Strip Element Research Articles

Piezoresistive properties for soft structures using hybrid CCB/CNT-based natural rubber latex composites

This study explores the development of flexible sensors for soft structures. Conductive carbon black (CCB) and carbon nanotubes (CNT) were incorporated into a natural rubber (NR) matrix using glutaraldehyde (GA) as a curing system. The sensor properties of latex-NR composites with 20 phr of CCB, including variations of CNT content (0.5 to 3 phr), were examined. Increasing CNT content beyond 0.5 phr decreased tensile strength and elongation at break, but improved sensitivity and gauge factor (GF). Additionally, applying a voltage over 5 V caused a joule heating of the latex-NR composite strip elements. When integrated onto a soft tendon-based TPU bending actuator, higher CNT content reduced electrical signal drift during cyclic bending, enhancing long-term monitoring. This research highlights the potential of CCB/CNT-based latex-NR composites for soft structure applications, including soft robotics and health monitoring.

Active dual-control electromagnetically induced transparency analog in metal- vanadium dioxide-photosensitive silicon hybrid metamaterial

We investigate an active dual-control metamaterial leveraging electromagnetically induced transparency (EIT), exploiting near-field interactions between electric and magnetic dipole resonances. Our hybrid strip element, combining metal and vanadium dioxide, generates electric dipole resonance, while split-ring resonators integrating metal and photosensitive silicon induce magnetic dipole resonance. Simulations confirm coupling validity and demonstrate dynamic adjustability of EIT via temperature and light intensity changes. EIT modulation transitions between transparent and non-resonant states due to temperature fluctuations, or resonant states with varying light intensity. Temperature adjustments dominate when both factors are altered. Analysis via a coupled oscillator model reveals modulation of damping rates as the origin of disappearance curve variations. This innovative design enhances tunable EIT metamaterial versatility, with implications for high transmission ratios and adaptable slow-light effects in terahertz applications.

A unified impact response analysis for FG-CNTRC and 3D-GrF sandwich composite sector- rectangular coupled plates

This paper proposes a general method for analyzing the dynamic response characteristics of sector- rectangular coupled plates subjected to external impacts. This method combines the method of reverberation-ray matrix (MRRM) with the strip transfer function method, referred to as the strip method of reverberation-ray matrix (S-MRRM). The traditional MRRM has some limitations for the dynamic modeling of the sector structure and also requires the Lévy-type exact solution, leading to simply supported boundary conditions in certain direction of the structure. The present method can not only address the aforementioned limitations but also maintain the efficiency advantage of the wave method for solution. The investigated structure consists of sandwich panels composed of functionally graded carbon nanotube reinforced (FG-CNTRC) panels and the three-dimensional graphene foam (3D-GrF) core. The structure is discretized into several strip elements by the strip transfer function method, and the whole dynamic model of the structure is obtained through matrix assembly. The motion differential equation in matrix form is derived by using Hamilton principle, followed by obtaining the matrix-form wave number equation. Upon deriving the wave solution of the structure based on this equation, the transient and steady-state responses of the structure are obtained by employing MRRM. Convergence analysis is conducted on these calculation results, followed by comparison with FEM results to validate its prediction accuracy. Finally, through a comprehensive parametric study, the impacts of various factors such as CNTs distribution form, CNTs volume fraction, 3D-GrF pore distribution form, 3D-GrF porosity, and sandwich panel thickness ratio on both transient and steady-state responses of these structures were investigated, thereby providing guidance for engineering applications.

Use of the Sub Array From Microstrip Elements in Dielectric Layers Before the Aperture of Phased Antenna Array for Impedance Matching at Scanning

The solution of an electrodynamics’ problem of radiation of the Phased antenna array (PAR), representing the infinite periodic structure generated from the open ends of waveguides is offered. Before an aerial aperture sub array from strip (tape) elements in the dielectric layers is installed. The array in the dielectric layers f organizes of strip-geometry elements artificial medium. The problem is reduced to system of the integrated equations of 1-st sort which is decided concerning unknown fields in the aperture of the open ends of waveguides and currents on stripe-geometry elements. In a wide frequency band the numerical analysis of radiation parameters artificial dielectric medium on PAR electrodynamics’ characteristics at beam steering.

View factors from a longitudinal strip to cylindrical segments and disk sectors

Analysis of temperature distribution and net radiation heat exchange in a cylindrical enclosure, when the temperature varies with the directions, requires view factors between relevant finite surfaces, viz. between a pair of finite cylindrical segments on the lateral surface, and between a finite cylindrical segment and a sector on the base disk. A review of literature shows that analytical expressions or data are not available for the referred view factors. In this paper, analytical expressions for the view factors from a differential area on the lateral surface of cylinder to cylindrical segments, and also to sectors on the base disk are derived by contour integration method. Such expressions are integrated analytically to obtain the view factors from a longitudinal strip element on inner lateral surface of cylinder to segments of cylinder, and sectors on base disk. A representative parametric study is carried out for the latter view factors. These expressions are applicable for the two dimensional analysis of space radiator tubes.

Efficient time-domain spectral element with zigzag kinematics for multilayered strips

Efficient structural elements are widely sought for fast computation of wave propagation response of anisotropic multilayered structures for their design, non-destructive testing, and structural health monitoring purposes. Although zigzag theories are known to combine excellent accuracy with high computational efficiency, no spectral element has been developed so far based on these theories, which would enable fast and accurate simulation of guided waves in such structures. In this article, we develop an efficient time-domain spectral strip element for analyzing ultrasonic wave propagation in multi-material laminated beams and panels while accounting for the zigzag profile of the in-plane displacement across the thickness. The theory superimposes a layerwise linear (zigzag) variation of the in-plane displacement of a layerwise theory onto the global third-order variation of an equivalent single layer (ESL) third-order theory while retaining the computational advantage of the latter. The high-order element has an arbitrary number of unequally spaced nodes with only four kinematic variables at each node, regardless of the number of laminas. The recently proposed generalized Hermite-type C1-continuous Lobatto shape functions interpolate the deflection, while the axial displacement and shear rotation are interpolated using the C0-continuous Lobatto shape functions. A comprehensive numerical study establishes high efficiency, excellent accuracy, and fast convergence of the new element in analyzing free vibration and guided wave propagation in single-material composite and multi-material fiber-metal laminate structures. Its combined performance in terms of these parameters is much superior to its standard FE counterpart, the ESL theory-based elements, and the continuum elements in the considered frequency range.

Dynamic response of functionally graded plate under harmonic load with variable gradient parameters

Abstract This article used the strip element method to study the dynamics problems of the functionally graded plate with variable gradient parameters under the harmonic loads. The dynamic model of the functionally graded plate is established by using the strip element method, the rationality and accuracy of the theoretical results are verified by finite element method, and the displacement response under different gradient parameters is also calculated. The results show that under the different gradient parameters, the displacement varies harmonically with time, and with the increase of gradient parameters, the fluctuation period of displacement with time increases continuously, and the displacement peak also gradually increases. The displacement along the thickness direction also shows the harmonic form. Through comparison, it is found that the gradient parameters have a greater impact on the dynamic response for the functionally graded plate; with the increase in the gradient parameters, the displacement response also increases, but the displacement response trend slows down.

Lateral-distortional buckling of steel-concrete composite beams: Kinematics, constrained-mode GBT and analytical formulae

This paper investigates and sheds fresh light on the kinematics and mechanics involved in the lateral-distortional buckling (LDB) behaviour (involving web single or double curvature) of simply supported I-section steel beams elastically restrained by concrete slabs under uniform negative (hogging) bending. The findings obtained are used to derive and illustrate the application of analytical formulae to calculate LDB moments of the steel-concrete composite beams considered. The study is based on a Generalised Beam Theory (GBT) approach to perform buckling analyses using constrained deformation modes that incorporate the displacement/rotation restraints, thus making it possible to obtain accurate buckling results with only a few deformation modes. The formulae provide the solution of the LDB equilibrium equation when only one or two constrained deformation modes are involved. Their merits and accuracy are assessed through the application to problems of practical interest – the LDB moments determined are compared with values (i) provided by other available formulae and/or (ii) obtained from conventional GBT, finite strip and/or Ansys shell finite element analyses. It is found that (i) the proposed constrained-mode GBT clearly outperforms the conventional one, both in structural insight and computational efficiency, and (ii) the derived analytical formulae consistently yield accurate LDB moment estimates.

Finite strip-Riccati transfer matrix method for buckling analysis of tree-branched cross-section thin-walled members

Thin-walled components are gaining wide application in the field of modern engineering structures. The buckling analysis of thin-walled structures has thus become an important research topic. Here, we developed a new method named as finite strip-Riccati transfer matrix method (Riccati FSTMM) for buckling analysis of tree-branched cross-section thin-walled members. The method integrates Riccati transfer matrix method (Riccati TMM) for tree multi-body system with semi-analytical finite strip method (SA-FSM). Compared to SA-FSM, Riccati FSTMM features a smaller matrix and higher calculation efficiency, with no need for global stiffness matrix. In addition, by arranging uniformly distributed middle nodal lines inside strip elements, we developed the high order finite strip-Riccati transfer matrix method (Riccati HFSTMM) for buckling analysis of tree-branched cross-section thin-walled members. This method further improves the efficiency and accuracy of Riccati FSTMM. We tested the two proposed methods with two numerical examples, and demonstrated their superior reliability and efficiency over the finite element method (FEM).

Discussion on the manuscript entitled “Thermal residual stress in a functionally graded material system” by K. S. Ravichandran, Materials Science and Engineering A, 201(1–2), pp. 269-276

In the article entitled “Thermal residual stress in a functionally graded material system”, a strip element made of a combination of Al2O3 ceramic and Ni metal was considered as a functionally graded material to obtain the general expressions for thermal residual stresses. The results showed that the stress distribution changes continuously as the volume fraction of the ceramic varies according to a power function. However, an incorrect term for bending stiffness was used in this expression. In addition, the expression for the residual stress term, which is resulted from the uniform elongation of the strip fibers, should not be used to calculate the reactive bending moment. It must be obtained from the nonuniform distribution of thermal strain across the thickness. In this study, the derivation of the final expression for the thermal residual stress in a functionally graded strip element by the strain suppression method is discussed.

ЗАЛЕЖНІСТЬ ОПОРУ ПЕРЕМІЩЕННЯ ГНУЧКОЇ СМУГИ ПО ПОВЕРХНІ ВІД КРИВИНИ ЇЇ ОСІ

During considering the movement of the body on the surface, it is usually replaced by a material particle. It greatly simplifies the analytical description of the movement, which makes it possible with some probability to predict the impact of certain factors on the process. The particles can create a continuous environment, one of which may be a flexible strip. It is deformed during moving on the surface, acquiring its shape. This movement can occur during plowing the soil, permeated with roots. In this case, the slice can be taken as a strip of the rectilinear cross-section, the length of which does not change during deformation, i.e. it is incompressible. The article considers the movement of such a strip on a cylindrical surface with a horizontal arrangement of rectilinear generatrices. The strip can enter the surface perpendicularly to the generatrices and moves farther in this direction. In this case, the trajectory will be a flat curve – in fact, a cross-section of the cylinder. The article considers the variant when the strip enters the surface of the cylinder at a certain angle to the generatrices. In this case, the trajectory of the strip movement will be a spatial curve. Some effort is required to overcome the slip resistance of the strip. It is the sum of certain components: the effort to lift the strip, to overcome the friction, to its deformation in the case of an elastic strip. The article considers the forces, the magnitude of which is influenced by the curvature of the trajectory of the strip, for which its axis is taken. The force is determined by the summation of the elementary forces acting on the elements of the strip along its axis. It is considered that at the deformation of a strip the profile of its cross-section does not change and remains rectangular. On the basis of this rectangle, an elementary parallelepiped of a strip is formed, one of the dimensions of which is the differential of the arc of its axis. Thus, the definition of the force is reduced to the integration of the forces applied to the elementary parallelepiped along the length of the arc of the axis of the strip. One of such forces is the centrifugal force, which depends on the curvature of the trajectory along which the strip moves on the surface. The component of this force causes the pressure of the strip element on the surface, which causes the appearance of friction. If the strip is elastic, then there are deformation forces, which also depend on the curvature of the axis of the strip. Keywords: flexible strip, cylindrical surface, axis curvature, centrifugal force, friction force.

Dynamic instability analysis of general shells reinforced with polymeric matrix and carbon fibers using a coupled IG-SFSM formulation

In the present article, the dynamic instability of shells subjected to periodic in-plane and external pressure loadings in thermal environment is considered. The considered shells are made of laminated composite of carbon fibers and the reinforced polymeric matrix by randomly oriented carbon-nanotubes (CNTs) which is functionally distributed in each layer. Consequently, the considered material is made of three phases of fiber/polymer/CNT. The extended governing equilibrium and compatibility equations are solved by a coupled formulation which combines the isogeometric analysis (IGA) and finite element method (FEM) in two orthogonal direction of the parametric space. Since the proposed coupled IGA-FE method is developed in form of the finite strip (FS) elements, it is named isogeometric B-spline finite strip method (IG-SFSM). In order to perform the parametric studies, the effects of various geometrical and mechanical properties, boundary conditions and temperatures are considered. The obtained results show that IG-SFSM is an applicable method for dynamic instability assessment of the shells which can reduce the computational efforts comparing to the other prevalent methods such as FEM and element-free family, and also reduce the restrictions and shortcomings of the standard IGA methods.

A semi-analytical numerical method for modelling the normal wheel–rail contact

ABSTRACT A new semi-analytical boundary element method is proposed for determining the wheel–rail contact zone and the normal stress distribution within it. The potential contact area is discretised using strip elements, employing an iterative algorithm to satisfy the contact constraints. At each iteration, the length of the contact strips is updated using an analytical expression based on Hertz's theory. This simplified formulation provides good approximation of the pressure distribution, and consequently the contact area, in non-elliptic cases. The reduction in the number of system unknowns by using a semi-analytical methodology also enables fast computation speeds, an indispensable requirement in railway dynamics.

ESTIMATION METHODOLOGY OF HEATING THE CONTACT PLACE OF CONTACT WIRE WITH CONTACT STRIP OF PANTOGRAPH

Purpose. The main purpose of our work is to develop a method for assessing the heating temperature of the contact area of contact wire with contact strip of pantograph (the contact wire element – the contact strip element of pantograph, in abbreviated form – CWE – CSEP) for parking conditions when preparing the train for the trip with the determination of the maximum current load on given node. Methodology. We proposed to consider the CWE – CSEP contact from the point of view of the classical theory of electrical contact and heating of a homogeneous body. Findings. The features of thermal state of the current collection unit of CWE – CSEP in the conditions of preparing the electric rolling stock for the trip are considered. Within the framework of the study a methodology for assessing the heating temperature of the zone of power sliding contact in the conditions of train preparation for the trip has been developed. The application of the methodology will help reduce the number of burnings through of the contact wire due to the precise choice of the heating/conditioning time of the train for a certain heating/conditioning current when preparing the electric rolling stock for the trip. Originality. It has been established that the reason for burnings through the contact wire in stalls when preparing the train for the trip is the excess of permissible temperature of the power sliding contact as a result of prolonged action of the heating/conditioning current. In contrast to the standard approach for determining the duration of the train heating, the proposed methodology takes into account additional factors, namely, the wear and condition of the contact wire, condition of contact strip of the pantograph. This methodology is based on the classical theory of electrical contact and the theory of heating a homogeneous body, which allows accurate assessment of the thermal state of a power sliding contact, and is convenient enough for use in operating conditions. Practical value. The results of the work are of practical value, since the technology of preparing a train for a trip can be supplemented by calculating the temperature of the CWE – CSEP contact in accordance with the proposed methodology. This will allow applying a set of measures to prevent burnings through of the contact wire in case of possible temperature exceeding the permissible value for a specific train in specific conditions.

Geometrically nonlinear analysis of sandwich FGM and laminated composite degenerated shells using the isogeometric finite strip method

Isogeometric analysis (IGA) has become a strong tool for analysis of shell structures, which can be considered as a powerful alternative to the standard finite element method (FEM). Besides several advantages of IGA over FEM in geometric nonlinear analysis of the shells, it has some drawbacks corresponding to tensor-product of B-spline and NURBS surfaces. One of the solutions to eliminate or at least reduce the effects of the mentioned shortcomings is to combine IGA with the other methods, such as FEM. In the present paper, a novel version of the finite strip method (FSM) is developed to carry out the geometric nonlinear analysis, which employs a combination of FEM and IGA in the transversal and longitudinal directions, respectively and is named isogeometric B-spline finite strip method (IG-SFSM). The strip elements have been formulated based on the Degenerated-Shell method for Updated-Lagrangian (UL) approach. Then, it is examined by some examples incorporating various geometries, boundary conditions (BCs), and material properties, such as laminated composites and sandwich FGMs. The results exhibited that, to achieve the complicated nonlinear equilibrium paths of the shells, IG-SFSM requires a lower number of degrees of freedom (DOFs) and, consequently, computational efforts comparing to the other common methods, such as finite element and mesh-free methods.

Study on Plate Straightening Process Based on Elastic-Plastic B Spline Finite Strip Method

ABSTRACTAn elastic-plastic B spline finite strip method is proposed to investigate the continuous plate straightening process in this paper. First, the B spline displacement function that satisfies the boundary conditions of simply supported end and free end of the strip element is established, and then the stress-strain matrix is established. Second, the set method of total stiffness matrix based on B spline finite strip method for plate straightening problem is proposed, and the influence of nodal line number and strip elements number on the sparsity of total stiffness matrix is analyzed. Third, the loads on the strip elements are taken as linear uniform distribution, and the transformation matrix between the equivalent linear load and the actual load of the strip element is established. At last, the plate straightening simulation of 11 rolls straightening machine is made based on the elastic-plastic B spline finite strip method, the calculated results agree with the measured results, which approves that the elastic-plastic B spline finite strip method established can be applied to the plate straightening process.

Deterministic snap-through buckling and energy trapping in axially-loaded notched strips for compliant building blocks

Harnessing elastic instabilities has enabled recent advances in new classes of materials and devices due to the characteristics of amplifying force and augmented motion. Achieving these enhanced effects usually relies on using buckled beam or strips as the building block. In response to such a need, we investigate the contact-induced energy trapping of axially-loaded strips. To achieve the feature of energy trapping, we implement an ‘imperfection by design’ approach to trigger a controllable and predictable interactive buckling in axially-loaded strips. By combining finite-element simulations and desktop-scale experiments, we found that the contact of strip elements can be induced by strategically controlled the number, the location and the layout of local predefined geometric defects, leading to a deterministic on-demand snap-through buckling response compared to the ones without such geometric defects. Our study thereby opens avenues for the design of the next generation of compliant mechanisms with high fidelity and low sensitivity over a wide range of length scales.

Free vibration analysis of FGM cylindrical shells surrounded by Pasternak elastic foundation in thermal environment considering fluid-structure interaction

This paper presents an investigation on partially fluid-filled cylindrical shells made of functionally graded materials (FGM) surrounded by elastic foundations (Pasternak elastic foundation) in thermal environment. Material properties are assumed to be temperature dependent and radially variable in terms of volume fraction of ceramic and metal according to a simple power law distribution. The shells are reinforced by stiffeners attached to their inside and outside in which the material properties of shell and the stiffeners are assumed to be continuously graded in the thickness direction. The formulations are derived based on smeared stiffeners technique and classical shell theory using higher-order shear deformation theory which accounts for shear flexibility through shell's thickness. Displacements and rotations of the shell middle surface are approximated by combining polynomial functions in the meridian direction and truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. The governing equations of liquid motion are derived using a finite strip element formulation of incompressible inviscid potential flow. The dynamic pressure of the fluid is expanded as a power series in the radial direction. Moreover, the quiescent liquid free surface is modeled by concentric annular rings. A detailed numerical study is carried out to investigate the effects of power-law index of functional graded material, fluid depth, stiffeners, boundary conditions, temperature and geometry of the shell on the natural frequency of eccentrically stiffened functionally graded shell surrounded by Pasternak foundations.

Modelling and simulation of residual stress of strip during continuous annealing process

Purpose The purpose of this study is to solve the key problem of the residual stress of strip in buckling and deviation during the continuous annealing process (CAP). Design/methodology/approach Considering the one-to-one correspondence between deformation and residual stress, the strip was divided into multiple elements. To obtain the total deformation of each element, the influence model of some factors on the deformation of steel strip element was established. Then, according to the constitutive equation of residual stress and deformation, and the deformation coordination relation between strip elements, a set of calculation model, which is suitable for residual stress of strip during CAP was established, the model precision was verified by finite element method simulation, and the influences on residual stress of strip were also analyzed. Findings The weighted calculation of comparison between analytical results and simulation shows that the accuracy of the analytical method is within 10 per cent, which fully meets the requirements. Originality/value The different residual stress of steel strip can be displayed quickly and intuitively in the synchronous process segment according to this model, which is of great importance to the prevention of strip buckling and deviation.

Dielectric resonator antenna with top loaded parasitic strip elements for dual‐band operation

AbstractIn this article, a dual‐band hybrid cylindrical dielectric resonator antenna (CDRA) is designed, analyzed, and experimentally validated. Miniaturization and dual‐band frequency behavior are achieved by loading circular copper strips on top of the CDRA. Hence, the antenna resonates at 4.4 and 6.1 GHz covering −10 dB bandwidths of 600 MHz and 500 MHz, respectively. The proposed CDRA is excited using a rectangular slot for HEMY11 and HEMX11 modes. The proposed antenna demonstrates good gain (4.9 dBi at 4.4 GHz and 5.6 dBi at 6.1 GHz), high efficiency (>88% for all operating bands), and good FTBR (>10.08 dB in both principal planes for both operating bands). Moreover, the higher frequency band can be independently controlled by adjusting the parasitic strips width (d) and gap (g).