Haim Waisman

Active stiffening of laminated composite beams using piezoelectric actuators

Abstract The present study deals with the stiffening effects of a smart piezolaminated composite beam. The structure consists of piezoceramic layers or patches bonded on the surface of the beam. The analysis considers the linear piezoelectric constitutive relations and the first-order shear deformation theory (FSDT). The influence of the actuators is evaluated by means of the pin-force model and their size and location along the beam are taken into account. The three coupled equations of motion of a general non-symmetric piezolaminated composite beam subjected to axial and lateral tractions and various boundary conditions are numerically solved to obtain the natural frequencies and mode shapes. The results of the present model are compared with those based on a finite element analysis using the ANSYS code, as well as to results presented in the literature. All comparisons yielded very good matches. It is demonstrated that the stiffness of the beam can be actively altered using the piezoelectric bonded actuators, yielding significant changes in the natural frequencies and mode shapes of the beam.

Probabilistic Model Updating for Sizing of Hole-Edge Crack Using Fiber Bragg Grating Sensors and the High-Order Extended Finite Element Method

This paper presents a novel framework for probabilistic crack size quantification using fiber Bragg grating (FBG) sensors. The key idea is to use a high-order extended finite element method (XFEM) together with a transfer (T)-matrix method to analyze the reflection intensity spectra of FBG sensors, for various crack sizes. Compared with the standard FEM, the XFEM offers two superior capabilities: (i) a more accurate representation of fields in the vicinity of the crack tip singularity and (ii) alleviation of the need for costly re-meshing as the crack size changes. Apart from the classical four-term asymptotic enrichment functions in XFEM, we also propose to incorporate higher-order functions, aiming to further improve the accuracy of strain fields upon which the reflection intensity spectra are based. The wavelength of the reflection intensity spectra is extracted as a damage sensitive quantity, and a baseline model with five parameters is established to quantify its correlation with the crack size. In order to test the feasibility of the predictive model, we design FBG sensor-based experiments to detect fatigue crack growth in structures. Furthermore, a Bayesian method is proposed to update the parameters of the baseline model using only a few available experimental data points (wavelength versus crack size) measured by one of the FBG sensors and an optical microscope, respectively. Given the remaining data points of wavelengths, even measured by FBG sensors at different positions, the updated model is shown to give crack size predictions that match well with the experimental observations.

Variation of natural frequencies of beams using the active stiffening effect

Abstract The present study investigates the stiffening effects of a simply supported and clamped–free symmetric piezolaminated composite type beams. The structure consists of PZT layers or two sets of patches bonded to the surface of the beam. The analysis considers the linear piezoelectric constitutive relations and a first order shear deformation theory (FSDT). The influence of the actuators is evaluated by means of the pin-force model and their size and location along the beam are taken into account. Two coupled equations of motion for the lateral displacement and bending rotation and one uncoupled equation for the axial displacement of symmetric piezolaminated composite beam are solved numerically to obtain the natural frequencies and mode shapes. Numerical experiments demonstrate that the natural frequencies and mode shapes of the beam can be actively altered using the piezoelectric bonded actuators. The results of the present degenerated model are compared to results presented in the literature. The comparisons yielded excellent matches.

A Quasi-algebraic Multigrid Approach to Fracture Problems Based on Extended Finite Elements

The modeling of discontinuities arising from fracture of materials poses a number of significant computational challenges. The extended finite element method provides an attractive alternative to standard finite elements in that they do not require fine spatial resolution in the vicinity of discontinuities nor do they require repeated remeshing to properly address propagation of cracks. They do, however, give rise to linear systems requiring special care within an iterative solver method. An algebraic multigrid method is proposed that is suitable for the linear systems associated with modeling fracture via extended finite elements. The new method follows naturally from an energy minimizing algebraic multigrid framework. The key idea is the modification of the prolongator sparsity pattern to prevent interpolation across cracks. This is accomplished by accessing the standard levelset functions used during the discretization process. Numerical experiments illustrate that the resulting method converges in a fashion that is relatively insensitive to mesh resolution and to the number of cracks or their location.

Parallel preconditioners for monolithic solution of shear bands

Shear bands are one of the most fascinating instabilities in metals that occur under high strain rates. They describe narrow regions, on the order of micron scales, where plastic deformations and significant heating are localized which eventually leads to fracture nucleation and failure of the component.In this work shear bands are described by a set of four strongly coupled thermo-mechanical equations discretized by a mixed finite element formulation. A thermo-viscoplastic flow rule is used to model the inelastic constitutive law and finite thermal conductivity is prescribed which gives rise to an inherent physical length scale, governed by competition of shear heating and thermal diffusion. The residual equations are solved monolithically by a Newton type method at every time step and have been shown to yield mesh insensitive result. The Jacobian of the system is sparse and has a nonsymmetric block structure that varies with the different stages of shear bands formation.The aim of the current work is to develop robust parallel preconditioners to GMRES in order to solve the resulting Jacobian systems efficiently. The main idea is to design Schur complements tailored to the specific block structure of the system and that account for the varying stages of shear bands.We develop multipurpose preconditioners that apply to standard irreducible discretizations as well as our recent work on isogeometric discretizations of shear bands.The proposed preconditioners are tested on benchmark examples and compared to standard state of practice solvers such as GMRES/ILU and LU direct solvers. Nonlinear and linear iterations counts as well as CPU times and computational speedups are reported and it is shown that the proposed preconditioners are robust, efficient and outperform traditional state of the art solvers.

Mechanics of SWCNT Aggregates Studied by Incremental Constrained Minimization

AbstractThe stress-strain behavior of short single-walled carbon nanotube (SWCNT) aggregates is investigated by a novel incremental constrained minimization approach. An AIREBO potential is used to model the interactions within and between CNTs. The idea is to homogenously disperse SWCNTs in the computational cell at random positions and orientations following spherical uniform distributions, and incrementally deform the cell although restraining the movement of atoms at the ends of nanotubes. The stress-strain response of the system is obtained in each loading direction, and it is shown to converge to an isotropic behavior (a similar response in all directions) as the number of CNTs in the system increases. It is also shown that the Young’s modulus of the system increases linearly with the CNT aggregates density. Finally, the method is shown to agree well with results obtained from molecular dynamics simulations running at near zero degrees kelvin, however they are obtained at only a fraction of the CPU ...

Computational modeling of material deterioration at various length scales

In the past decade, a dominant theme in computational fracture mechanics has been to obtain a more fundamental understanding ofmaterial deterioration process, rather than relying on phenomenological or empirical approaches to make predictions. This is driven by a growing need to make predictions of the failure behavior of materials across length scales starting from first principles and going up to the continuum scale. In order to predict such material response, the development of rigorous computational models for modeling material deterioration process at various time and length scales has been of importance to the computational mechanics community. Several interesting approaches have thus been proposed to increase our understanding of the inter-related materials deterioration processes at disparate length scales. While experimental fracture mechanics is important for identifying the physical

A two-scale algorithm for detection of multiple flaws in structures modeled with XFEM

This paper presents a novel algorithm for detection of multiple flaws in structures as an inverse process, where the forward problem is based on eXtended Finite Element Method (XFEM). The proposed algorithm can be applied to quantify any flaw with arbitrary shape and size (e.g., cracks, voids, or their combination) whose number is unknown beforehand, and is shown to be significantly more efficient than other methods proposed in the literature. The basic concept is to employ a two-scale optimization framework, where first a coarse flaw region is detected and then fine scale convergence is used to zoom in on the flaw. Both optimization steps rely on a forward problem in which an XFEM model with both circular and elliptical enrichments is used. The advantage of XFEM is in the alleviation of costly remeshing techniques when candidate flaws keep updating with the optimization process. The proposed hierarchical optimizers include both heuristic and gradient-based algorithms, such as the discrete artificial bee colony (DABC) algorithms and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. In details, the first step employs a DABC optimization as a coarse-scale search where the optimizer is limited to specific solutions that correspond to locations and shapes of flaws, thus converting a continuous optimization problem into a discrete optimization with a small number of choices. The results of the first step provide local subdomains and rough identified flaw parameters, which can be considered as search space reduction and initial guess for a fine tuning optimization step. This solution zooming is carried out by the BFGS method and leads to a fast converging method as illustrated on two benchmark detection examples.

A stochastic finite element approach to determine the safety of suspension bridge cables

A new methodology to determine the safety of suspension bridge main cables is proposed and illustrated on a corrosion-deteriorated cable composed of 9061 wires. The approach is the first one incorporating a finite element (FE) model to predict the cable’s failure load, accounting for load recovery due to friction in broken wires and simulating the reduced cables strength as a three dimensional random field. In order to obtain the breaking load of a cable, the load is increased gradually (quasi-static loading) in a cable’s FE model, having wires break a few at a time according to their residual strength. Because of the load transfer to surrounding wires, the breakage of an individual wire affects the stress state inside the surrounding wires. This local damage eventually causes a global reduction in the load carrying capacity of the cable, up to a complete failure. The safety of the cable is determined through a Monte Carlo simulation, in which the reduced strength of the cable is generated for every realization through the Spectral Representation Method (SRM) and is input as a material parameter in the FE model. The statistics of the load that will drive a suspension bridge cable to failure under a hypothetical deterioration state are obtained at the end of the simulation. INTRODUCTION The structural function of the main cables in suspension bridges is to transfer the tension load, derived by supporting the roadway, to the towers. The main cables are composed of thousands of high strength parallel steel wires with a diameter of approximately 5 mm bundled together in strands either built in situ or prefabricated. These strands are then compacted and tightened together and eventually the cross section of the cable becomes semi-circular. The wires in pristine conditions have a strength ranging from 1570 MPa to 1800 MPa. However with aging, fatigue loading, and harsh environmental conditions, the wires strength reduces significantly (Shi et al., 2007). Field observations of aging suspension bridges indicate serious distress of