Basic Displacement Research Articles

A novel finite element for the vibration analysis of tapered laminated plates

AbstractIn the present study, a new tapered finite element is developed by incorporating the in‐plane effect in our recently introduced element for the vibration analysis of internally tapered laminated plates. Stress and strain fields for a laminated plate with varying thickness along two orthogonal directions are expressed through extending classical laminated plate theory. Shape functions regarding bending and membrane behavior are extracted from the bending and axial basic displacement functions of the Euler‐Bernoulli beam, respectively. Several laminated plates with different taper configurations have been studied, and the results obtained from vibration analysis are compared with those of the literature. Since the element can capture the exact form of variation in thickness, the solution has shown to be competitively accurate with considerably fewer total degrees of freedom and elements in comparison with conventional finite elements.Highlight A new finite element for thin, tapered, laminated plates is introduced. Laminates' stiffness matrix is obtained for arbitrary thickness variation. A novel method is adopted to derive in‐plane shape functions. C1 continuity is guaranteed along the edges of elements. Calculation cost is considerably reduced.

Grafted copolymers based on HPMC with excellent thermo-viscosifying and salt-tolerant properties at low concentration for enhanced oil recovery

The conventional acrylamide-based polymers are greatly restricted under the reservoir conditions of high temperature and high salt due to their linear molecular structures. In this article, a grafted water-soluble copolymer based on hydroxypropyl methyl cellulose (HPMC) with excellent thermal viscosifying and salt-tolerant properties at low concentration was prepared via the “graft from” method, with acrylamide (AM) and methyl allyl polyoxyethylene ether (HPEG) as grafted monomers. The structure of the copolymer was identified by 1H nuclear magnetic resonance spectroscopy (1H NMR), Fourier transform infrared spectroscopy (FT-IR), thermogravimetric analysis (TGA) and scanning electron microscopy (SEM). The basic displacement properties of the copolymers under extreme conditions were systematically studied. The results showed that due to the symbiotic effects of the rigid heterocyclic structure of HPMC and the hydrophobic inter-molecular aggregation of thermosensitive HPEG units in the copolymer chain, the copolymer exhibited better thermal thickening ability (the viscosity enhancements changes from 7.1 to 19.9 times from 25 °C to 95 °C in brine solution with total salinity 9350.08 mg.L−1), salt resistance (the viscosity enhancements changes from 1.13 to 2.29 times with salts concentration from 0.0 wt% to 2.0 wt% at 85 °C), shear tolerance (the viscosity retention rate was from 18.6% to 24.2% at 1000s−1) and anti-aging properties (the viscosity retention rate up to 73.7% at 65 °C for three weeks) than polyacrylamide at low concentration (0.2 wt%). Furthermore, the polymer flooding test showed that the copolymer yielded a higher recovery rate of 23.2% higher than that yielded by polyacrylamide (14.5%), elucidating that the copolymer synthesized herein was suitable for enhanced oil recovery in reservoirs with severe conditions.

A New Rectangular Finite Element for Static and Dynamic Analysis of Arbitrarily Tapered Plates

This paper presents the formulation of a new efficient and conforming rectangular finite element for analysis of thin plates with any arbitrary variation of thickness along both edges. Shape functions of this new element are derived from multiplying shape functions of non-prismatic Euler–Bernoulli beam extracted from basic displacement functions. To provide [Formula: see text] consistency along the edges of elements, twist is added to conventional degrees of freedom, namely deflection and slopes resulting in an element with 16 degrees of freedom. The proposed element is used to solve various static and dynamic problems, and it is seen that the convergence of a new formulation occurs with much fewer elements compared to existing finite elements as a direct result of considering the variation of geometry in the derivation of shape functions, which renders the formulation competitive in both exactness and economy.

Molecular Logic Gate Based on DNA Strand Displacement Reaction

In this paper, I construct an XOR logic gate based on DNA strand displacement reaction, and verify our design through corresponding biochemical experiment. I designed several different DNA strands. Based on two basic DNA strand displacement reaction mechanisms, by adding different input strands and taking the signal of FAM fluorescent group as the output, the XOR logic gate is realized. The result shows that DNA strand displacement technology has important application value in DNA computing, especially in the construction of DNA molecular logic gates.

Dynamic capillarity during displacement process in fractured tight reservoirs with multiple fluid viscosities

AbstractDynamic capillarity commonly exists for multiphase flow in porous media, during which fluid viscosity varies and has strong influence. Displacement experiments are conducted on water‐wet, fractured tight rock at in situ pressure and temperature of an oil reservoir via a specially designed apparatus to investigate the effects of fluid viscosity on the dynamic capillarity. The dynamic effect in the matrix is examined through the measurement and calculation of capillary pressure, the dynamic coefficient, and the fluid flow behavior. The results show that with a higher oil viscosity: (a) both the steady and the dynamic capillary pressures reverse their directions more quickly and behave as larger resistances in the matrix; (b) the difference between the steady and the dynamic capillary pressures becomes around 5%‐19% more significant; (c) water saturation changes more slowly corresponding to the lower water relative permeability, while oil relative permeability quickly becomes lower than that during the basic displacement process; and (d) the dynamic coefficient becomes 2‐3 times higher, and the dynamic contact angle becomes 10%‐25% larger, showing a more variable interface. A contact angle advancement coefficient is proposed to identify the significance of contact angle advancement and the competition between capillary pressure and viscous force. The findings of this study can help for better understanding of multiphase flow in tight reservoirs and enhancing oil recovery.

Modular and conservative procedure for the quantification of amino functionalities bonded to solid porous matrices

Nowadays solid materials in which amino groups are linked to silica matrices through alkyl chains of different length (C18, C8, C4) are successfully employed in CO2 capture and storage technologies, as well as in a variety of chromatographic applications. In particular, their use as stationary phases finds remarkable success in performing HILIC separations and, in general, in the effective resolution of important compound classes (e.g. mixtures of mono- or oligo-saccharides). In this study an original and operationally simple procedure designed to quantify the density of basic groups (typically amino groups) chemically bonded to the surface of porous solids, which also allows a full recovery of the analysed material, is presented. The method is based on the preventive acid-base reaction of the basic groups linked to the solid by 3,5-dinitrobenzoic acid (DNBA). The quantification of the basic functionalities is then performed by an UV-spectrophotometric retro-titration of the thus salified solid matrix (or, alternatively, by HPLC approach), resorting to a preventive either acid or basic displacement of DNBA from the matrix. The uncertainty of the density measurements is assessed by 13%.

A Study of the Stress State of Underground Gas Pipelines in Mine Working Zones Using the Method of Internal Response Function

The stress state of pipelines in mine working zones, where the main loading factor is longitudinal soil displacements caused by the gradual filling of mine voids, has been calculated. Differential equations of pipe deformation have been formulated, for the solution of which the method of internal response function is proposed, which takes into account the mutual displacement of the pipe and soil in each iteration using a classical three-part nonlinear model of pipe–soil interaction. The type of interaction is determined on the basis of the concept of the basic displacement of the pipe, which is refined using displacements calculated in the previous iteration. The procedure of refining the basic solution is an important component of the method, where the basic solution in the next iteration is found as the sum of the previous solution and the difference between the calculated and previous solutions, multiplied by the convergence-control factor of the iterative procedure. To check the convergence accuracy and rate of the proposed iterative procedure, a comparative analysis with other existing procedures and results, obtained with the aid of commercial finite element programs, has been performed. To diagnose the stress state of pipelines during the working of longwall faces, a system for their continuous monitoring has been created. The correctness of the results of the performed numerical modeling of the stress state of a gas pipeline and the effectiveness of the measures that are developed to reduce the high stress level in its individual zones have been confirmed by relevant monitoring data, which are important both for refining the physical characteristics of pipe–soil interaction and for further taking into account the relaxation of these relations in time.

A new nine-node element for analysing plates with varying thickness using basic displacement functions

The capability of the Finite Element Method in producing accurate and efficient results largely depends on the shape functions adopted to frame the displacement field inside the element. In this paper, a new nine-node Lagrangian element was developed to analyse thin plates with varying cross-sections using the shape functions obtained for non-prismatic straight beams with minimum number of elements. The formulated shape functions, which represent vertical displacements and rotations throughout elements, are rooted from a purely mechanical functions called Basic Displacement Functions (BDFs). These functions are obtained by implementing the force method in Euler–Bernoulli beam theory, which ensures that equilibrium equation is satisfied in all interior points of elements. To verify the competency of the proposed element, solutions for the static analysis of isotropic rectangular plates under various loading conditions, together with free vibration analysis of plates with linear thickness variation were obtained and compared with the previous literature. Results showed that the proposed nine-node Lagrangian element was computationally more cost-effective compared to other competing methods when small number of elements is employed.

Basic Displacements in the Problem of Core Perturbations of a Thin Isochronous Vortex Ring

Periodic perturbations in the core of a thin isochronous vortex ring in an inviscid incompressible fluid are investigated in the linear approximation. The aim of the study is to construct the system of basic displacements, namely, the complete system of solutions of the Helmholtz equation for vorticity perturbations inside the core of a vortex ring with a given frequency in the form of expansion in the ring thinness parameter μ. The structure of basic displacements depends substantially on the fact to what extent the frequency of the forcing action is close to the resonance frequencies of the system. If the difference between these frequencies is small, then, in addition to the ring thinness μ, the second small parameters arises in the problem. This leads to significant complication of the procedure of obtaining the solution and appearance of considerable corrections in the subsequent approximations of the expansion procedure. The case of isochronous vortex ring in which the periods of revolution of liquid particles are identical is considered. Obtaining the threedimensional oscillations in such flows turns out to be the simplest since there are no perturbations of the continuous spectrum for the isochronous ring. The system of basic displacements is the necessary element in deriving the dispersion relation for the eigen-oscillations of the vortex ring. The solutions obtained can also serve as an instrument to analyze the reaction of flows with curvilinear vortex lines or flows localized in toroidal regions to the external excitation.

Analysis of Euler-Bernoulli nanobeams: A mechanical-based solution

The accuracy and efficiency of the elements proposed by finite element method (FEM) considerably depend on the interpolating functions namely shape functions used to formulate the displacement field within the element. In the present study, novel functions, namely basic displacements functions (BDFs), are introduced and exploited for structural analysis of nanobeams using finite element method based on Eringen’s nonlocal elasticity and EulerBernoulli beam theory. BDFs are obtained through solving the governing differential equation of motion of nanobeams using the power series method. Unlike the conventional methods which are almost categorized as displacement-based methods, the flexibility basis of the method ensures true satisfaction of equilibrium equations at any interior point of the element. Accordingly, shape functions and structural matrices are achieved in terms of BDFs by application of merely mechanical principles. In order to evaluate the competency and accuracy of the proposed method with different boundary conditions, several numerical examples with various boundary conditions are scrutinized. Carrying out several numerical examples, the results in stability analysis, free longitudinal vibration and free transverse vibration show a complete accordance with those in literature.

Spatial Finite Element Analysis for Dynamic Response of Curved Thin-Walled Box Girder Bridges

According to the flexural and torsional characteristics of curved thin-walled box girder with the effect of initial curvature, 7 basic displacements of curved box girder are determined. And then the strain-displacement calculation correlations were established. Under the curvilinear coordinate system, a three-noded curved girder finite element which has 7 degrees of freedom per node for the vibration characteristic and dynamic response analysis of curved box girder is constructed. The shape functions are used as the interpolation functions of variable curvature and variable height to accommodate to the variation of curvature and section height. A MATLAB numerical analysis program has been implemented.

On the FEM Analysis of Higher-Order Shear Deformable Beams: Validation of an Efficient Element

Since the accuracy of results obtained through displacement-based finite element method (FEM) considerably depends on the accuracy of shape functions used to interpolate the displacement field within an element, this paper aims at presenting a new efficient element for static and free vibration analysis of higher-order shear deformable beams using FEM with introducing basic displacement functions (BDFs). First, BDFs are introduced and computed. Afterward, new efficient shape functions are developed in terms of BDFs during the procedure based on the mechanical behavior of the element in which presented shape functions benefit generality and accuracy from stiffness and force method, respectively. Finally, deriving structural matrices of the beam with respect to new shape functions, static and free vibration behavior of the higher-order shear deformable beam is studied using FEM. The accuracy and economy of the method are demonstrated through several numerical examples.

3-node Basic Displacement Functions in Analysis of Non-Prismatic Beams

Purpose– Analysis of non-prismatic beams has been focused of attention due to wide use in complex structures such as aircraft, turbine blades and space vehicles. Apart from aesthetic aspect, optimization of strength and weight is achieved in use of this type of structures. The purpose of this paper is to present new shape functions, namely 3-node Basic Displacement Functions (BDFs) for derivation of structural matrices for general non-prismatic Euler-Bernoulli beam elements. Design/methodology/approach– Static analysis and free transverse vibration of non-prismatic beams are extracted studied from a mechanical point of view. Following structural/mechanical principles, new static shape functions are in terms of BDFs, which are obtained using unit-dummy-load method. All types of cross-sections and cross-sectional dimensions of the beam element could be considered in this method. Findings– According to the outcome of static analysis, it is verified that exact results are obtained by applying one or a few elements. Furthermore, it is observed that results from both static and free transverse vibration analysis are in good agreement with the previous published once in the literature. Research limitations/implications– The method can be extended to structural analysis of curved and Timoshenko beams as well as plates and shells. Furthermore, exact dynamic shape functions can be derived using BDFs by solving the governing equation for transverse vibration of beams. Originality/value– The present investigation introduces new shape functions, namely 3-node Basic Displacement Functions (BDFs) extended from 2-node functions, and then compares its performance with previous element.

Analysis of Tapered Thin Plates Using Basic Displacement Functions

Presenting new functions, basic displacement functions (BDFs), a novel method is introduced for the analysis of arbitrarily tapered thin plates in preference to primarily mathematically based methodologies. BDFs are obtained through applying unit load theorem and considering two orthogonal strips of unit width in tapered plates based on static deformations. It is shown that new shape functions and consequently structural matrices could be derived in terms of BDFs through a mechanical approach. On the other hand, BDFs could be used to calculate new shape functions, whereas Hermitian functions are used in several elements such as ACM and BFS. It is demonstrated that the accuracy of these new shape functions is significantly improved by considering the geometrical and mechanical properties of the plate element in the evaluation of the structural matrices. So, contrary to usual shape functions used in FE methods, they are susceptible to the thickness variation and then higher accuracy and more rapid convergence could be expected with fewer elements. In order to verify the competency of the proposed method, several numerical examples for classical boundary conditions are carried out and the results are compared with those in the literature.

Research on Seismic Design and Modeling of City Viaduct

This paper gives the basic methods for the analysis of the seismic response of viaduct based on elastic-plastic response spectrum method, and established indicators correspond with the method of strength, deformation, basic displacement and other performance. Practical example shows that the elastic-plastic response spectrum analysis response can be careful examining structure of each target in strong earthquake action value, and compare with the nonlinear time-history analysis, the method is concise, efficient, stable, and has the statistical significance of spectrum analysis, that can be used as a city track traffic high bridge and practical method.

Free Vibration of Tapered Mindlin Plates Using Basic Displacement Functions

Introducing the concept of basic displacement functions (BDFs) in plate elements, a novel method is proposed to calculate new shape functions of tapered Mindlin plates for the free vibration analysis using BDFs. The BDFs are obtained from dynamic deformations of an arbitrary point in tapered Mindlin plate using Ritz method and substituting boundary equations of Clamped–Clamped–Free–Free plate in them. It is shown that exact shape functions and consequently structural matrices could be derived from BDFs. Unlike current shape functions used in FE method, the new shape functions take thickness variation and eigenfrequencies of the plates into account. So, higher accuracy and more rapid convergence could be expected with fewer elements. To verify the competency of the present shape functions, the results of several numerical examples are compared with those in the literature. It is shown that these shape functions derived from BDFs have quite satisfactory accuracy and low computational cost.

A Mechanical-Based Solution for Axially Functionally Graded Tapered Euler-Bernoulli Beams

In this article, structural analysis of axially functionally graded tapered beams is studied from a mechanical point of view using a finite element method. Introducing the concept of basic displacement functions (BDFs), it is shown that exact shape functions could be explicitly obtained in terms of BDFs via application of basic principles of structural mechanics. BDFs are obtained using the unit-dummy-load method. Carrying out static analysis, it is verified that exact results are provided by applying one or a few elements. The competency of the present element in stability and free vibration analyses is verified through several numerical examples.

Free Vibration Analysis of Centrifugally Stiffened Tapered Functionally Graded Beams

Free vibration of rotating tapered beams made of functionally graded (FG) materials is studied through a finite element approach. A new element is introduced that takes advantage of the exact shape functions for nonrotating tapered FG beam elements. Developing a new type of unit-dummy-load method, special functions, namely, basic displacement functions (BDFs) are derived from which the exact shape functions are obtained. The element is employed in free vibration analysis where the effects of taper ratio, rotational speed, and hub radius are investigated. The present results could be efficiently used for future research works in this field.

New shape functions for non-uniform curved Timoshenko beams with arbitrarily varying curvature using basic displacement functions

Basic Displacement Functions (BDFs) are introduced and derived using the basic principles of structural mechanics. BDFs are then utilized to obtain new shape functions for arbitrarily curved non-uniform beams, including the effects of shear deformation and extensibility of neutral axis. The main virtue of the proposed shape functions is their susceptibility to the variations in cross-sectional area, moment of inertia, and curvature along the axis of the beam element. Competence of the present method in static and free vibration analyses, as well as its applicability to the special case of straight Timoshenko beam has been verified through several numerical examples.

Elasto-Plastic Analysis of Thick Cylinders Subjected to Internal Electro-Magnetic Loading

AbstractA study of elasto-plastic deformation of circular cylindrical shells subjected to internal electromagnetic forces is presented in this paper. The five governing equations in terms of resultant forces and resultant moments with respect to basic displacement vector components u, v and w are used. Theoretical formulations, based on the first-order shear deformation theory (FSDT), take into consideration transverse shear deformation and rotary inertia. The deformation theory of plasticity is employed for constitutive equations. The cylinders are composed of an elastic-plastic material with the von Mises yield criteria and non-linear plastic behaviour. Galerkin method is employed to convert the partial differential equations (PDEs) to ordinary differential equations (ODEs). The Newmark family of methods is used to numerically time integration of system of coupled second order ODEs. In order to prove the validity of the presented method and the solving process, the results obtained with the present analysis are compared with a set of available data. Good agreement observed between the results of the two approaches. Certainly, the aim of this paper is to create a more reliable and precise mathematical model of hollow-cylinders to avoid performing several experiments.