Semi-analytical Finite Element Approach Research Articles

The mechanics of the Gentle Driving of Piles

Gentle Driving of Piles (GDP) is a new vibratory installation technology for tubular (mono)piles. It is characterized by the simultaneous application of low-frequency axial and high-frequency torsional vibrations, envisaged to achieve both high installation performance and reduced underwater noise emissions. The concept of GDP has been demonstrated experimentally in a medium-scale onshore field campaign, showcasing the potential of the method in terms of installation and post-installation performances. To further comprehend the mechanics of the GDP method, the driving process is studied by means of a novel pile–soil model; this framework has been recently developed and successfully applied to the problem of axial vibratory driving. In particular, the pile is treated as a thin cylindrical shell via a Semi-analytical Finite Element (SAFE) approach and a linear elastic layered soil half-space is considered via the Thin-Layer Method (TLM) coupled with Perfectly Matched Layers (PMLs). The pile–soil coupling is realized through a hereditary frictional interface and an elasto-plastic tip formulation, both characterized by standard geotechnical in-situ measurements. The comparison of numerical results with field data is favourable for drivability purposes, showcasing the potential of the numerical framework for the analysis of GDP. Conclusively, the mechanics of the installation process are deciphered and the redirection of the friction force vector – induced by high-frequency torsion – is identified as the main driving mechanism of GDP.

Thermal Postbuckling Characteristics Of Angle-ply Laminated Truncated Circular Conical Shells

Here, the nonlinear thermoelastic pre- and post-buckling characteristics of angle-ply laminated composite conical shells subjected to uniform temperature rise are studied using semi-analytical finite element approach. The finite element formulation is based on first-order shear deformation theory and field consistency principle. The nonlinear governing equations, considering geometric nonlinearity based on von Karman’s assumption for moderately large deformation, are solved using Newton-Raphson iteration procedure coupled with displace- ment control method to trace the prebuckling followed by postbuckling equilibrium path. The presence of asymmetric perturbation in the form of small magnitude load spatially proportional to the linear buckling mode shape is assumed to initiate the bifurcation of the shell deformation. The study is carried out to highlight the influences of semi-cone angle, ply-angles, number of layers and number of circumferential waves on the nonlinear prebuckling/postbuckling thermoelastic response of the laminated circular conical shells. The participation of axisymmetric and asymmetric modes in the total response of the shells is brought out through the deformation shape analysis.

Cavity expansion solutions applied to help assess the partial drainage behavior characterization of the piezocone test

The present paper presents cavity expansion applications to help assess the drainage behavior characterization during piezocone tests. The solution considered a semi-analytical model and finite element approach with Drucker Prager plasticity models. The semi-analytical model initially presented by Dienstmann et al. (2017) is briefly presented to focus on a revision of the initial state of excess pore pressure, which adds more consistency to the previous work. We compared the numerical results and performed a complementary and broader sensitivity analysis based on this modification. Sequentially the solutions were applied in a set of parameters representative of piezocone tests performed at different rates on silty materials (gold tailings) and clay mixtures (kaolin and clayey sand). The results proved useful in identifying the transitional rates of behavior, especially from undrained to partially drained behavior.

Semi-Analytical Finite Element Approach for 6-DOF Characterizations of PMB Load

A typically new semi-analytical finite element approach has been used to calculate the force and moment of permanent magnet bearing (PMB) in this article. PMB stator and rotor consist of ring-type cylindrical magnets having an axial magnetization. This article focuses on the characterization of magnetic moment, stiffness matrix, model validation, and comparisons of the moment with other simulating software. This article also explains how angular stiffness or resisting magnetic moment of PMB improves with the change of rotor magnet length and positional shift of the rotor.

Nonlinear ultrasonic evaluation of disorderedly clustered pitting damage using an in situ sensor network

Pervasive but insidious, pitting damage—from pitting corrosion in maritime structures through electrical pitting in bearings to debris cloud–induced pitting craters in spacecraft—is a typical modality of material degradation and lesion in engineering assets in harsh service environment. Pitting damage may feature hundreds of clustered, localized craters, cracks, and diverse microscopic defects (e.g. dislocation, micro-voids, and cracks) disorderedly scattered over a wide area. Targeting accurate, holistic evaluation of pitting damage (mainly the existence, location, and size of the pitted area), an insight into the generation of nonlinear features in guided ultrasonic waves (i.e. high-order harmonics) that are triggered by pitting damage, is achieved using a semi-analytical finite element approach, based on which a monotonic correlation between the nonlinear ultrasonic features and the holistic severity of pitting damage is established. With such correlation, a structural health monitoring framework is developed, in conjunction with the use of an in situ sensor network comprising miniaturized piezoelectric wafers, to characterize pitting damage accurately and monitor material deterioration progress continuously. The framework is experimentally validated, in which highly complex pitting damage in a space structure, engendered by a hypervelocity debris cloud, is evaluated precisely.

Detection of damage in welded joints using high order feature guided ultrasonic waves

Abstract Topographical features such as welds, stiffeners, and bends in plate-like structures have been identified as special local waveguides, which are able to render ultrasonic wave energy preferentially guided along themselves. Such feature guided waves (FGW) at low frequencies have been reported in the literature as an effective screening tool for long-range features, which, however, can only detect relatively large defects. In this study, the existence of high order FGW modes, categorized into multiple wave families, are revealed via the modal analysis of an unbounded welded plate at high frequencies, by using the semi-analytical finite element (SAFE) approach. These FGWs exhibit strong mode confinement in specific regions of the weld, which can potentially offer enhanced interrogation of the localized area in long welds and provide improved detection sensitivity to small defects. A series of high order shear horizontal (SH) type weld-guided modes are investigated in both three-dimensional finite element (3D FE) simulations and experiments, for detecting axial and transverse cracks of sub-wavelength size in the weld bead. A new superposition technique is proposed to coherently enhance the amplitude of the selected mode in a multi-modal waveform, leading to an attractive single-mode inspection capability at high frequencies. Both small cracks are identified numerically and experimentally in the superposed reflection of the SH 1 -like weld-guided wave, and results are in close agreement. The feasibility of using high order weld-guided modes for inspecting small defects inside the weld has been demonstrated.

Guided wave excitation and propagation in damped composite plates

Guided wave attenuation in composites due to material damping is strong, anisotropic, and cannot be neglected. Material damping is a critical parameter in selection of a particular wave mode for long-range structural health monitoring in composites. In this article, a semi-analytical finite element approach is presented to model guided wave excitation and propagation in damped composite plates. The theoretical framework is formulated using finite element method to describe the material behavior in the thickness direction while assuming analytical expressions in the wave propagation direction along the plate. In the proposed method, the Kelvin–Voigt damping model using a complex frequency-dependent stiffness matrix is utilized to account for anisotropic damping effects of composites. Thus, the existing semi-analytical finite element approach is being extended to include material damping effect. Theoretical predictions are experimentally validated using scanning laser Doppler vibrometer measurements of guided wave propagation generated by a circular piezoelectric wafer active sensor transducer in a unidirectional carbon fiber reinforced polymer composite plate. The proposed method achieves good agreement with the experimental results.

Feature guided wave inspection of bond line defects between a stiffener and a composite plate

Adhesive bonding is widely used in aerospace composite structures. A continuous well-cured bond can offer good joint strength and improved fatigue and impact resistance, and is therefore crucial to the performance of the entire structure. This paper explores the feasibility of using feature guided waves (FGW) for rapid screening of the bond line between a stiffener and a carbon fiber reinforced polymer (CFRP) composite panel. Such FGWs are capable of focusing the wave energy along the stiffener and the bond layer, with limited radiation to the adjacent plate. The Semi-Analytical Finite Element (SAFE) approach is employed to understand the modal properties of FGWs that exist in the structure, and criteria are suggested to choose proper mode-frequency combination that is sensitive to adhesive defects. A shear horizontal type FGW mode is identified to be well suited, as it is easy to excite, and propagates with little dispersion and relatively low attenuation, while it retains sufficient energy around the bond layer. Both 3D Finite Element (FE) simulations and experiments are performed to study the interaction of the selected FGW mode with defects in the adhesive bond, and the results show excellent agreement. The reflection behavior and the wave-defect resonance phenomenon are investigated, which demonstrate the capability of the FGW for the bond line inspection.

Guided wave propagation in thermal media through the semi analytical finite element method

In this paper, the issue of the estimation of wave propagation characteristics in thermal media is dealt with. A formulation, named the Thermal Semi Analytical Finite Element, based on the semi analytical finite element approach coupled with the thermal effect is offered. Temperature variations affect the mechanical properties of the waveguide. The question of dispersion curves and group velocities is studied. This study is expected to be of use in the sensitivity analysis of guided waves for wave propagation in thermal environment. Comparisons between numerical and analytical results are given to show the effectiveness of the proposed approach.

A boundary element method for detection of damages and self-diagnosis of transducers using electro-mechanical impedance

In this paper, for the first time, a boundary element method (BEM) for modelling the electro-mechanical responses of three-dimensional structures is reported. Within an electro-mechanically coupled system, the host structure is formulated using the 3D dual boundary element method in order to be able to take into account the possible existence of cracks, and the piezoelectric transducers, which are the key to measuring electro-mechanical impedance (EMI), are modelled using a semi-analytical finite element approach. The analyses of the coupled system are performed in the frequency domain. The EMI signatures computed by the BEM developed in this work show excellent agreement with those obtained using the finite element method and from experiments. Using parametric studies, the potential of using EMI signatures for the detection of damages in structures and for the self-diagnosis of transducers is assessed.

A boundary element model for structural health monitoring using piezoelectric transducers

In this paper, for the first time, the boundary element method (BEM) is used for modelling smart structures instrumented with piezoelectric actuators and sensors. The host structure and its cracks are formulated with the 3D dual boundary element method (DBEM), and the modelling of the piezoelectric transducers implements a 3D semi-analytical finite element approach. The elastodynamic analysis of the structure is performed in the Laplace domain and the time history is obtained by inverse Laplace transform. The sensor signals obtained from BEM simulations show excellent agreement with those from finite element modelling simulations and experiments. This work provides an alternative methodology for modelling smart structures in structural health monitoring applications.

Winkler Springs (p-y curves) for pile design from stress-strain of soils: FE assessment of scaling coefficients using the Mobilized Strength Design concept

In practice, analysis of laterally loaded piles is carried out using beams on non-linear Winkler springs model (often known as p-y method) due to its simplicity, low computational cost and the ability to model layered soils. In this approach, soil-pile interaction along the depth is characterized by a set of discrete non-linear springs represented by p-y curves where p is the pressure on the soil that causes a relative deformation of y. p-y curves are usually constructed based on semi-empirical correlations. In order to construct API/DNV proposed p-y curve for clay, one needs two values from the monotonic stress-strain test results i.e., undrained strength (su) and the strain at 50% yield stress (e50). This approach may ignore various features for a particular soil which may lead to un-conservative or over-conservative design as not all the data points in the stress-strain relation are used. However, with the increasing ability to simulate soil-structure interaction problems using highly developed computers, the trend has shifted towards a more theoretically sound basis. In this paper, principles of Mobilized Strength Design (MSD) concept is used to construct a continuous p-y curves from experimentally obtained stress-strain relationship of the soil. In the method, the stress-strain graph is scaled by two coefficient NC(for stress) and MC(for strain) to obtain the p-y curves. MC and NC are derived based on Semi-Analytical Finite Element approach exploiting the axial symmetry where a pile is modelled as a series of embedded discs. An example is considered to show the application of the methodology.

Dispersion analysis of leaky guided waves in fluid-loaded waveguides of generic shape

A fully coupled 2.5D formulation is proposed to compute the dispersive parameters of waveguides with arbitrary cross-section immersed in infinite inviscid fluids.The discretization of the waveguide is performed by means of a Semi-Analytical Finite Element (SAFE) approach, whereas a 2.5D BEM formulation is used to model the impedance of the surrounding infinite fluid. The kernels of the boundary integrals contain the fundamental solutions of the space Fourier-transformed Helmholtz equation, which governs the wave propagation process in the fluid domain. Numerical difficulties related to the evaluation of singular integrals are avoided by using a regularization procedure. To improve the numerical stability of the discretized boundary integral equations for the external Helmholtz problem, the so called CHIEF method is used.The discrete wave equation results in a nonlinear eigenvalue problem in the complex axial wavenumbers that is solved at the frequencies of interest by means of a contour integral algorithm. In order to separate physical from non-physical solutions and to fulfill the requirement of holomorphicity of the dynamic stiffness matrix inside the complex wavenumber contour, the phase of the radial bulk wavenumber is uniquely defined by enforcing the Snell–Descartes law at the fluid–waveguide interface.Three numerical applications are presented. The computed dispersion curves for a circular bar immersed in oil are in agreement with those extracted using the Global Matrix Method. Novel results are presented for viscoelastic steel bars of square and L-shaped cross-section immersed in water.

Thermal Buckling of Multiwalled Carbon Nanotubes Using a Semi-Analytical Finite Element Approach

In this article, a semi-analytical finite element approach based on the nonlocal elastic shell model is proposed to study the thermal buckling of multiwalled carbon nanotubes (MWCNTs). By taking nonlocality into consideration, the small scale effect is incorporated into the model presented herein. Based upon the Eringen nonlocal elasticity, the displacement field equations coupled by the van der Waals interaction force are derived. Comprehensive results for the thermal buckling of multiwalled carbon nanotubes are given. The influences of the small scale parameter and boundary conditions on the thermal instability of MWCNTs are examined. It is indicated that the possibility of the radial buckling mode of deformation due to radially elevated temperature is significantly higher than that of axial buckling mode of deformation due to uniformly reduced temperature when carbon nanotubes experience thermal loads.

Noncontact Ultrasonic Guided Wave Detection of Rail Defects

Recent train accidents, increasing tonnage, and aging rail transportation infrastructure have reaffirmed the need to improve current rail inspection technologies, consisting primarily of ultrasonic wheel testing. A recent development in rail inspection is the use of ultrasonic guided waves in the 20 kHz to 1 MHz range and noncontact probing techniques. This paper first reports on theoretical studies of ultrasonic guided wave propagation in rails based on a semianalytical finite element approach. The paper then describes the latest version of the University of California, San Diego, and FRA rail defect detection prototype, which is based on noncontact guided wave testing and real-time statistical pattern recognition for defect detection and classification. The system specifically targets transverse head cracks such as transverse fissures and detail fractures. It is also expected to be sensitive to longitudinal head cracks such as vertical split heads and mixed-mode cracks such as compound fractures. The system was field tested in March 2008 at speeds of up to 10 mph with excellent results under changing environmental conditions. Plans are in place for further improvements, including higher test speeds of up to 40 mph and installation of the system in an FRA research car for technology demonstration.

Postbuckling of angle-ply laminated cylindrical shells with meridional curvature

The influence of meridional curvature on the postbuckling behaviour of angle-ply laminated cylindrical shells subjected to external pressure, torsional load, axial compression and uniform temperature rise is investigated using the semi-analytical finite element approach. The nonlinear governing equations are solved using Newton–Raphson iterative technique coupled with the adaptive displacement control method. The presence of asymmetric perturbation in the form of a small magnitude load spatially proportional to the linear buckling mode shape is considered to trace the postbuckling path. The variation of ply-angle and ply-thickness along the meridional direction is considered. The results presented reveal that the imperfection sensitivity of the cylindrical shells having negative Gaussian curvature decreases with the increase in the magnitude of H/ r 0 ratio for all the loading cases considered. The imperfection sensitivity of the positive Gaussian curvature shells increases for external pressure, torsional and thermal loading cases, whereas it decreases for axial loading case with the increase in H/ r 0 ratio.

Postbuckling characteristics of angle-ply laminated truncated circular conical shells

The postbuckling characteristics of the angle-ply laminated composite conical shells subjected to the torsion, the external pressure, the axial compression, and the thermal loading considering uniform temperature change are studied using the semi-analytical finite element approach. The finite element formulation is based on the first-order shear deformation theory and the field consistency principle. The variations in the stiffness coefficients along the meridional direction due to the changes in the ply-angle and the ply-thickness of the filament wound conical shells are incorporated in the finite element formulation. The nonlinear governing equations are solved using the Newton–Raphson iteration procedure coupled with the displacement control method to trace the prebuckling followed by the postbuckling equilibrium path. The presence of asymmetric perturbation in the form of a small magnitude load spatially proportional to the linear buckling mode shape is considered to initiate the bifurcation of the shell deformation. The influence of semi-cone angle, ply-angle and number of circumferential waves on the prebuckling/postbuckling response of the anti-symmetric angle-ply laminated circular conical shells is investigated.

Nonlinear thermo-elastic buckling characteristics of cross-ply laminated joined conical–cylindrical shells

Here, the nonlinear thermo-elastic buckling/post-buckling characteristics of laminated circular conical–cylindrical/conical–cylindrical–conical joined shells subjected to uniform temperature rise are studied employing semi-analytical finite element approach. The nonlinear governing equations, considering geometric nonlinearity based on von Karman’s assumption for moderately large deformation, are solved using Newton–Raphson iteration procedure coupled with displacement control method to trace the pre-buckling/post-buckling equilibrium path. The presence of asymmetric perturbation in the form of small magnitude load spatially proportional to the linear buckling mode shape is assumed to initiate the bifurcation of the shell deformation. The study is carried out to highlight the influences of semi-cone angle, material properties and number of circumferential waves on the nonlinear thermo-elastic response of the different joined shell systems.

Polynomial approach for calculating added mass for fluid-filled cylindrical shells

Cylindrical shells find wide applications in many engineering fields. Free vibration analysis of cylindrical shells filled with fluid has been dealt using finite element approach for both structure and fluid domain or using finite element for structure and Bessel function approach for fluid. The present paper deals with a novel method on the usage of polynomial functions for fluid domain in contrast to the usual Bessel function approach. A semi-analytical finite element approach has been used to discretise the shell structure. The fluid domain has been analysed by using polynomial functions instead of Bessel function. The study has been carried out for conventional shells as well as viscoelastic shells. The present study obviates necessity of limiting the studies to certain boundary conditions. The results of both frequency and damping corroborate well with those found in literature.

Thermal Postbuckling Characteristics of Laminated Conical Shells with Temperature-Dependent Material Properties

The nonlinear thermoelastic buckling/postbuckling characteristics of laminated circular conical/cylindrical shells subjected to uniform temperature rise are studied employing semi-analytical finite element approach based on first-order shear deformation theory and field consistency principle. The nonlinear governing equations, con- sidering geometric nonlinearity based on von Karman's assumption for moderately large deformation, are solved using Newton-Raphson iteration procedure coupled with displacement control method to trace the prebuck- ling/postbuckling equilibrium path. The presence of asymmetric perturbation in the form of small magnitude load spatially proportional to the linear buckling mode shape is assumed to initiate the bifurcation of the shell deforma- tion. The study is carried out to highlight the influences of semicone angle, number of layers, material properties, and number of circumferential waves on the nonlinear thermoelastic response of the laminated circular coni- cal/cylindrical shells. The participation of axisymmetric and asymmetric modes in the total response of the shells is brought out through the deformation shape analysis. The comparison of thermoelastic pre- and postbuckling characteristics of shells with temperature-dependent material properties is made with those considering constant material properties, and the behavior is found to be significantly different depending upon the shell parameters and degradation rate of material properties. The shells exhibit softening type of prebuckling nonlinear response and snap-through-type/stable postbuckling response depending upon the geometrical/material parameters.