Arbitrary Cross Section Research Articles

Analytic model of 3D beam dynamics in a wakefield device

In this paper we suggest an analytic model, and derive simple formulas, for the beam dynamics in a wakefield structure of arbitrary cross-section. The results could be applied to estimate an upper limit of the projected beam size in devices such as the dechirper and the wakefield streaking device. The suggested formalism is also applicable to the case when slices of the beam are distributed along an arbitrary line in 3D.

An energy-based approach to buckling modal decomposition of thin-walled members with arbitrary cross-sections, Part 2: Modified global torsion modes, examples

This paper is a companion to (Khezri and Rasmussen, 2019) [1], where the generalised strain energy-based method for the modal decomposition of buckled shapes of thin-walled members is introduced. The paper presents the application of the proposed method for full modal decomposition to various thin-walled members. A series of numerical examples are presented in order to verify the robustness and capabilities of the proposed modal finite strip method (mFSM). In addition, the problem of global torsional modes in sections with closed cell(s) is revisited in this paper. In sections with closed loops, the classical global torsion modes does not exist due to presence of in-plane shear strains. In the context of the proposed energy-based method, a modified global torsion buckling mode is derived that allows for the occurance of shear in closed cell. The pure global buckling curves obtained incoporating the modified global torsion base vectors are compared with the generalised constrained FSM (cFSM) and generalised beam theory (GBT) results. It is shown that the proposed modal decomposition method is capable to accurately capture the modal behaviour of thin-walled sections.

A novel automatic device to measure deformation inside transparent soil based on digital image correlation technology

In geotechnical engineering, the measurement of soil deformation is one of the most important foundations of soil mechanics research. Transparent soil is a desired choice to obtain information on spatial deformation inside the soil. Based on this, a novel measuring device was developed to automatically record laser speckle images at different laser cross-sections, and the displacement deformation of transparent soil at arbitrary cross-section positions was determined by the planar digital image correlation (DIC) technique. The measuring system was built with two high-precision motorized linear stages. An industrial camera was used in the system to capture the laser speckle images, and synchronization control methods of both the laser transmitter and industrial camera were introduced. The planar DIC technique employed in this paper has been described in detail. The high-precision motorized linear stages proved to have excellent repeatability and the displacement field of a certain laser cross-section in transparent soil can be obtained. Theoretically, the spatial deformation inside the transparent soil can be built based on the displacement fields of multiple laser cross-sections. Finally, the design scheme was confirmed by the model pile experiment. The experiment results show that the automatic measuring system has stable operation, and the deformation of arbitrary laser cross-sections inside transparent soil can be obtained easily. This automatic measurement method can be regarded as an innovation in geotechnical physical model experiments.

Modal approach to optical forces between waveguides as derived by transformation optics formalism

Optical force between two lossless waveguides has been described by two approaches. One approach is the explicit description of the force by the Maxwell stress tensor. Another approach is to describe the modal force in terms of the derivative of the eigenmode frequency with respect to the distance variation. Here, we analytically prove the equivalence of these two approaches for lossless waveguides having arbitrary cross sections through the use of transformation optics formalism. Our derivation is applicable to both pressure and shear forces. We also show that these two approaches are not equivalent in the presence of loss.

Accurate stress fields of post-buckled laminated composite beams accounting for various kinematics

Highly flexible laminated composite structures, prone to suffering large-deflection and post-buckling, have been successfully employed in a number of scenarios. Therefore, accurate predictions of their stress distributions in the geometrically nonlinear analysis are of paramount importance for their design and failure evaluation. In this paper, for composite beams subjected to large-deflection and post-buckling, we investigate the effectiveness of different geometrically nonlinear strain approximations for the description of their nonlinear static response and for the determination of stress distributions. For this purpose, a unified formulation of geometrically nonlinear refined beam theory based on the Carrera Unified Formulation (CUF) and a total Lagrangian approach constitutes the basis of our analysis. Accordingly, various kinematics of one-dimensional structures are formulated via an appropriate index notation and an arbitrary cross-section expansion of the generalized variables, leading to lower- to higher-order beam models with only pure displacement variables for laminated composite beams. In view of the intrinsic scalable nature of CUF and by exploiting the principle of virtual work and a finite element approximation, nonlinear governing equations corresponding to various nonlinear strain assumptions can be straightforwardly and easily formulated in terms of fundamental nuclei, which are independent of the theory approximation order. Several numerical assessments are conducted, including large-deflection and post-buckling analyses of asymmetric and symmetric laminated beams under compression loadings. The numerical solutions are solved by using a Newton–Raphson linearization scheme along with a path-following method based on the arc-length constraint. Our numerical findings demonstrate the capabilities of the CUF model to calculate the large-deflection and post-buckling equilibrium curves as well as the stress distributions with high accuracy, which could be a basis to assess the validation ranges of various kinematics and different nonlinear strain approximations.

FermiSurfer: Fermi-surface viewer providing multiple representation schemes

FermiSurfer is a newly developed Fermi-surface viewer designed to facilitate the understanding of the physical properties of metals. It can display the Fermi surfaces of a material, color plots of arbitrary k-dependent quantities, the Fermi surface at arbitrary cross sections (Fermi lines), cross- or parallel-eye three-dimensional stereogram views, nodal lines, extremal orbits, and highlight the occupied or empty side of the Fermi surface. In addition, various first-principles software packages can produce input for FermiSurfer. This paper explains how to use FermiSurfer and demonstrates its usefulness by investigating the origin of the anisotropic superconductivity of YNi2B2C. Program summaryProgram Title: FermiSurferProgram Files doi:http://dx.doi.org/10.17632/36992zhpvk.1Licensing provisions: MITProgramming language: CNature of problem: The anisotropy of quantities on Fermi surfaces (the character of orbitals, etc.) strongly affects electronic properties, such as superconductivity or thermoelectricity, in metals. Observing the anisotropy, however, remains difficult. Thus, a graphical tool that can elucidate how quantities vary over complicated Fermi surfaces is highly desirable.Solution method: FermiSurfer uses the tetrahedron method to compute Fermi surfaces. The French-curve interpolation is used to display smooth Fermi surfaces.Additional comments including restrictions and unusual features : The parallel- and cross-eye stereograms are available to enhance the visibility of complicated Fermi surfaces. This program works on any operating system, such as Linux, UNIX, macOS, and Windows, in which OpenGL library is installed.

An accurate and efficient series solution for the longitudinal vibration of elastically restrained rods with arbitrarily variable cross sections

Longitudinal vibration of non-uniform rod has been of great significance in various engineering occasions. The existing works are usually limited to the certain area variation and/or classical boundary condition. Motivated by this limitation, an efficient accurate solution is developed for the longitudinal vibration of a general variable cross-section rod with arbitrary boundary condition. Displacement function is invariantly expressed as the summation of standard Fourier series and supplementary polynomials, with an aim to make the calculation of all derivatives more straightforwardly in the whole solving region [0, L]. Energy principle is employed for system dynamics formulation, with the elastic boundaries considered as potential energy stored in the restraining spring. Arbitrary cross-section area variation is uniformly expanded into Fourier series. Numerical examples are presented for the natural frequency and mode shapes of non-uniform rod of free and clamped boundary conditions and compared with literature data. Results show good agreement with the previous analytical solutions. Influence of cross section area variation on vibration characteristics of non-uniform rods is then studied and discussed. One of the most advantages of the proposed model is that there is no need to reformulate the problem or rewrite the codes when the cross-section area distribution and/or boundary conditions change arbitrarily.

Mutually touching infinite cylinders in the 3D world of lines

Recently we gave arguments that only two unique topologically different configurations of 7 equal all mutually touching round cylinders (the configurations being mirror reflections of each other) are possible in 3D, although a whole world of configurations is possible already for round cylinders of arbitrary radii. It was found that as many as 9 round cylinders (all mutually touching) are possible in 3D while the upper bound for arbitrary cylinders was estimated to be not more than 14 under plausible arguments. Now by using the chirality and Ring matrices that we introduced earlier for the topological classification of line configurations, we have given arguments that the maximal number of mutually touching straight infinite cylinders of arbitrary cross-section (provided that its boundary is a smooth curve) in 3D cannot exceed 10. We generated numerically several configurations of 10 cylinders, restricting ourselves with elliptic cylinders. Configurations of 8 and 9 equal elliptic cylinders (all in mutually touching) are generated numerically as well. A possibility and restriction of continuous transformations from elliptic into round cylinder configurations are discussed. Some curious results concerning the properties of the chirality matrix (which coincides with Seidel's adjacency matrix important for the Graph theory) are presented.

Wave radiation from a truncated cylinder of arbitrary cross section

In this paper, a semi-analytical model for solving wave radiation from a truncated cylinder of arbitrary cross section is presented based on linear potential flow theory. The water domain is divided into the interior domain beneath the cylinder and the exterior domain outside the vertical cylinder column. Radiated spatial potentials in these subdomains are expressed as a series expansion of eigen-functions using the method of separation of variables. The continuity conditions for pressure and velocity are satisfied at the interface of the two domains, where the Fourier series expansion method is employed to deal with the radius function associated terms. Therefore, the unknown coefficients in the radiated potential expressions are determined by means of the eigen-function matching method. Hydrodynamic coefficients of the truncated cylinder are evaluated directly based on the radiated spatial potentials. Case studies on wave radiation from a truncated cylinder with “cosine” and “circular” cross sections show a good agreement between the semi-analytical results of added-mass/radiation damping and numerical ones/published data. The validated semi-analytical model is then adopted to study the hydrodynamic characteristics of truncated cylinders with “circular”, “cosine”, “elliptical” and “quasi-elliptical” sections. For the latter case, the influence of draft on wave radiation is also investigated.

UAV-Based 3D Point Clouds of Freshwater Fish Habitats, Xingu River Basin, Brazil

Dense 3D point clouds were generated from Structure-from-Motion Multiview Stereo (SFM-MVS) photogrammetry for five representative freshwater fish habitats in the Xingu river basin, Brazil. The models were constructed from Unmanned Aerial Vehicle (UAV) photographs collected in 2016 and 2017. The Xingu River is one of the primary tributaries of the Amazon River. It is known for its exceptionally high aquatic biodiversity. The dense 3D point clouds were generated in the dry season when large areas of aquatic substrate are exposed due to the low water level. The point clouds were generated at ground sampling distances of 1.20–2.38 cm. These data are useful for studying the habitat characteristics and complexity of several fish species in a spatially explicit manner, such as calculation of metrics including rugosity and the Minkowski–Bouligand fractal dimension (3D complexity). From these dense 3D point clouds, substrate complexity can be determined more comprehensively than from conventional arbitrary cross sections.

Asymptotic Expansion and Numerical Solution for Gravity Waves in a Porous Media

In this paper, we study wave interaction with a porous structure. A nonlinear diffusive wave equation is used to describe gravity surface wave propagation in a porous media. We solve the equations using asymptotic expansion method and numerically using a staggered finite volume method. We then derive the dispersion relation that holds for gravity waves inside a porous structure. This dispersion relation explains the diffusive mechanism of wave amplitude inside the porous structure. Analysis of the dispersion relation shows that amplitude reduction depends on porous medium parameters such as porosity, friction coefficient, length of the structure, and wave frequency. To validate our numerical scheme, we compare the wave reduction amplitude from the numerical result with the asymptotic solution. A good agreement of the comparison is observed. Furthermore, the numerical model is employed to investigate the effectiveness of porous media in dissipating wave energy of an incoming wave. The results from this paper can be used to determine the optimum dimension of the porous medium so that the incoming wave can be reduced as much as possible to protect shoreline. References H.J.S. Fernando, S.P. Samarawickrama, S. Balasubramanian, S.S.L. Hettiarachchi, and S. Voropayev. Effects of porous barriers such as coral reefs on coastal wave propagation. Journal of Hydro-environment Research, 1(3):187 – 194, 2008. Pengzhi Lin and S. A. Karunarathna. Numerical study of solitary wave interaction with porous breakwaters. Journal of Waterway, Port, Coastal, and Ocean Engineering, 133(5):352–363, 2007. Philip L.-F. Liu, Pengzhi Lin, Kuang-An Chang, and Tsutomu Sakakiyama. Numerical modeling of wave interaction with porous structures. Journal of Waterway, Port, Coastal, and Ocean Engineering, 125(6):322–330, 1999. Patrick J. Lynett, Philip L.-F. Liu, Inigo J. Losada, and Cesar Vidal. Solitary wave interaction with porous breakwaters. Journal of Waterway, Port, Coastal, and Ocean Engineering, 126(6):314–322, 2000. O.S. Madsen. Wave transmission through porous structures. Journal of Waterways, Harbors, Coastal Engineering, 100:169–188, 1974. I. Magdalena, S. R. Pudjaprasetya, and L. H. Wiryanto. Wave interaction with an emerged porous media. Advances in Applied Mathematics and Mechanics, 6(5):680–692, 06 2015. S.R. Pudjaprasetya and I. Magdalena. Momentum conservative scheme for dam break and wave run up simulations. East Asia Journal on Applied Mathematics, 4(2):152–165, 2014. Panagiotis D. Scarlatos and Vijay P. Singh. Long-wave transmission through porous breakwaters. Coastal Engineering, 11(2):141 – 157, 1987. C.K. Sollitt and R.H. Cross. Long-wave transmission through porous breakwaters. Proc. 13th Coastal Eng. Conf. 3, pages 1827–1846, 1972. W. Sulisz. Wave reflection and transmission at permeable breakwaters of arbitrary cross-section. Coastal Engineering, 9:371–386, 1985. M. R. A. Van Gent. Wave interaction with permeable coastal structures. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 33(6):277A, 1996.

Higher buckling and lateral buckling strength of unrestrained and braced thin-walled beams: Analytical, numerical and design approach applications

The present study investigates the flexural-torsional struts buckling and beam lateral buckling analyses. In the highlight of braced structures, analytical solutions are derived for higher 3D buckling modes of simply supported struts with arbitrary cross-sections. Closed-form solutions are also investigated for lateral buckling strength of beams with doubly symmetric cross-sections. For more general cases, the finite element approach is adopted. In presence of torsion, warping is of primary importance. For this aim, 3D beams with 7 degrees of freedom (DOFs) per node are adopted in the analysis. The model is able to carry out higher buckling modes of bars under compression or lateral buckling modes of beams initially in bending. The analytical and the numerical results of the present model are compared to some available benchmark solutions of the literature and to finite element simulations of some commercial codes (Abaqus, Adina). The efficiency of the closed form solutions and the numerical approach is successfully verified. Applications of higher buckling modes in design of braced structures are considered according to Eurocode 3 code. A particular attention is pointed out to torsion and flexural-torsional buckling modes not considered in bar strength. At the end, some solutions are proposed in order to cover the full strength of columns and beams in presence of instabilities. This proposal makes steel structures more performant and attractive when effects of instabilities are limited at a minimum.

On using load-axial shortening plots to determine the approximate buckling load of short, real angle columns under compression

In the present paper, a methodology for determination of an approximate value of the lowest buckling load of the thin-walled column under compression and with an arbitrary cross-section, affected by initial imperfections, whose amplitude does not exceed half the thickness of the wall, using a load-axial shortening plot, is presented. It has been shown that the load corresponding to an alternation in rigidity of the real structure on the load-axial shortening plot determines the buckling load with high accuracy. The attained results have been compared to the values corresponding to the bifurcation load and the lowest buckling loads determined with commonly used methods based on post-buckling equilibrium paths (i.e., P-w method, P-w2 method, inflection point method).The formulated problem of nonlinear buckling has been solved with the analytical-numerical method and the FEM. An influence of the imperfection amplitude on an approximate value of the lowest buckling load of laminated thin-walled structures has been analysed on the determined post-buckling equilibrium paths and the load-axial shortening plot. Non-symmetric configurations of laminate layers that additionally exhibit various types of the membrane and bending state coupling have been selected. Detailed computations have been conducted for short angle sections (i.e. angle columns) under uniform compression.

Fragmentation model of ring with arbitrary cross-section under its fast radial expansion

Fragmentation model of ring with arbitrary cross-section under its fast radial expansion

Surface Subsidence Prediction Method for Coal Mines with Ultrathick and Hard Stratum

Overburden conditions consisting of ultrathick and hard stratum (UTHS) are widespread in China and other countries, but existing surface subsidence prediction methods ignore the strong impact of UTHS on surface subsidence. They are thus not applicable for surface subsidence prediction for coal mining with the presence of UTHS. We conducted actual measurements of surface and UTHS subsidence in the Tingnan Coal Mine. The results showed that under the UTHS mining condition, the required gob dimension is much larger than the empirical value when the surface reaches sufficient mining and that the actual measured maximum value of surface subsidence is much smaller than the empirical value. The UTHS subsidence is approximately equal to the surface subsidence. The movement of UTHS has a strong impact on surface subsidence and has a controlling function for it. It was proposed that surface subsidence could be approximately predicted by calculating the UTHS subsidence. The UTHS movement characteristics were studied using Winkler’s theory of beams on an elastic foundation, the subsidence prediction equation of the main sections in the strike and dip directions was obtained under different mining dimensions, and the subsidence prediction equation of any arbitrary cross section parallel to the two main sections was established. Then, the surface subsidence prediction method for coal mining with the presence of UTHS was developed, and the influences of UTHS thickness, strength, and layer position on the surface subsidence were discussed. The Tingnan Coal Mine was taken as an example, and the subsidence curves of the strike and dip main sections were calculated using different mining dimensions. Subsequently, the surface subsidence after the mining of working faces 204, 205, 206, and 207, respectively, was predicted, and the prediction method was verified by comparing the results with the measured surface subsidence results of working faces 204, 205, and 206.

Constructing Yield Loci for Rigid-Plastic Reinforced Plates Considering the 2D Stress State in Fibers

Models of unidirectionally and orthogonally fiber-reinforced hybrid media of a regular periodic structure allowing one to determine the yield loci for these composites are constructed. Phase materials of the compositions are isotropic, and their mechanical behavior is described by the associated flow rule for rigid-plastic bodies with the Tresca yield condition. A plane stress state is assumed in the composition and all its components, and fibers are oriented along the directions of principal stresses in the composite body. The cases of rectangular and arbitrary cross sections of reinforcing fibers are considered. Analytical expressions for equations describing the regimes of yield conditions are obtained. Different passages to the limit of a homogeneous medium are investigated. Yield loci calculated by the models proposed and the widely used structural model with a one-dimensional stress state in fibers are compared. Yield loci in the case of imperfect adhesion between the reinforcement and binder material are constructed.

Permeability Model for Porous Transducer With Glass Spheres Packing

A theoretical model is developed for predicting permeability of a porous transducer, which is a crucial component of liquid circular angular accelerometer and sintered by glass microspheres. The proposed permeability model of the transducer is determined with consideration of its shape factor, tortuosity, and particle size distribution (PSD) characterized by equivalent mean diameter and skewness. A novel analytical method for calculating the shape factor for the arbitrary cross-section area is derived. In addition, a tortuosity model is designed by fitting skewness and tortuosity of particle packing beds in a regular tetrahedron microspheres arrangement structure. Together with the analytical model of shape factor, the tortuosity fitting model and a method to determine equivalent diameter from PSD, the permeability model is implemented to compare with Kozeny–Carman (KC) model. The experiments are performed to measure the permeability of four types of porous transducers fabricated with different PSDs and consequently validate the permeability model. The results indicate that the proposed model can be utilized for predicting permeability of porous transducer with higher precision.

Bending by explosion of a multilayered concrete beam on a visco-elastic basis

In this work, the problem of bending of a multilayered concrete beam of arbitrary cross-section by explosive loading on a visco-elastic basis is considered. It is assumed that different grades of concrete can be realized in layers in the cross-section. The property of concrete resistance to tension and compression is considered in work. It is assumed that the dynamic loading is caused by consecutive explosion of two charges over the middle of the span of beam. The distribution of bending moments and deflections of the beam at each time is determined. The time of the end of motion and the residual deflection of beam are found.

Longitudinal cracks in non-linear elastic beams exhibiting material inhomogeneity

Longitudinal fracture behavior of non-linear elastic beam configurations is studied in terms of the strain energy release rate. It is assumed that the beams exhibit continuous material inhomogeneity along the width as well as along the height of the cross-section. The Ramberg-Osgood stress-strain relation is used for describing the non-linear mechanical behavior of the inhomogeneous material. A solution to strain energy release rate is derived that holds for inhomogeneous beams of arbitrary cross-section under combination of axial force and bending moments. Besides, the solution may be applied at any law of continuous distribution of the modulus of elasticity in the beam cross-section. The longitudinal crack may be located arbitrary along the beam height. The solution is used to investigate a longitudinal crack in a beam configuration of rectangular cross-section under four-point bending. The crack is located symmetrically with respect to the beam mid-span. It is assumed that the modulus of elasticity varies continuously according a cosine law in the beam cross-section. The longitudinal fracture behavior of the inhomogeneous beam is studied also by applying the J-integral approach for verification of the non-linear solution to the strain energy release rate derived in the present paper. Effects of material inhomogeneity, crack location along the beam height and non-linear mechanical behavior of the material on the longitudinal fracture behavior are evaluated. Thus, the solution derived in the present paper can be used in engineering design of inhomogeneous non-linear elastic structural members to assess the influence of various material and geometrical parameters on longitudinal fracture.

Forced Vibration Analysis of Non-Uniform Piezoelectric Rod by Complementary Functions Method

Piezoelectric materials, which have fast response and low energy usage features, are widely used in sensors and actuators. Due to the active role of their working principle, it is important to know the vibration characteristic of each piezoelectric material. In this paper, forced vibration analysis of arbitrary non-uniform piezoelectric rod has been performed. The governing differential equations have variable coefficients which are functions of mechanical and electrostatic properties. Analytical solution of these linear differential equations is limited to specific cross-section area models, so numerical method is inevitable. Numerical model of the forced vibration of cantilever piezoelectric (PZT-4) rod with an arbitrary non-uniform cross-section area is obtained in the Laplace space and then solved numerically by Complementary Functions Method (CFM). Solutions were transformed from Laplace domain to the time domain by applying modified Durbin’s procedure. The technique is validated for a uniform piezoelectric rod that can also be solved analytically. In order to demonstrate the effect of arbitrary geometry on the dynamic feature of the rod, numerical examples are employed.