An exponential matrix method for the buckling analysis of underground pipelines subjected to landslide loads

Abstract Due to their dimensions, long pipelines often cross areas that are highly susceptible to landslides. In Italy, this problem requires special attention, as many slow-moving landslides interact with buried pipelines. The paper analyzes such interaction problem with particular reference to buckling analysis, tackling the solution of the governing equations by an exponential matrix method. In the paper the basic equation, its computational aspects and numerical analysis options are outlined. Representative results of the proposed methodology and potential applications on buckling analysis of buried pipes are presented

Theories and analyses of functionally graded circular plates

This paper presents the governing equations and analytical solutions of the classical and shear deformation theories of functionally graded axisymmetric circular plates. The classical, first-order, and third-order shear deformation theories are presented, accounting for through-thickness variation of two-constituent functionally graded material, modified couple stress effect, and the von Kármán nonlinearity. Analytical solutions for bending of the linear theories, some of which are not readily available in the literature, are included to show the influence of the material variation, boundary conditions, and loads

Diffraction-free light droplets for axially-resolved volume imaging

An ideal direct imaging system entails a method to illuminate on command a single diffraction-limited region in a generally thick and turbid volume. The best approximation to this is the use of large-aperture lenses that focus light into a spot. This strategy fails for regions that are embedded deep into the sample, where diffraction and scattering prevail. Airy beams and Bessel beams are solutions of the Helmholtz Equation that are both non-diffracting and self-healing, features that make them naturally able to outdo the effects of distance into the volume but intrinsically do not allow resolution along the propagation axis. Here, we demonstrate diffraction-free self-healing three-dimensional monochromatic light spots able to penetrate deep into the volume of a sample, resist against deflection in turbid environments, and offer axial resolution comparable to that of Gaussian beams. The fields, formed from coherent mixtures of Bessel beams, manifest a more than ten-fold increase in their undistorted penetration, even in turbid milk solutions, compared to diffraction-limited beams. In a fluorescence imaging scheme, we find a ten-fold increase in image contrast compared to diffraction-limited illuminations, and a constant axial resolution even after four Rayleigh lengths. Results pave the way to new opportunities in three-dimensional microscopy

Theories and analysis of functionally graded beams

This is a review paper containing the governing equations and analytical solutions of the classical and shear deformation theories of functionally graded straight beams. The classical, first-order, and third-order shear deformation theories account for through-thickness variation of two-constituent functionally graded material, modified couple stress (i.e., strain gradient), and the von Karman nonlinearity. Analytical solutions for bending of the linear theories, some of which are not readily available in the literature, are included to show the influence of the material variation, boundary conditions, and loads

Breaking the Contrast Limit in Single-Pass Fabry-Pérot Spectrometers

The development of high-resolution Fabry-Pérot interferometers has enabled a wide range of scientific and technological advances—ranging from the characterization of material properties to the more fundamental studies of quasi particles in condensed matter. Spectral contrast is key to measuring weak signals and can reach a 103 peak-to-background ratio in a single-pass assembly.At its heart, this limit is a consequence of an unbalanced field amplitude across multiple interfering paths, with an ensuing reduced fringe visibility. Using a high-resolution, high-throughput virtually imaged phased array spectrometer, we demonstrate an intensity-equalization method to achieve an unprecedented 1000-fold increase in spectral contrast in a single-stage, single-pass configuration. To validate the system, we obtain the Brillouin spectrum of water at high scattering concentrations where, unlike with the standard scheme, the inelastic peaks are highly resolved. Our method brings the interferometer close to its ultimate limits and allows rapid high-resolution spectral analysis in a wide range of fields, including Brillouin spectroscopy, mechanical imaging, and molecular fingerprinting

Stacking sequences in composite laminates through design optimization

AbstractComposites are experiencing a new era. The spatial resolution at which is to date possible to build up complex architectured microstructures through additive manufacturing-based and sintering of powder metals 3D printing techniques, as well as the recent improvements in both filament winding and automated fiber deposition processes, are opening new unforeseeable scenarios for applying optimization strategies to the design of high-performance structures and metamaterials that could previously be only theoretically conceived. Motivated by these new possibilities, the present work, by combining computational methods, analytical approaches and experimental analysis, shows how finite element Design Optimization algorithms can be ad hoc rewritten by identifying as design variables the orientation of the reinforcing fibers in each ply of a layered structure for redesigning fiber-reinforced composites exhibiting at the same time high stiffness and toughening, two features generally in competition each other. To highlight the flexibility and the effectiveness of the proposed strategy, after a brief recalling of the essential theoretical remarks and the implemented procedure, selected example applications are finally illustrated on laminated plates under different boundary conditions, cylindrical layered shells with varying curvature subjected to point loads and composite tubes made of carbon fiber-reinforced polymers, recently employed as structural components in advanced aerospace engineering applications

Elastoplastic buckling analysis of thin-walled structures

The study is concerned with the elastoplastic buckling of thin-walled beams and stiffened plates, subjected to in-plane, uniformly distributed, uniaxial and biaxial load. The ruling differential equations have been solved analytically by using the Kantorovich technique and the obtained displacement field has been employed in a general procedure that, by using the framework derived by the finite element method, is able to analyze the elastoplastic buckling behaviorof prismatic beams and stiffened plates with arbitrary cross-section. The inelastic effect is modeledthrough a stress–strain law of the Ramberg–Osgood type, and both the incremental deformation theory and the J2flow theory are here considered. The reliability of the numerical procedure is illustrated for rectangular plates, and the contradicting results obtained by using the two plastic theories are discussed in detail. Finally, the performance of the method is illustrated through the analysis of a C-section and five different closed section columns

AN ENHANCED ANALYTICAL MODEL FOR BUCKLING INVESTIGATION OF MINDLIN PLATES

Buckling analysis of isotropic, rectangular plates subjected to uniformly axial and biaxial and pure shear loads is presented in this paper. In order to take into account the effect of transverse shear deformation, the Mindlin first order shear theory has been applied to the plate’s analysis. The novelty of the paper is that, assuming that the solution is separable, a closed-form solution is developed by an extended Kantorovich method without any use of approximation for the boundary conditions. A range of numerical applications is described for isotropic plates of thin, moderately thick and thick geometry. The good agreement of the results obtained using the proposed method, compared to other published results achieved by other numerical approaches and analytical solutions available in literature, illustrates the applicability, the effectiveness and the accuracy of the method. 1 INTRODUCTION Motivated by the great interest in numerous engineering applications, buckling of twodimensional systems has been extensively investigated in literature. The simplest model adopted in literature for the analysis of thin plates is based on the classical Kirchhoff thin plate theory [1] and extensive analysis for elastic stability of plates based on analytical [2] or numerical [3] solutions of the Kirchhoff equation have been carried out. However, because the Kirchhoff model neglects the effects of transverse shear deformations, it can underestimates deflection and overestimates the buckling loads when such effects are significant, and a more refined model may be necessary. For moderately thick plates, models based on Mindlin plate theory [4] are usually very satisfactory, and elastic stability of rectangular plates has been largely studied and – due to the difficulties encountered to analytically solve the governing equilibrium equation – several semianalytical or numerical approaches has been proposed in literature. For its generality, the numerical analyses based on the finite element method are the most commonly used in handling buckling problems of structure with general geometry and boundary conditions [5]. Boundary element method [6], least squares-based finite difference method [7], finite strip method [8], are some of the alternative methods available in literature for the buckling analysis of Mindlin plates. When the geometry of the structure is sufficiently regular, ad-hoc, more efficient semianalytical techniques can be successfully adopted, and the obtained solution are often very useful fo

An enhanced exponential matrix approach aimed at the stability of piecewise beams on elastic foundation

In this paper, an enhanced exponential collocation method for the stability assessment of piecewise beams resting on elastic foundation and subjected to both non-uniform distributed and concentrated loads is presented. The exponential basis functions usually adopted in literature are enriched with trigonometric functions that make the eigenvalue analysis well-posed without reducing the original simplicity of the method. A measure of the error occurring from the proposed approach and its improvement are also proposed. Several examples aimed at estimating the buckling loads under typical end supports are discussed. A comparison with exact and with other numerical results that are available in literature are carried out. Such a comparison shows the high accuracy and the fast convergence of the proposed approach

An analytical model for the buckling of plates under mixed boundary conditions

An analytical approach for the buckling analysis of rectangular plates under mixed boundary conditions is presented. In order to solve the partial differential equation governing the problem at hand a method of separation of variables is here adopted, by introducing the displacement field as a result of the scalar product of two vectors which combine prescribed and unknown scalar functions. By following this strategy, exact buckling solutions for a wide class of problems, in which mixed boundary conditions can be assigned relaxing some usual constraints, are determined, and buckling load of plates, where biaxial tensile and compressive loads are applied in presence of piecewise clamped and partially supported sides, obtained analytically. Several cases of engineering interest are finally analyzed, and comparisons of the theoretical outcomes with literature data and Finite Element-based numerical results are also shown, in order to highlight the effectiveness of the proposed strategy