Strip Element Research Articles

Complementary Evaluation of Diagonal Tension Field Inclination Angle in Steel Plate Shear Walls

Complementarily to previous studies, research was conducted to investigate whether the equivalent constant angle of diagonal tension field action should be taken as either 40° or 45° for ductile steel plate shear walls (SPSW) designed per current codes. A two-dimensional finite element (FE) model was first calibrated against results from a prior study of “limited-ductility SPSW” by comparing effective stress contours and average angle of diagonal tension field action at different locations across the web plate. Then, this SPSW was redesigned as a ductile SPSW in compliance with the 2016 AISC Seismic Provisions (AISC, 2016a) to have fully restrained beam-to-column connections and analyzed using strip models and finite element models, respectively. The AISC moment-axial force interaction equation was used to compare demands in the SPSW boundary elements obtained from the strip and finite element models. With respect to the use of a single angle in design, it is shown that using an inclination angle of 45° is slightly (but not significantly) more conservative than using 40° as far as boundary element design is concerned. On the basis of these observations, along with findings from previous research on the diagonal tension field inclination angle, it is recommended that a single constant angle of either 40°or 45° be used for the design of SPSW.

Numerical Simulation of the Semi-Rigid Behaviour of Integrally Attached Timber Folded Surface Structures

Timber folded surface structures assembled using semi-rigid multiple tab and slot joints (MTSJ) have been shown to form feasible structural systems with high load bearing potential. However, for their further development and use on large building scales, a pertinent model for prediction of their structural behaviour has yet to be developed. This paper focuses on simplified numerical methods for accurately modelling the semi-rigid structural behaviour of bidirectional timber folded surface structures with multiple tab and slot connections. Within this scope, the structure behaviour is considered to be in the elastic stage. Three practical methods of analysis for such structural systems are presented. The first two approaches use the Finite Element Method (FEM), where the theory of plates and shells are applied. In the first method, the MTSJs are modeled using strip element models, while, in the second strategy, spring models are used. The third modeling strategy elaborates on the new macroscopic mechanical models, referred to as macro models. Sets of one-dimensional (1D) elements are used to represent the mechanical behaviour of the entire system. Both linear and geometric nonlinear analysis are performed for all three modeling strategies. The numerical results are then validated against the large scale experiments. Comparison of the strip and spring element model results have shown that the strips represent more accurately the experimentally obtained values. Concerning the macro modelling approach, very good agreement with both detailed FE modelling approaches, as well as experimental results, were obtained. The results indicate that both linear and nonlinear analysis can be used for modelling the displacements within the elastic range. However, it is essential to include geometric nonlinearities in the analysis for accurate modelling of occurring strains as well as for displacements when considering higher load levels. Finally, it is demonstrated that including semi-rigidity in the numerical models is of high importance for analysing the behaviour of timber folded surface structures with MTSJ.

A simple spline finite strip for buckling analysis of composite cylindrical panel with cutout

Abstract In this study, a new sub-parametric strip element is developed to simulate the axially loaded composite cylindrical panel with arbitrary cutout. For this purpose, a code called SSFSM is developed in FORTRAN to analyze the buckling of panels. The first order shear deformation theory is used to form the strain-displacement relations. Spline and Lagrangian functions are used to derive element shape functions in the longitudinal and transverse directions, respectively. The computational cost of the SSFSM is decreased dramatically, as mapping functions of the strip element are very simple. The results obtained from the SSFSM are compared with those of the literature and the results obtained by ABAQUS to show the validity of the proposed approach. A parametric study is performed to show the capability of the SSFSM in calculating the panel buckling load. Results indicate that increasing the panel thickness and panel central angles cause an increase in panel buckling load. The cutout shape is an important factor influencing the panel buckling load. For instance, when the angle between the direction of big chord of the elliptical cutout and compressive load direction are 0 and 90 degrees, the panel buckling load reaches its minimum and maximum magnitude, respectively.

Analysis of Vertical Dynamic Cross Interaction between Adjacent Footings for Railway Tracks through Soil

An efficient semi-analytical method is presented for the vertical analysis of adjacent railway tracks considering the dynamic cross interaction (DCI) effect through the semi-infinite soil medium. The interfaces between soil and tracks are discretized into a series of strip elements to solve the unknown contact pressure influenced by DCI effect. The Green function for each element under uniform harmonic excitation is derived and calculated by the piecewise integration and Cauchy principal value integral. The vertical impedance matrix is finally obtained by the superposition method. The accuracy and the effectiveness in high frequency range are verified by the convergence study, as well as the comparison study with the rigorous results from the mix-boundary-value method. The influence of the soil properties and the tracks distance on the DCI effect are discussed in detail in the parameter studies. It is shown that the DCI effect increases with the decrease of the distance ratio S/L.

Diffraction of electromagnetic waves on the resonance graphene metasurfaces

By using three independent numerical approaches to solve the 3D diffraction boundary problems the reflection, transmittance coefficients and losses of metasurfaces of graphene strip elements, depending on the frequency and values of the chemical potential were calculated in the terahertz frequency range. The results of numerical simulation of performances of tuned by the external bias electric field THz absorbers and THz polarizers based on the resonance metasurfaces of single square and two connected rectangular graphene strips in the unit cell placed on the dielectric or multilayer graphene-dielectric substrates were obtained.

A hybrid method for modelling damage in composites and its effect on natural frequency

Delamination is a frequent cause of failure in laminated structures, reducing their overall stiffness and hence their critical buckling loads. Delaminations tend to grow rapidly in postbuckling, causing further reductions in structural strength and leading ultimately to sudden structural failure. Many studies have investigated the effects of delaminations on buckling and vibration of composite structures. Finite element analysis is often used to model complex geometries, loading and boundary conditions, but incurs a high computational cost. The exact strip method provides an efficient alternative approach using an exact dynamic stiffness matrix based on a continuous distribution of stiffness and mass over the structure, so avoiding the implicit discretization to nodal points in finite element analysis. However due to its prismatic requirements, this method can model damaged plates directly only if the damaged region extends along the whole length of the plate. This paper introduces a novel combination of exact strip and finite element analysis to model more complex cases of damaged plates. Comparisons with pure finite element analysis and a previous smearing method demonstrate the capability and efficiency of this hybrid method for a range of isotropic and composite plates. The effect of damage on the lowest natural frequency is studied.

A Broadband Cavity-Backed Slot Radiating Element in Transmission Configuration

A planar technology stripline-fed slot radiating element in transmission configuration is proposed. Its main advantages are the broad impedance bandwidth achieved and the property that it only radiates into half-space, which are obtained, respectively, with the use of its complementary strip element and using a cavity-backed slot. A lattice network circuit model is proposed both to explain the behavior of the structure and to establish a design methodology. Its capabilities are shown through simulation and demonstrated in a proof of concept prototype. Measurement results show a unidirectional broadside radiation pattern and a fractional bandwidth of 48%, significantly superior to other slot-based radiating elements found in the literature. The element has the ideal characteristics for building series-fed reconfigurable arrays for wide-band applications.

Updated Bayes identification of displacement constants of curve indeterminate box girder with variable scale theory

For curve indeterminate box girder, updated Bayes identification model of displacement constants was derived and studied with the variable-scale optimization theory. First, the updated Bayes objective function of displacement constants of the structure was founded. The gradient matrix of the objective function to displacement constants and the calculative covariance matrix were both deduced. Then, with finite curve strip element method, mechanical analysis of curve indeterminate box girder was completed. With automatic search scheme of quadratic parabola interpolation for optimal step length, the variable scale theory was utilized to optimize the updated Bayes objective function. Then, the identification steps were expounded, and the identification procedure was developed. Through typical examples, it is achieved that the updated Bayes identification model of displacement constants has numerical stability and perfect convergence. The stochastic performances of systematic parameters and systematic responses are simultaneously deliberated in updated Bayes objective function, which can synchronously take the actual measured information at different times into account. The variable-scale optimization method continually changes the spatial matrix scale to generate renewed search directions during the iterations, which certainly accelerates the identification of the displacement constants.

A high order finite strip transfer matrix method for buckling analysis of single-branched cross-section thin-walled members

Thin-walled members have been used in many modern engineering structures, and their buckling analysis has attracted many attentions. A new efficient method named as High Order Finite Strip Transfer Matrix Method (HFSTMM) is proposed to determine the buckling factor and buckling model of the thin-walled member with single-branched cross-section. For the first time, thin-walled members with loaded edges simply supported can be discretized in the cross-section by high order semi-analytical finite strip method. Then the control equations of the strip elements will be innovatively rewritten as the transfer equations, which include the effect of the middle nodal lines of high order finite strip and do not increase the matrix dimension. Four thin-walled members with different cross-section can be taken as examples to verify HFSTMM and buckling loads by FEM and HFSTMM are agreeable very well. The computational consumption of FEM, Finite Strip Transfer Matrix Method (FSTMM) and HFSTMM of one example shows the high efficiency of HFSTMM. All results confirm that HFSTMM is an efficient method for the buckling analysis of thin-walled members with single-branched cross-section.

Numerical Analysis of Twin-Roll Casting of Strips With Profiled Cross-Section

The relatively high production costs of innovative materials with tailored properties such as Tailor Welded Blanks, Patchwork Blanks, Tailor Heat Treated Blanks and Tailor Rolled Blanks are responsible for a growing interest in new cost-effective production methods. One of the promising energy-saving and environmental friendly technologies for the production of tailored blanks is twin-roll casting. In the study a new alternative method for twin-roll casting of strips with profiled cross-section is proposed, which uses one or more preloaded endless steel strips with an antiadhesive coating for profiling of the formed strip on a pair of the common cylindrical shells. As a primary stage for the practical process design, numerical simulation of the process using the finite element software package ANSYS is realized. In this way, dependencies of the strip elements outlet temperature, deformation zone length and elements outlet speed on the varied strips thickness and total solidification-deformation zone length are established. Based on the simulation results, a procedure for the twin-roll casting process design is suggested.

Free vibration and buckling analysis of thin plates subjected to high gradients stresses using the combination of finite strip and boundary element methods

Free vibration and buckling analysis of thin plates under arbitrary loading is investigated taking the advantages of both boundary element and finite strip methods. In the first step, the governing differential equation is converted to equivalent integral equation using static fundamental solutions of bi harmonic equation. Moreover, domain integrals due to inertia and in-plane forces are evaluated applying the finite strip interpolation functions to express the displacement field. This leads to a reduction of the size of the problem so that the mesh generation becomes easier and the computational efforts are reduced. In the buckling analysis, the near boundary stresses are calculated using a transformation method to cope with singularities. The proposed method can be easily applied to arbitrarily distributed and concentrated edge loading for different boundary conditions. The accuracy and efficiency of the presented method has been investigated through the solution of some sample problems for rectangular and skew plates.

Equivalent constitutive model of steel plate shear wall structures

To accurately and efficiently predict seismic responses of steel plate shear wall structures using simplified strip element models, an improved uniaxial equivalent constitutive model was proposed. Skeleton curves were employed, respectively, to quantify the effect of appreciable cyclic hardening characteristics of different steel materials and to take into account the influence of compressive residual stress. Simplified hysteretic criteria were suggested to capture pinching phenomena, reloading process and unloading process in details. Then, the proposed model was incorporated into the general finite element software ABAQUS as a user defined material (UMAT). Together, the model was validated against a series of typical experimental results. Finally, parametric analyses of the prototypes with a wide range of width-to-thickness ratios and loading patterns were conducted, with focus on the feasibility and applicability of the proposed model. These analyses demonstrated that: the proposed model could better evaluate the hysteretic behavior of steel plate shear wall structures with a wide range of width-to-thickness ratios and different steel materials. Meanwhile, it guarantees both the computational accuracy and efficiency, providing a valuable tool for nonlinear analysis of overall steel plate shear wall structures.

The Displacement Analysis Investigation for Variable Gradient Parameters Functionally Graded Materials Based on Strip Element Method

This paper adopted the strip element method to research the displacement response of functionally graded material structure with variable gradient parameters under mechanical loading. Based on the dynamic equilibrium equation of the system, strip element method theory was established through the principle of virtual work to get the control equations of functionally graded materials plane problem, using the modal superposition method to complete the solution of the equation and obtain the displacement distribution of the FGM plates with variable gradient parameters. The accuracy of the calculation method was verified by comparison with the result of finite element method. The results show that the displacement response of the strip element method is consistent with the finite element method. With the increase of the gradient coefficient, the ceramic content is increased and the material stiffness is also increased; then the displacement response caused by external loading is decreased. With the increase of the gradient coefficient, the influence of the gradient coefficient on the displacement response is decreased gradually.

A Simple Model for Vertical Dynamic Interactions among a Group of Strip Footings Rested on Homogeneous Half‐Space

A simple model for vertical dynamic interactions among a group of strip footings rested on half‐space is presented in this paper. An analytical method is presented to obtain the contact pressures and the impedance matrix for a group of surface strip footings. In order to conveniently solve the unknown contact pressures between the soil and footings, the soil‐footing interfaces are discretized into a series of strip elements. The Green function for each element under uniform harmonic force is derived and calculated by the piecewise integration and Cauchy principal value integral. The influences of footing and soil parameters on contact pressures and vertical dynamic impedances of footing groups are discussed in detail. The SSSI effect between adjacent footings increases with the decrease of the distance ratio S/L. For three footings in a group, the middle footing experiences greater cross‐interactional effect than the side ones. The present method has high accuracy, which is not only simple but also suitable for the high‐frequency analysis.

Inductive loaded compact monopole antenna for ultra‐wideband applications

An effective method to design an ultra-wideband antenna using a vertical narrow strip element is described. The proposed low profile antenna has good radiation characteristics such as polarisation purity, omnidirectional radiation pattern and good efficiency over the entire band of operation, which are the most desirable characteristics required for a wireless system to operate in the present high interference environment. The designed antenna has a measured return loss of below −10 dB and low cross polarised uniform omnidirectional pattern measured in anechoic chamber for the frequency range of 2.85 to 10.6 GHz.

Scattering Control Using Nonlinear Smart Metasurface with Internal Feedback

The ideology of creation of a nonlinear smart metasurface with internal feedback for the adaptive control by spectral composition of scattered field is offered. The metasurface contains a lattice of strip elements with nonlinear loads-sensors. They are included in a circuit of internal feedback for the adaptive control of scattered field. Numerically it is shown that maximal levels of the second harmonic in the spectrum of scattered far field correspond to maximum of voltage rectified on metasurface. Experimentally the prototype of the plane smart covering on the basis of the metasurface in the form of strip lattice with controlled nonlinear loads-sensors is investigated for an idea confirmation.

Development of paddy stripper header mechanism

Stripping is the process of removing the seeds from the plant and straw remained anchored to the soil. The main advantages of stripping is the increasing capacity of the combine harvester with reduced amount of material other than grain ratio (MOG) and power requirement for threshing and cleaning which promotes to develop small and light weight mechanism suitable for small and fragmented land. A laboratory stripper header mechanism (SHM) was developed for stripping paddy grains and collecting them in grain tank. It consisted of stripping rotor, stripping elements, hood, frame and grain tank. Two profiles of stripping elements viz., slender arrow head (A) and spaced slender arrow head (B) of stripping elements were used. The performance of the developed SHM was evaluated on specially developed test rig to study the effect of two levels of forward speed (1.65 and 2.25 km/h) and four levels of peripheral speed (16.95, 19.78, 22.6 and 25.45 m/s) on shattered and un-stripped grain loss was studied. It consisted of track, platform and crop holders. SHM was stationary and platform was movable on track. Minimum shattered grain loss of 5.78 per cent was obtained with stripping element A at 2.25 km/h forward speed and at 19.78 m/s peripheral speed. Minimum un-stripped grain loss of 0.84 per cent was obtained with stripping element A at 2.25 km/h forward speed and 25.45 m/s peripheral speed. The performance of the slender arrow head stripping element was found to be better as compared to spaced slender arrow head.

Analytical approach to calculate bending, longitudinal and torsional local stiffness of an asymmetric circumferential crack with contact condition

In this paper, bending, longitudinal and torsional stiffness of an eccentric circumferential crack is investigated with taking into account contact condition on the crack surfaces based on fracture mechanics. Although several researches have analyzed stress intensity factors of symmetric circumferential crack, the stiffness of an asymmetric circumferential crack in different directions (along and perpendicular to eccentricity) regarding contact condition has not been studied by an analytical method until now. In this paper we aim to describe behavior of eccentric circumferential crack under axial loading and establish a relation between axial force and the resulting displacement vector. The twisting angle of asymmetric circumferential crack due to torsional loading is also calculated and compared to twisting angle of a symmetric crack. In order to simulate the local bending stiffness in the contact condition, nonlinear governing equations of bending stiffness associated to cracked beam section is developed by dividing it to strip elements and utilizing stiffness equations related to noncontact condition. It is validated by 3D finite element (FE) nonlinear model. Results show a significant compatibility between presented analytical and 3D FE methods. Moreover results of simulations show that without taking into account contact condition, axial, torsional and bending stiffness of symmetric and asymmetric circumferential crack are equal and radius of un-cracked area is the only influential factor.

파괴면을 고려한 블록식 보강토 옹벽의 거동 특성 연구

본 연구에서는 최근 보강토 옹벽의 보강재와 시공법에 대한 국산화에 대한 요구로 전면벽체나 토목섬유 등을 대체할 수 있는 공법에 대한 개발 수요가 많아짐에 따라 경제적이고, 안정한 블록식 보강토 옹벽의 개발을 실시하고, 새롭게 고안된 블록식 보강토 옹벽에 대해 수치해석을 실시하여 거동특성에 대해 분석하였다. 제안된 보강토 옹벽은 첫째, 블록에 전단키를 두어 벽체를 일체화 하였으며, 둘째, 이론적인 파괴면에 보강재를 집중적으로 시공하여 전단 파괴면을 보강함으로써 옹벽의 안정성을 만족시키는 공법이다. 블록식 옹벽의 거동 특성을 분석하기 위해 해석에서 보강재의 사용 요소는 cable 요소와 strip 요소에 대해 수치해석을 실시하였으며, 보강재 길이, 간격, 블록의 일체화의 조건을 변화하여 해석하였다. 이러한 조건으로 해석한 결과 파괴면만 보강하는 경우보다 전면 벽체 블록과 체결을 위해 긴 보강재를 설치하는 경우가 보강효과를 증가시키고, 변위를 많이 구속할 수 있는 것으로 판단되었으며, 전면 벽체와 체결과 함께 일체화를 고려하기 위해 전단키를 설치하는 경우가 벽체를 개별요소로 해석한 경우보다 변위 구속효과가 있었다. 또한, 긴 보강재를 1간격과 2간격으로 시공한 경우의 발생 변형량은 AASHTO의 시공중 허용 발생변형량에 비해 작게 발생되어 본 연구에서 제안한 공법은 구조물의 중요도에 따라 보강재의 간격을 달리하여 현장에 적용할 수 있는 안정한 공법으로 판단된다. In this study, more economical than conventional reinforced soil retaining walls, we compared the behavior characteristic about the safety block type numerically for reinforced retaining wall. In this study, reinforced soil retaining wall, first, was integrated a wall putting shear key on the blocks. Second, construction reinforcement focused on the theoretical failure surface was satisfied with the stability of a retaining wall reinforced by a shear plane. when analyzing, element of using reinforcement was carried out a numerical analysis for the cable element and the strip element, and they were analyzed under the conditions according to the stiffener length, distance, with or without shear key. Analysis for the integration of the front wall was reinforced soil retaining walls by installing a larger displacement shear key confinement effect, if reinforced construction and reinforcement with 1 interval and 2 interval, the failure surface was bigger displacement constraints. Generating a deformation amount was smaller than the generation amount of deformation accrued during construction of AASHTO so that it was stable.

Bloch theorem for isogeometric analysis of periodic problems governed by high-order partial differential equations

With the emergence of isogeometric analysis (IGA), numerical rotation-free solutions to high-order partial differential equations (PDEs) are facilitated. Indeed, IGA allows the use of high-order-continuous basis functions through the domain. For periodic systems, the Bloch theorem is useful for analyzing wave propagation, restricting the analysis to a single unit cell and applying periodic boundary conditions. However, in the literature, boundary conditions are only accounting for C0-continuity, and we propose in the present paper to enforce the G1-continuity as well or to maintain the angle in case of unit cells meeting at kinks. While G1-continuity is enforced by maintaining the collinearity between adjacent control points, in the presence of kinks, variations of the field derived with respect to opposite in-plane edge normals are linked by the Rodrigues rotation matrix. This method applied at collocation points belonging to the unit cell edges can be viewed as a novel approach of coupling multi-patch geometries with kinks, avoiding the use of nonlinear multipliers or additional bending strip elements. Both transfer-matrix and indirect methods of the Bloch theorem are investigated, for respectively quasi-one and quasi-two-dimensional wave propagation in periodic structures discretized by NURBS-based IGA. Dispersion curves of a set of numerical problems treating isogeometric rotation-free extensible elastica (beams) and Kirchhoff–Love shells are then analyzed.