Reappraisal of the effective elastic thickness for the sub-Andes using 3-D finite element flexural modelling, gravity and geological constraints

P>Estimates of effective elastic thickness (T(e)) for the western portion of the South American Plate using, independently, forward flexural modelling and coherence analysis, suggest different thermomechanical properties for the same continental lithosphere. We present a review of these T(e) estimates and carry out a critical reappraisal using a common methodology of 3-D finite element method to solve a differential equation for the bending of a thin elastic plate. The finite element flexural model incorporates lateral variations of T(e) and the Andes topography as the load. Three T(e) maps for the entire Andes were analysed: Stewart & Watts (1997), Tassara et al. (2007) and Perez-Gussinye et al. (2007). The predicted flexural deformation obtained for each T(e) map was compared with the depth to the base of the foreland basin sequence. Likewise, the gravity effect of flexurally induced crust-mantle deformation was compared with the observed Bouguer gravity. T(e) estimates using forward flexural modelling by Stewart & Watts (1997) better predict the geological and gravity data for most of the Andean system, particularly in the Central Andes, where T(e) ranges from greater than 70 km in the sub-Andes to less than 15 km under the Andes Cordillera. The misfit between the calculated and observed foreland basin subsidence and the gravity anomaly for the Maranon basin in Peru and the Bermejo basin in Argentina, regardless of the assumed T(e) map, may be due to a dynamic topography component associated with the shallow subduction of the Nazca Plate beneath the Andes at these latitudes.

The interaction of flexural-gravity waves with periodic geometries

A periodic structure of finite extent is embedded within an otherwise uniform two-dimensional system consisting of finite-depth fluid covered by a thin elastic plate. An incident harmonic flexural-gravity wave is scattered by the structure. By using an approximation to the corresponding linearised boundary value problem that is based on a slowly varying structure in conjunction with a transfer matrix formulation, a method is developed that generates the whole solution from that for just one cycle of the structure, providing both computational savings and insight into the scattering process. Numerical results show that variations in the plate produce strong resonances about the ‘Bragg frequencies’ for relatively few periods. We find that certain geometrical variations in the plate generate these resonances above the Bragg value, whereas other geometries produce the resonance below the Bragg value. The familiar resonances due to periodic bed undulations tend to be damped by the plate.

Analytical investigation of squeeze film dampers

Squeeze film damping effects naturally occur if structures are subjected to loading situations such that a very thin film of fluid is trapped within structural joints, interfaces, etc. An accurate estimate of squeeze film effects is important to predict the performance of dynamic structures. Starting from linear Reynolds equation which governs the fluid behavior coupled with structure domain which is modeled by Kirchhoff plate equation, the effects of nondimensional parameters on the damped natural frequencies are presented using boundary characteristic orthogonal functions. For this purpose, the nondimensional coupled partial differential equations are obtained using Rayleigh-Ritz method and the weak formulation, are solved using polynomial and sinusoidal boundary characteristic orthogonal functions for structure and fluid domain respectively. In order to implement present approach to the complex geometries, a two dimensional isoparametric coupled finite element is developed based on Reissner-Mindlin plate theory and linearized Reynolds equation. The coupling between fluid and structure is handled by considering the pressure forces and structural surface velocities on the boundaries. The effects of the driving parameters on the frequency response functions are investigated. As the next logical step, an analytical method for solution of squeeze film damping based upon Green’s function to the nonlinear Reynolds equation considering elastic plate is studied. This allows calculating modal damping and stiffness force rapidly for various boundary conditions. The nonlinear Reynolds equation is divided into multiple linear non-homogeneous Helmholtz equations, which then can be solvable using the presented approach. Approximate mode shapes of a rectangular elastic plate are used, enabling calculation of damping ratio and frequency shift as well as complex resistant pressure. Moreover, the theoretical results are correlated and compared with experimental results both in the literature and in-house experimental procedures including comparison against viscoelastic dampers.

Nonlinear Variational Inequalities Depending on a Parameter

This paper develops the results announced in the Note [14]. Using an eigenvalue problem governed by a variational inequality, we try to unify the theory concerning the post-critical equilibrium state of a thin elastic plate subjected to unilateral conditions.

On the Application of Beam on Elastic Foundation Theory to the Analysis of Stiffened Plate Strips

The main objective of this thesis is to show that plate strips subjected to transverse line loads can be analysed by using the beam on elastic foundation (BEF) approach. It is shown that the elastic behaviour of both the centre line section of a semi infinite plate supported along two edges, and the free edge of a cantilever plate strip can be accurately predicted by calculations based on the two parameter BEF theory. The transverse bending stiffness of the plate strip forms the foundation. The foundation modulus is shown, mathematically and physically, to be the zero order term of the fourth order differential equation governing the behaviour of BEF, whereas the torsion rigidity of the plate acts like pre tension in the second order term. Direct equivalence is obtained for harmonic line loading by comparing the differential equations of Levy's method (a simply supported plate) with the BEF method. By equating the second and zero order terms of the semi infinite BEF model for each harmonic component, two parameters are obtained for a simply supported plate of width B: the characteristic length, 1/ λ, and the normalized sum, n, being the effect of axial loading and stiffening resulting from the torsion stiffness, nlin. This procedure gives the following result for the first mode when a uniaxial stress field was assumed (ν = 0): 1/λ = √2B/π and nlin = 1. For constant line loading, which is the superimposition of harmonic components, slightly differing foundation parameters are obtained when the maximum deflection and bending moment values of the theoretical plate, with v = 0, and BEF analysis solutions are equated: 1 /λ= 1.47B/π and nlin. = 0.59 for a simply supported plate; and 1/λ = 0.99B/π and nlin = 0.25 for a fixed plate. The BEF parameters of the plate strip with a free edge are determined based solely on finite element analysis (FEA) results: 1/λ = 1.29B/π and nlin. = 0.65, where B is the double width of the cantilever plate strip. The stress biaxial, v > 0, is shown not to affect the values of the BEF parameters significantly the result of the geometric nonlinearity caused by in plane, axial and biaxial loading is studied theoretically by comparing the differential equations of Levy's method with the BEF approach. The BEF model is generalised to take into account the elastic rotation stiffness of the longitudinal edges. Finally, formulae are presented that take into account the effect of Poisson's ratio, and geometric non linearity, on bending behaviour resulting from axial and transverse inplane loading. It is also shown that the BEF parameters of the semi infinite model are valid for linear elastic analysis of a plate strip of finite length. The BEF model was verified by applying it to the analysis of bending stresses caused by misalignments in a laboratory test panel. In summary, it can be concluded that the advantages of the BEF theory are that it is a simple tool, and that it is accurate enough for specific stress analysis of semi infinite and finite plate bending problems.

Fractional order and dynamic simulation of a system involving an elastic wide plate

Numerous researchers have studied about nonlinear dynamics in several areas of science and engineering. However, in most cases, these concepts have been explored mainly from the standpoint of analytical and computational methods involving integer order calculus (IOC). In this paper we have examined the dynamic behavior of an elastic wide plate induced by two electromagnets of a point of view of the fractional order calculus (FOC). The primary focus of this study is on to help gain a better understanding of nonlinear dynamic in fractional order systems. © 2011 American Institute of Physics.

The folded plate model in structural analysis. Elastic, plastic and dynamic formulations for nonprismatic structures

A specific numerical procedure for the analysis of arbitrary nonprismatic folded plate structures is presented. An elastic model is studied and compared with a harmonic solution for a prismatic structure. An extension to the plastic analysis is developed, and the influence of the structural geometry and loading pattern is analyzed. Nonprismatic practical cases, with arbitrary geometry and loading are shown, as well in the elastic range as in the plastic one. Finally, a dynamic formulation is outlined

Finite elastic analysis of an infinite plate with an elliptic hole.

1. Plane strain.

Analysis of functionally graded sandwich plate structures with piezoelectric skins, using B-spline finite strip method

Functionally graded materials are composite materials wherein the composition of the constituent phases can vary in a smooth continuous way with a gradation which is function of its spatial coordinates. This characteristic proves to be an important issue as it can minimize abrupt variations of the material properties which are usually responsible for localized high values of stresses, and simultaneously providing an effective thermal barrier in specific applications. In the present work, it is studied the static and free vibration behaviour of functionally graded sandwich plate type structures, using B-spline finite strip element models based on different shear deformation theories. The effective properties of functionally graded materials are estimated according to Mori-Tanaka homogenization scheme. These sandwich structures can also consider the existence of outer skins of piezoelectric materials, thus achieving them adaptive characteristics. The performance of the models, are illustrated through a set of test cases. (C) 2012 Elsevier Ltd. All rights reserved.

Cubic approximation for the transverse displacement in BEM for elastic plates analysis

This work presents an application for the plate analysis formulation by BEM where 3 boundary equations are used, written for the transverse displacement w and the normal and tangential derivatives partial derivativew/partial derivativen and partial derivativew/partial derivatives. In this extension, the transverse displacement w is approximated by a cubic polynomial and, as a consequence, partial derivativew/partial derivatives has a quadratic approximation. This alternative BEM formulation improves the analysis of thin plates, when compared to the formulation using the linear approximation for the displacements, mainly in the obtaining of the bending moments at the boundary of the plate. The implementation of this proposal to the computational codes is simple. (C) 2004 Published by Elsevier Ltd.

Damage Detection in Flexible Plate Using Lamb Waves

This paper presents an experimental technique for structural health monitoring (SHM) based on Lamb waves approach in an aluminum plate using piezoelectric material as actuators and sensors. Lamb waves are a form of elastic perturbation that remains guided between two parallel free surfaces, such as the upper and lower surfaces of a plate, beam or shelf. Lamb waves are formed when the actuator excites the surface of the structure with a pulse after receiving a signal. Two PZTs were placed in the plate surface and one of them was used to send a predefined wave through the structure. Thus, the other PZT (adjacent) becomes the sensor. Using this methodology, this paper presents one case of damage detection considering the aluminum plate in the free-free-free-free boundary condition. The damage was simulated by adding additional mass on the plate. It is proposed two damage detection indexes obtained from the experimental signal, involving the Fast Fourier Transform (FFT) and the power spectral density (PSD) that were computed using the output signal. The results show the viability of the presented methodology to damage detection in smart structures

Strain rate of the South American lithospheric plate by SIRGAS-CON geodetic observations

A multiyear solution of the SIRGAS-CON network was used to estimate the strain rates of the earth surface from the changing directions of the velocity vectors of 140 geodetic points located in the South American plate. The strain rate was determined by the finite element method using Delaunay triangulation points that formed sub-networks; each sub-network was considered a solid and homogeneous body. The results showed that strain rates vary along the South American plate and are more significant on the western portion of the plate, as expected, since this region is close to the subduction zone of the Nazca plate beneath the South American plate. After using Euler vectors to infer Nazca plate movement and to orient the velocity vectors of the South American plate, it was possible to estimate the convergence and accommodation rates of the Nazca and South American plates, respectively. Strain rate estimates permitted determination of predominant contraction and/or extension regions and to establish that contraction regions coincide with locations with most of the high magnitude seismic events. Some areas with extension and contraction strains were found to the east within the stable South American plate, which may result from different stresses associated with different geological characteristics. These results suggest that major movements detected on the surface near the Nazca plate occur in regions with more heterogeneous geological structures and multiple rupture events. Most seismic events in the South American plate are concentrated in areas with predominant contraction strain rates oriented northeast-southwest; significant amounts of elastic strain can be accumulated on geological structures away from the plate boundary faults; and, behavior of contractions and extensions is similar to what has been found in seismological studies. © 2013 Elsevier Ltd.

Constructability Testing of Folded Plate Girders

A new steel girder bridge system was developed at the University of Nebraska. The innovative girder design is a box girder folded from a single steel plate that has a trapezoid shape with an opening on the bottom. The girder has application in short span bridges and accelerated construction situations. The structural performance of the girder requires investigation in all stages of a bridge’s lifecycle. This thesis contains descriptions and results from the first two tests from a series of tests developed to evaluate this new girder shape. The objective of these two tests was to investigate the constructability of the girders. During construction a bridge is in its least stable condition and it is important that the bridge components exhibit both adequate strength and stability during this critical stage. To this end, two girders were tested in flexure over a simple span as a non-composite beam simulating the loading the girders would be subjected to during construction. The results of the two tests indicate that the folded girder as a whole, and its components, provide adequate strength and stability at construction load levels. Failure occurred at loads that were above normal construction load levels and resulted in a ductile failure mode, which is a well documented benefit of steel components. The girders remained stable through all phases of loading including failure. The top flange was the weakest component of the beam during construction due to its role as a compression element that has a slender and un-braced form. The compression in the top flange caused local buckling in the top flange even at elastic load levels. This was the cause for loss of stiffness and failure in both specimens. Incorporation of a ridge at the center of the top flange of specimens, results of which are not reported in this thesis, proved to resolve this very early buckling issue.

Behaviour and applications of elastic waves in structures and metamaterials

The present thesis focuses on elastic waves behaviour in ordinary structures as well as in acousto-elastic metamaterials via numerical and experimental applications. After a brief introduction on the behaviour of elastic guided waves in the framework of non-destructive evaluation (NDE) and structural health monitoring (SHM) and on the study of elastic waves propagation in acousto-elastic metamaterials, dispersion curves for thin-walled beams and arbitrary cross-section waveguides are extracted via Semi-Analytical Finite Element (SAFE) methods. Thus, a novel strategy tackling signal dispersion to locate defects in irregular waveguides is proposed and numerically validated. Finally, a time-reversal and laser-vibrometry based procedure for impact location is numerically and experimentally tested. In the second part, an introduction and a brief review of the basic definitions necessary to describe acousto-elastic metamaterials is provided. A numerical approach to extract dispersion properties in such structures is highlighted. Afterwards, solid-solid and solid-fluid phononic systems are discussed via numerical applications. In particular, band structures and transmission power spectra are predicted for 1P-2D, 2P-2D and 2P-3D phononic systems. In addition, attenuation bands in the ultrasonic as well as in the sonic frequency regimes are experimentally investigated. In the experimental validation, PZTs in a pitch-catch configuration and laser vibrometric measurements are performed on a PVC phononic plate in the ultrasonic frequency range and sound insulation index is computed for a 2P-3D phononic barrier in the sonic frequency range. In both cases the numerical-experimental results comparison confirms the existence of the numerical predicted band-gaps. Finally, the feasibility of an innovative passive isolation strategy based on giant elastic metamaterials is numerically proved to be practical for civil structures. In particular, attenuation of seismic waves is demonstrated via finite elements analyses. Further, a parametric study shows that depending on the soil properties, such an earthquake-proof barrier could lead to significant reduction of the superstructure displacement.

Biomechanical evaluation of different angle-stable locking plate systems for mandibular surgery

PURPOSE To compare the initial stability and stability after fatigue of three different locking systems (Synthes(®), Stryker(®) and Medartis(®)) for mandibular fixation and reconstruction. METHOD Standard mandible locking plates with identical profile height (1,5 mm), comparable length and screws with identical diameter (2,0 mm) were used. Plates were fixed with six screws according a preparation protocol. Four point bending tests were then performed using artificial bone material to compare their initial stability and failure limit under realistic loading conditions. Loading of the plates was performed using of a servo hydraulic driven testing machine. The stiffness of the implant/bone construct was calculated using a linear regression on the experimental data included in a range of applied moment between 2 Nm and 6 Nm. RESULTS No statistical difference in the elastic stiffness was visible between the three types of plate. However, differences were observed between the systems concerning the maximal load supported. The Stryker and Synthes systems were able to support a significantly higher moment. CONCLUSION For clinical application all systems show good and reliable results. Practical aspects such as handling, possible angulation of screw fixation, possibility of screw/plate removal, etc. may favour one or the other plating system.