing engineering structures, theoretical background

The concept presented for the safety assessment of concrete structures integrates nonlinear finite element analysis with stochastic and reliability technology into an advanced engineering tool. The basic aim of the stochastic nonlinear analysis is to calculate the safety index of an existing engineering structure, which characterizes its reliability (and failure probability). The nonlinear solution enables a realistic estimation of the structural response statistics to be obtained (failure load, deflections, cracks, stresses, etc.). The possibility of randomization for such computationally intensive problems is shown. Latin hypercube sampling is used in order to keep the number of required simulations at an acceptable level. Statistical correlation, which is important for a realistic solution, is imposed by using a stochastic optimization technique called simulated annealing. The sensitivity of results to random input parameters can be evaluated using nonparametric rank-order correlation coefficients. The safety index of the analysed structure is calculated from the stochastically obtained structural resistance and expected load distribution using appropriate reliability techniques. The presented approach for the safety assessment of engineering structures supersedes the usual methods based on simplified formulas. It can lead to considerably improved results since the structure is analysed more precisely. Therefore, it supports a higher level of decision-making process in bridge administration and maintenance of transport macrostructure.

Static analysis of uncertain structures using interval eigenvalue decomposition

Static analysis is an essential procedure to design a structure. Using static analysis, the structure's response to the applied external forces is obtained. This response includes internal forces/moments and internal stresses that are used in the design process. However, the mechanical characteristics of the structure possess uncertainties that alter the structure's response. One method to quantify the presence of these uncertainties is interval variables. In this work, a new method is developed to obtain the bounds on a structure's static response using interval eigenvalue decomposition of the stiffness matrix. The bounds of eigenvalues are obtained using monotonic behaviour of eigenvalues for a symmetric matrix subjected to non-negative definite perturbations. Moreover, the bounds of eigenvectors are obtained using perturbation of invariant subspaces for symmetric matrices. Using this method, it is shown that obtaining the bound on static response of an uncertain structure does not require a combinatorial or Monte-Carlo simulation procedure.

Design of a Robust, High-rate Wireless Sensor Network for Static and Dynamic Structural Monitoring

Over recent years, there has been much interest in the use of low-cost wireless transceivers for communication of sensor data to alleviate the expense of widely distributed cable-based sensors in structural monitoring systems. However, while the number of unique wireless sensor platforms has continued to expand rapidly, the lack of success in replicating the number of deployed sensors and sampling rates utilized in previous cable-based systems has led to disillusionment over their use for this application. This article presents a wireless sensing system designed for concurrent measurement of both static and dynamic structural response through strain transducers, accelerometers, and temperature sensors. The network protocol developed supports real-time, high-rate data acquisition from large wireless sensor arrays with essentially no data loss. The current network software enables high-rate acquisition of up to 40 channels across 20 wireless units on a single peer-to-peer network with system expansion enabled through additional networks operating simultaneously on adjacent communication channels. Elements of the system design have been specifically tailored towards addressing condition assessment of highway bridges through strain-based load ratings as well as vibration-based dynamic analysis. However, the flexible system architecture enables the system to serve essentially as an off-the-shelf solution for a wide array of wireless sensing tasks. The wireless sensing units and network performance have been validated through laboratory tests as well as dense large-scale field deployments on an in-service highway bridge.

Probabilistic and Interval Static Response Analysis of Truss Structures with Uncertain Parameters

This paper presents the random factor method (RFM) and interval factor method (IFM) for the static analysis of truss structures with uncertainty. From the static governing equations of finite element method, the computational expressions for the mean value and standard deviation of structural displacement and stress are developed by using the RFM. The computational expressions for the lower and upper bounds of structural static response are also derived by means of the interval operations when system parameters are interval variables. The effect of uncertainty of individual structural parameters and loads on structural static response is demonstrated by truss structures.

Semidefinite programming for uncertain linear equations in static analysis of structures

This paper presents a method for computing a minimal bound that contains the solution set to the uncertain linear equations. Particularly, we aim at finding a bounding ellipsoid for static response of structures, where both external forces and elastic moduli of members are assumed to be imprecisely known and bounded. By using the S -lemma, we formulate a semidefinite programming (SDP) problem which provides an outer approximation of the minimal bounding ellipsoid. Bounding ellipsoids are computed for nodal displacements of uncertain braced frames as the solutions of the presented SDP problems by using the primal-dual interior-point method.

Ellipsoidal bounds for static response of framed structures against interactive uncertainties

This paper presents an optimization-based method for computing a minimal bounding ellipsoid that contains the set of static responses of an uncertain braced frame. Based on a non-stochastic modeling of uncertainty, we assume that the parameters both of brace stiffnesses and external forces are uncertain but bounded. A brace member represents the sum of the stiffness of the actual brace and the contributions of some non-structural elements, and hence we assume that the axial stiffness of each brace is uncertain. By using the <TEX>$\mathcal{S}$</TEX>-lemma, we formulate a semidefinite programming (SDP) problem which provides an outer approximation of the minimal bounding ellipsoid. The minimum bounding ellipsoids are computed for a braced frame under several uncertain circumstances.

Ellipsoidal bounds for static response of framed structures against interactive uncertainties

This paper presents an optimization-based method for computing a minimal bounding ellipsoid that contains the set of static responses of an uncertain braced frame. Based on a non-stochastic modeling of uncertainty, we assume that the parameters both of brace stiffnesses and external forces are uncertain but bounded. A brace member represents the sum of the stiffness of the actual brace and the contributions of some non-structural elements, and hence we assume that the axial stiffness of each brace is uncertain. By using the S-lemma, we formulate a semidefinite programming (SDP) problem which provides an outer approximation of the minimal bounding ellipsoid. The minimum bounding ellipsoids are computed for a braced frame under several uncertain circumstances.

The static displacement and the stress analysis of structures with bounded uncertainties using the vertex solution theorem

In practical engineering, on account of physical imperfections, model inaccuracies, and system complexities, almost all structures have physical and geometrical uncertainties in some degrees. In this paper, we focus on the static response problem and the stress distribution of structures with bounded uncertainties. In terms of the vertex notation in interval analysis, a new mathematical proof of the vertex solution theorem which is used to determine the supremum and the infimum of the static responses of structures with bounded uncertainties is given. Then, we extend this theorem for calculating the interval stress and the deformation distributions, which was only used to determine the supremum and the infimum of the static responses of structures with bounded uncertainties. The basic idea of the vertex solution theorem is to convert the interval linear equations into systems of equivalent deterministic linear equations. The resulting deterministic linear equations are then solved by using the familiar techniques like the Gauss elimination method or the Gauss–Seidel iteration method. Another advantage of this method is that the increase in number of the uncertain parameters in a structure element will not result in the increase in number of the uncertain elements in the stiffness matrix. For practical engineering problem with bounded uncertainties, the chief thing is to avoid the disadvantages of large calculation and much runtime of the vertex solution. In this paper, we present the parallel arithmetic of the vertex solution theorem, which can be used in large-scale computations in practical engineering to avoid much runtime. On the other hand, we can use the symmetrical characteristic of the stiffness matrix and the substructure method to reduce the computational effort in practical engineering. The numerical results of the typical example presented by Deif calculated by the proposed vertex solution theorem show that the width between the supremum and the infimum on the static response yielded by the vertex solution theorem is tighter than those produced by the KCN’s method presented by Köylüoğlu, Cakmak, and Nielson. The numerical examples of the two-dimensional shell with an edge fixed and the two-dimensional shell with surrounding fixed are used to illustrate the computational feasibility of the vertex solution theorem.

Does amplitude scaling of ground motion records result in biased nonlinear structural drift responses?

AbstractLimitations of the existing earthquake ground motion database lead to scaling of records to obtain seismograms consistent with a ground motion target for structural design and evaluation. In the engineering seismology community, acceptable limits for ‘legitimate’ scaling vary from one (no scaling allowed) to 10 or more. The concerns expressed by detractors of scaling are mostly based on the knowledge of, for example, differences in ground motion characteristics for different earthquake magnitude–distance (Mw–Rclose) scenarios, and much less on their effects on structures. At the other end of the spectrum, proponents have demonstrated that scaling is not only legitimate but also useful for assessing structural response statistics for Mw–Rclose scenarios. Their studies, however, have not investigated more recent purposes of scaling and have not always drawn conclusions for a wide spectrum of structural vibration periods and strengths. This article investigates whether scaling of records randomly selected from an Mw–Rclose bin (or range) to a target fundamental‐mode spectral acceleration (Sa) level introduces bias in the expected nonlinear structural drift response of both single‐degree‐of‐freedom oscillators and one multi‐degree‐of‐freedom building. The bias is quantified relative to unscaled records from the target Mw–Rclose bin that are ‘naturally’ at the target Sa level. We consider scaling of records from the target Mw–Rclose bin and from other Mw–Rclose bins. The results demonstrate that scaling can indeed introduce a bias that, for the most part, can be explained by differences between the elastic response spectra of the scaled versus unscaled records. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Inelastic response analysis of reinforced concrete structures using modified force analogy method

AbstractA modified force analogy method (MFAM) is developed to simulate the nonlinear inelastic response of reinforced concrete (RC) structures. Beam–column elements with three different plastic mechanisms are utilized to simulate inelastic response caused by moment and shear force. A multi‐linear hysteretic model is implemented to simulate the nonlinear inelastic response of RC member. The P‐Δ effect of the structure is also addressed in MFAM. Static and dynamic inelastic response of structure, damage condition and failure type for structural element, structural limit state and collapse time can also be simulated using MFAM. Compared with the general algorithm, the MFAM provides less computational time especially in the case of large structural system. It is also easier to be written as computer program. Three test data groups, which include cyclic loading test data of a non‐ductile RC bridge column, a two‐storey RC frame, and dynamic collapse test data of a non‐ductile RC portal frame, are selected to confirm the effectiveness of applying MFAM to simulate the inelastic behaviour of structures. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Finite Element Analysis of Structures with Interval Parameters

AbstractThis paper present a new method called the interval factor method for the finite element analysis of truss structures with interval parameters. Using the interval factor method, the structural parameters and loads can be considered as interval variables, and the structural stiffness matrix can then be divided into the product of two parts corresponding to its deterministic value and the interval factors. The computational expressions for lower and upper bounds, mean value and interval change ratio of structural placement and stress responses are derived from the static governing equations by means of the interval operations. The effect of the uncertainty of the structural parameters and loads on the structural static responses is demonstrated by truss structures.

Recent results on the effect of the transverse core compressibility on the static and dynamic response of sandwich structures

This paper is devoted to a study of the effects played by transverse core compressibility of sandwich plates and shells on their static and dynamic behavior. The analysis is based on a higher-order structural model using the standard Kirchhoff–Love assumption for the face sheets and a higher order displacement representation for the core layer. The model accounts for the geometrical nonlinearities that are considered in the von Kármán sense and for initial geometric imperfections. Transverse shear effects are included in the soft-core layer. Consistent equations of motion and boundary conditions are derived via the application of Hamilton’s principle. In the cases that are analyzed and presented in this paper, it was revealed that the static and dynamic buckling/response and postbuckling of flat and curved sandwich structures, are strongly affected by transverse compressibility of the core. It is also shown that in the context of this structural model, the wrinkling instability and response are captured directly from the derived governing equations, and not, as customarily, via a post-processing analysis.

Performance evaluation and damage assessment of steel frame buildings under main shock–aftershock earthquake sequences

AbstractStructures subjected to earthquake ground motions may be subjected to one or more aftershocks within a short period following the occurrence of the principal earthquake shock. Strong aftershocks have the potential to cause extensive structural damage, property losses and injuries to building occupants. This paper investigates the potential for aftershocks to cause additional damage to steel moment frame buildings, and provides a probabilistic description of structural damage states prior to and following those aftershocks. Statistics of structural response and damage states for steel frame buildings subjected to main shock–aftershock sequences are calculated using the enhanced uncoupled modal response history analysis (EUMRHA) method, a modification of an efficient and accurate method for predicting nonlinear response of frames. The frame connections are modelled by a moment–rotation relationship that takes brittle fracture of the connection welds into account. Damage accumulation is analysed in terms of a normalized ‘damage ratio’ and maximum inter‐storey drift. Simple probabilistic tools are proposed for purposes of rapid structural evaluation and condition assessment of damaged buildings. Copyright © 2007 John Wiley &amp; Sons, Ltd.

An integrated GPS–accelerometer data processing technique for structural deformation monitoring

Global Positioning System (GPS) is being actively applied to measure static and dynamic displacement responses of large civil engineering structures under winds. However, multipath effects and low sampling frequencies affect the accuracy of GPS for displacement measurement. On the other hand, accelerometers cannot reliably measure static and low-frequency structural responses, but can accurately measure high-frequency structural responses. Therefore, this paper explores the possibility of integrating GPS-measured signals with accelerometer-measured signals to enhance the measurement accuracy of total (static plus dynamic) displacement response of a structure. Integrated data processing techniques using both empirical mode decomposition (EMD) and an adaptive filter are presented. A series of motion simulation table tests are then performed at a site using three GPS receivers, one accelerometer, and one motion simulation table that can simulate various types of motion defined by input wave time histories around a pre-defined static position. The proposed data processing techniques are applied to the recorded GPS and accelerometer data to find both static and dynamic displacements. These results are compared with the actual displacement motions generated by the motion simulation table. The comparative results demonstrate that the proposed technique can significantly enhance the measurement accuracy of the total displacement of a structure.