Latin American Journal of Solids and Structures, Volume: 11, Issue: 5, Published: 2014
  • Damage identification from uniform load surface using continuous and stationary wavelet transforms

    Masoumi, M.; Ashory, M. R.

    Abstract in English:

    Derived from flexibility matrix, Uniform Load Surface (ULS) is used to identify damages in beam-type structures. This method is beneficial in terms of more participating the lower order modes and having less prone to noise and irregularities in the measured data in comparison with the original flexibility matrix technique. Therefore, these characteristics make this approach a practical tool in the field of damage identification. This paper presents a procedure to employ stationary wavelet transform multi-resolution analysis (SWT-MRA) to refine ULS obtained from the damaged structure and then using continuous wavelet transform (CWT) for localizing the discontinuity of improved ULS as a sign of damage site. Evaluation of the proposed method is carried out by examining a cantilever beam as a numerical case, where the ULS is formed by using mode shapes of damaged beam and two kinds of wavelets (i.e. symmetrical 4 and bior 6.8) is applied for discerning the induced crack. Moreover, a laboratory test is conducted on a free-free beam to experimentally evaluate the practicability of the technique.
  • Stochastic multi-scale analysis of homogenised properties considering uncertainties in cellular solid microstructures using a first-order perturbation

    Basaruddin, Khairul Salleh; Kamarrudin, Nur Saifullah; Ibrahim, Ishak

    Abstract in English:

    Randomness in the microstructure due to variations in microscopic properties and geometrical information is used to predict the stochastically homogenised properties of cellular media. Two stochastic problems at the micro-scale level that commonly occur due to fabrication inaccuracies, degradation mechanisms or natural heterogeneity were analysed using a stochastic homogenisation method based on a first-order perturbation. First, the influence of Young's modulus variation in an adhesive on the macroscopic properties of an aluminium-adhesive honeycomb structure was investigated. The fluctuations in the microscopic properties were then combined by varying the microstructure periodicity in a corrugated-core sandwich plate to obtain the variation of the homogenised property. The numerical results show that the uncertainties in the microstructure affect the dispersion of the homogenised property. These results indicate the importance of the presented stochastic multi-scale analysis for the design and fabrication of cellular solids when considering microscopic random variation.
  • Finite element modeling for buckling analysis of hybrid piezoelectric beam under electromechanical loads

    Rahman, Najeeb ur; Alam, M. Naushad

    Abstract in English:

    A one-dimensional finite element model for buckling analysis of hybrid piezoelectric beams under electromechanical load is presented in this work. The coupled zigzag theory is used for making the model. The inplane displacement is approximated as a combination of a global third order variation across the thickness with an additional layer wise linear variation. The longitudinal electric field is also taken into account. The deflection field is approximated to account for the transverse normal strain induced by electric fields. Two nodded elements with four mechanical and a variable number of electric degrees of freedom at each node are considered. To meet the convergence requirements for weak integral formulation, cubic Hermite interpolation function is used for deflection and electric potential at the sub-layers and linear interpolation function is used for axial displacement and shear rotation. The expressions for the variationally consistent stiffness matrix and load vector are derived and evaluated in closed form using exact integration. The present 1D-FE formulation of zigzag theory is validated by comparing the results with the analytical solution for simply-supported beam and 2D-FE results obtained using ABAQUS. The finite element model is free of shear locking. The critical buckling parameters are obtained for clamped-free and clamped-clamped hybrid beams. The obtained results are compared with the 2D-FE results to establish the accuracy of the zigzag theory for above boundary conditions. The effect of lamination angle on critical buckling load is also studied.
  • Stability of concrete beam-columns under follower forces

    Sharma, Mamta R.; Singh, Arbind K.; Benipal, Gurmail S.

    Abstract in English:

    An axial follower force acting on the free end of a beam-column is known to remain tangential to its elastica at that point. Elastic beam-columns exhibit infinitely high buckling resistance to static compressive follower load. Loss of their dynamic stability is known to occur at critical follower loads, by flutter characterized by vanishing lateral displacement and infinitely high natural frequency. Classical theory deals with physically linear nonconservative beam-columns. Physical nonlinearity exhibited by concrete beam-columns under service loads is caused by the closing and reopening of the extant transverse cracks. In this Paper, analytical expressions for the lateral displacement and lateral stiffness of such concrete beam-columns are derived. Using these expressions, the stability of physically nonlinear elastic flanged concrete beam-columns under the action of a follower compressive axial force and a lateral force is investigated. The significance of the analytical approach and the theoretical predictions is discussed.
  • Dynamic pull-in instability of geometrically nonlinear actuated micro-beams based on the modified couple stress theory

    Sedighi, Hamid M.; Chan-Gizian, Maziar; Noghreha-Badi, Aminreza

    Abstract in English:

    This paper investigates the dynamic pull-in instability of vibrating micro-beams undergoing large deflection under electrosatically actuation. The governing equation of motion is derived based on the modified couple stress theory. Homotopy Perturbation Method is employed to produce the high accuracy approximate solution as well as the second-order frequency- amplitude relationship. The nonlinear governing equation of micro beam vibrations predeformed by an electric field includes both even and odd nonlinearities. The influences of basic non-dimensional parameters on the pull-in instability as well as the natural frequency are studied. It is demonstrated that two terms in series expansions are sufficient to produce high accuracy solution of the micro-structure. The accuracy of proposed asymptotic approach is validated via numerical results. The phase portrait of the system exhibits periodic and homoclinic orbits.
  • A single loop reliability-based design optimization using EPM and MPP-based PSO

    Liao, Kuo-Wei; Ivan, Gautama

    Abstract in English:

    A reliability-based design optimization (RBDO) incorporates a probabilistic analysis with an optimization technique to find a best design within a reliable design space. However, the computational cost of an RBDO task is often expensive compared to a deterministic optimization, which is mainly due to the reliability analysis performed inside the optimization loop. Theoretically, the reliability of a given design point can be obtained through a multidimensional integration. Integration with multiple variables over the safety domain is, unfortunately, formidable in most cases. Monte- Carlo simulation (MCS) is often used to solve this difficulty. However, the inherit statistic uncertainty associated with MCS sometimes causes an unstable RBDO solution. To avoid this unstable solution, this study transforms a multi-variable constraint into a single variable constraint using an exponential function with a polynomial coefficient (EPM). The adaptive Gauss-Kronrod quadrature is used to compute the constraint reliability. The calculated reliability and its derivative are incorporated with an optimizer such as sequential quadratic programming (SQP) or most probable point particle swarm optimization (MPP-based PSO) to conduct the RBDO task. To ensure the design accuracy, the stability of the RBDO algorithm with respect to the initial point is investigated through several numerical examples.
  • Application of nonlocal elasticity and DQM to dynamic analysis of curved nanobeams

    Kananipour, Hassan; Ahmadi, Mehdi; Chavoshi, Hossein

    Abstract in English:

    In this paper, a new numerical technique, the differential quadrature method (DQM) has been developed for dynamic analysis of the nanobeams in the polar coordinate system. DQ approximation of the required partial derivatives is given by a weighted linear sum of the function values at all grid points. A semicircular arch with small-scale effects is investigated by the nonlocal continuum theory with simply supported boundary conditions. The governing equations for Euler-Bernoulli nonlocal beam models are derived. The expressions of the bending displacement are presented analytically. The convergence properties and the accuracy of the DQM for bending of curved nanobeams are investigated through a number of numerical computations. It can be observed that use of DQM, which is independent of domain discretization to be efficient.
  • Vibration of plate on foundation with four edges free by finite cosine integral transform method

    Zhong, Yang; Zhao, Xue-feng; Liu, Heng

    Abstract in English:

    The analytical solutions for the natural frequencies and mode shapes of the rectangular plate on foundation with four edges free is presented by using the finite cosine integral transform method. In the analysis procedure, the classical Kirchhoff rectangular plate is considered and the foundation is modelled as the Winkler elastic foundation. Because only are the basic dynamic elasticity equations of the thin plate on elastic foundation adopted, it is not need prior to select the deformation function arbitrarily. Therefore, the solution developed by present paper is reasonable and theoretical. In order to illuminate the correction of formulations, the numerical results are also presented to comparing with that of the other references.
  • A numerical study on seismic response of self-centring precast segmental columns at different post-tensioning forces

    Nikbakht, Ehsan; Rashid, Khalim; Hejazi, Farzad; Osman, Siti A.

    Abstract in English:

    Precast bridge columns have shown increasing demand over the past few years due to the advantages of such columns when compared against conventional bridge columns, particularly due to the fact that precast bridge columns can be constructed off site and erected in a short period of time. The present study analytically investigates the behaviour of self-centring precast segmental bridge columns under nonlinear-static and pseudo-dynamic loading at different prestressing strand levels. Self-centring segmental columns are composed of prefabricated reinforced concrete segments which are connected by central post-tensioning (PT) strands. The present study develops a three dimensional (3D) nonlinear finite element model for hybrid post-tensioned precast segmental bridge columns. The model is subjected to constant axial loading and lateral reverse cyclic loading. The lateral force displacement results of the analysed columns show good agreement with the experimental response of the columns. Bonded post-tensioned segmental columns at 25%, 40% and 70% prestressing strand stress levels are analysed and compared with an emulative monolithic conventional column. The columns with a higher initial prestressing strand levels show greater initial stiffness and strength but show higher stiffness reduction at large drifts. In the time-history analysis, the column samples are subjected to different earthquake records to investigate the effect post-tensioning force levels on their lateral seismic response in low and higher seismicity zones. The results indicate that, for low seismicity zones, post-tensioned segmental columns with a higher initial stress level deflect lower lateral peak displacement. However, in higher seismicity zones, applying a high initial stress level should be avoided for precast segmental self-centring columns with low energy dissipation capacity.
  • Simple extension of Lemaitre's elastoplastic damage model to account for hydrolytic degradation

    Fancello, Eduardo A.; Lindenmeyer, Leandro P.; Roesler, Carlos R. M.; Salmoria, Gean V.

    Abstract in English:

    Being motivated by the technological applications of bioabsorbable polymeric materials in the fields of biomechanics and medicine, this paper presents a simple but efficient extension of Lemaitre's elastoplastic damage model by incorporating a chemical-based (hydrolysis) degradation term. The aim is to allow the simulation of devices subjected to both mechanical and chemical environments. The model applicability is tested by a set of numerical finite-element examples. The encouraging results show expected adequate coupling between the elastoplastic and chemical damages. Although the model is presently restricted to linear kinematics, the basic idea can be extended to finite strains.
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