Finite Strip Research Articles

Free Vibration and Stability Analyses of Functionally Graded Plates Resting on Elastic Foundations Based on 2D and Quasi-3D Shear Deformation Theories Using the Finite Strip Method

Free Vibration and Stability Analyses of Functionally Graded Plates Resting on Elastic Foundations Based on 2D and Quasi-3D Shear Deformation Theories Using the Finite Strip Method

Higher-order finite strip method (H-FSM) with nonlocal strain gradient theory for analyzing bending and free vibration of orthotropic nanoplates

Higher-order finite strip method (H-FSM) with nonlocal strain gradient theory for analyzing bending and free vibration of orthotropic nanoplates

A non-uniform compound strip method for effective buckling analysis of stiffened structures

In this paper, a versatile compound strip method (CSM) with non-uniform spline functions is developed for buckling analysis of stiffened structures. The proposed method further extends the existing CSM by permitting the flexible modification of local knots to place the stiffeners along the strip arbitrarily. In addition, a reasonable knot arrangement can achieve an accurate solving procedure with improved convergence. The displacements of stiffeners are expressed compatibly by the fundamental parameters of skin according to the beam-plate model. Consequently, the reinforcement of stiffeners is naturally incorporated by adding the beam stiffness matrix to the corresponding strips. Based on the first-order shear deformation plate theory and non-uniform spline functions, the semi-analytical formulations of stiffened structures are established. The present method provides the possibility to achieve the local mesh refinement in the finite strip methods. The convergence and validation study is demonstrated through the comparisons with the results of the existing literature solution and finite element method. In conclusion, a more efficient and applicable CSM is proposed to analyze the buckling behaviors of stiffened structures.

Nonlinear free vibration analysis of moderately thick sandwich plates with viscoelastic core using finite strip method

Nonlinear free vibration analysis of moderately thick sandwich plates with viscoelastic core using finite strip method

Formulas determining the local critical stress of I-shape sections under axial compression

The I-shaped steel sections should be checked for local buckling conditions during design. When local buckling occurs, there is interaction between thin-walled components of the section. Design codes have provided formulas to determine local critical stress for I-shaped steel sections, but they do not account for this interaction. This paper proposes equations for determining the local ultimate stress of I-shaped sections under axial compression, considering web and flange interaction when ratios between the height and width of the section, the flange thickness and web thickness change. The local critical stress is determined by the semi-analytical finite strip method carried out in the CUFSM program. The equations are proposed based on the parametric study. The reliability of formulas is confirmed when comparison to published and numerical results.

Strength and behavior of axially and eccentrically loaded built-up closed sections using four cold-formed steel open sections

Innovation in cold-formed steel framing systems is needed for opening flexibility and application in mid-rise buildings. Hence, this study proposes a closed built-up section using four cold-formed steel (CFS) open sections with a high load bearing capacity that potentially enables the development of high-performance cold-formed steel framing systems for these. The closed section by combining four open CFS sections using fasteners can effectively enhance the load capacity of the sections under axial loading. With a specially designed intersections gusset plate this built-up section offers more potential configurations of beam-column moment connections for CFS structures. First, a heuristic optimization was performed to identify a high-performance section based on the local and distortional buckling strengths using the finite strip method. Second, a test program was developed to investigate the load bearing capacity and failure behaviors of the optimized built-up closed section under axial and eccentric loading. Third, their load bearing capacities were compared with several other closed sections such as the rectangular hollow tube (RHS) of equal cross-sectional area or equal moment of inertia to highlight the high material efficiency. This study paved the groundwork for exploring high-performance cold-formed steel framing systems with this unique closed built-up section.

Computation of shear buckling stress of thin-walled sections using constrained spline finite strip method

The direct strength method (DSM) design for shear incorporates the elastic shear buckling stress of the cross-section to evaluate the ultimate shear capacity of thin-walled members. To calculate the shear buckling stress using the finite strip method (FSM), the shape functions for longitudinal interpolation are an issue, while capturing the phase change of displacements along the plate strip. This paper presents a novel constrained spline finite strip method (cSFSM) that eliminates the phase change of displacements. Although constrained buckling analysis for shear stresses is reported in the literature based on FSM, the present study is unique in determining pure buckling stresses for simply supported members subjected to shear edge stress. The formulation also provides an accurate representation of the variation of shear stress along the longitudinal and transverse directions of the plate. Hence, coarse discretization of cross-section is sufficient to obtain the accurate shear buckling stress. The formulation is demonstrated on channel sections with lips subjected to shear edge stresses, and elastic buckling stresses are compared with results available in the literature and also with the finite element method (FEM). Illustrative examples are presented on lipped channel members with different end conditions and longitudinal stiffeners on flanges and webs, to calculate the pure elastic buckling stresses under shear edge stresses. The calculation of buckling stresses for members subjected to longitudinal variation of shear and flexural stresses is also presented to calculate coupled and uncoupled buckling stresses.

Bending performance analysis of variable stiffness composite laminates

AbstractFor fiber‐reinforced polymer structures, the out‐of‐plane stiffness is much lower than the in‐plane stiffness and is extremely prone to damage and instability. The potential of variable stiffness (VS) laminates was explored to enhance the stiffness in the thickness direction. Based on the finite strip method (FSM), a semi‐analytical solution for bending problems of laminates was derived, which is called the variable‐stiffness discrete strip (VSDS) method. By comparing with traditional constant stiffness (CS) laminates, the influence of design parameters of VS laminates on the bending shape and stress distribution of laminates under two load cases were studied. Combining the results of FE models, the accuracy of VSDS has been verified, and the strategy of VS layout configuration design to improve the bending resistance was proved.Highlights Variable stiffness discrete strips (VSDS) method was presented based on FSM. Bending performances of VS laminates under two load conditions were studied. The method has the ability to reduce the computation cost of bending problems. The solutions of VSDS agree well with the results of FE models. The improvement mechanism of VS laminates on bending resistance was explored.

Revisiting classical concepts of Linear Elastic Fracture Mechanics - Part II: Stretching finite strips weakened by single edge parabolically-shaped notches

This is the second part of a short three-paper series, aiming to revisit some classical concepts of Linear Elastic Fracture Mechanics. Being the intermediate step of the analysis between infinite domains (discussed in Part-I) and finite bodies (that will be discussed analytically in the third part of the series), the present part offers an alternative theoretical approach for the confrontation of problems dealing with both infinite and finite bodies with geometrical discontinuities. The method is here applied to a stretched, single-edge notched strip. Assuming that the strip is made of a linearly elastic and isotropic material, the complex potentials technique is used. The solution is achieved by extending Mushkelishvili’s procedure, for the confrontation of the prob­lem of an infinite perforated plane. Closed form, full-field formulae are obtained for the stresses all over the notched strip. Using these formulae, the stress concentration factor at the base (tip) of the notch is quantified and studied in terms of the geometrical features of the notch and its dimensions relatively to the respective ones of the strip. The stress distributions plotted along characteristic loci, resemble closely, from a qualitative point of view, the respective ones provided by well-established analytical solutions. Preliminary numerical analyses in progress provide results in very good agreement with those of the present analysis.

Thermal shock fracture in a cracked strip: Incorporating convective heat transfer between lateral surfaces and ambient environment

This paper presents a comprehensive analysis of transient temperature and thermal stress around a thermal insulated crack in a finite thermoelastic strip subjected to thermal shock based on the dual-phase-lag (DPL) heat conduction. A detailed investigation of the effect of convective heat exchange between the lateral surfaces of the strip and the ambient environment is conducted. By employing integral transform technique, the thermoelastic crack problem is reduced to a set of singular integral equations, and solutions for the transient temperature distribution and dynamic stress intensity factors (SIFs) at the crack tips are then obtained. Numerical results reveal a considerable temperature gradient near the heating surface when both the high convective heat transfer coefficient and thin strip are involved. Consequently, the SIFs in such scenarios where cracks are located close to the heating surface are significantly larger compared to those calculated by neglecting the convective heat loss. Furthermore, during the initial period following a thermal shock, the SIFs may exhibit higher magnitudes than the steady-state values. These findings emphasize the importance of accounting for the influence of convective heat exchange with the ambient environment in material design and optimization to enhance fracture resistance under transient thermal loading.

Flexural capacity and local buckling half-wavelength of high strength steel tubular beams under moment gradients: An experimental study

An experimental investigation into the effect of moment gradients on the flexural behaviour of hot-rolled high strength steel square hollow section (SHS) beams is presented in this paper. In total, 20 beam specimens in steel grades S690 and S770, and with cross-sections spanning from Class 2 to Class 4 based on the Eurocode 3 slenderness limits, were tested under three- and four-point bending. In the three-point bending tests, the beam spans were varied to achieve a range of moment gradients; the influence of different stiffening arrangements at the loading point was also considered. Local geometric imperfections were measured by means of 3D laser-scanning prior to testing and digital image correlation (DIC) was adopted to monitor the displacement and strain fields at critical regions and to assess the local buckling half-wavelengths of the test specimens for which a consistent measurement approach was proposed. The measured local buckling half-wavelengths were compared against the elastic local buckling half-wavelengths calculated using the finite strip method. It was observed that while the measured local buckling half-wavelengths remained approximately constant up to first yield, a significant reduction in half-wavelength was observed with increasing moment due to the non-uniform spread of plasticity. The comparisons also revealed that the local buckling half-wavelengths reduced with both the presence of moment gradients and intermediate stiffeners, with a new parameter proposed to quantify the local moment gradient. It was shown from the tests that the specimens subjected to moment gradients, despite the presence of shear, exhibited higher ultimate moment capacities (up to 10.5% for stiffened specimens and 3.4% for unstiffened specimens) than those subjected to uniform moments. This is attributed to the delay in the local buckling of the critical cross-section of beams under moment gradients due to the restraint provided by the less heavily stressed adjacent cross-sections.

Customary light-gauge steel framing construction with flat strap bracing: seismicity limits for low to mid-rise buildings in Europe

AbstractOrdinary (customary) light gauge steel framing is a convenient construction technology; however, given the studs low axial capacity, it has been considered mainly for low-rise buildings in low seismicity regions. This paper investigates the boundaries of application of this type of steel framing (in moderate and high seismicity areas) by designing the structures of three representative 5, 7 and 10-storey buildings in order to examine their feasibility. The necessity of using built-up columns consisting of two or more sections is investigated. The axial capacity of studs is estimated by code-type analyses. The critical buckling stress is determined with well-known closed-form expressions; as they do not contemplate the flexibility of the screwed connections (in built-up sections), the obtained results are complemented with those of the finite strip method and generalized beam theory formulations.

Pure/combined buckling mode calculation of thin-walled members constraining general shell FE models

This paper proposes a technique for decomposing the buckling solution of thin-walled members into pure deformation modes (global, distortional, local, or other), aiming at providing an insight into the buckling behavior of these members. The calculation of critical loads associated with a specific or combined deformation mode is performed constraining general finite element models. A general constraining procedure is presented, in which the critical load of any mode, combining different section deformation modes and different harmonic shape functions in the longitudinal direction, can be determined. Cases where all possible harmonic terms may be automatically considered are also described. Cross-section deformation modes are defined in the context of the constrained finite strip method (base vectors), and the proposed constraining procedure is implemented by means of relationships between degrees of freedom of the finite element mesh in commercial software. Calculation of combined buckling modes inherently makes it possible to quantify the participation of the considered modes, including along specific longitudinal segments of the member. Results from the analysis of a lipped channel member are presented to demonstrate the concepts and, later, the analysis of a member with a more complex cross-section and intermediate boundary conditions along length is detailed. A discussion on the base vectors chosen for the constraining method is presented. Finally, the potential of the proposed method is discussed.

Geometry optimization of steel formwork for steel–concrete composite slabs

The use of steel formwork incorporated into composite steel–concrete slabs stands out for contributing to sustainable development in civil construction. However, this construction system still has limited usage in Brazil, which may be due to the restricted availability of formwork geometries in the national market. As such, this study aims to determine the optimal steel geometry that results in the lowest steel consumption during manufacture of the composite slabs, taking into consideration the initial construction phase, in which the formwork is under the highest load demand. The Direct Strength Method (DSM) and the traditional Effective Width Method (EWM) are applied for designing the steel formwork during the construction phase, where the cold-formed steel profile resists the applied forces independently. For DSM, the critical buckling moments are determined using the elastic stability analysis program CUFSM, via Finite Strip Methods. The solution of the optimization problem was implemented in MATLAB® using Particle Swarm Optimization and considering two design variables: the thickness and the bend angle of the formwork web. In addition, the reliability of the proposed formulation was evaluated in the implementation phase of DSM and EWM. Numerical analyses are carried out on four different steel geometries currently available in the Brazilian market. The main results showed that the developed computational program was successful in finding optimal solutions for said geometries, as the optimization reduced steel consumption by an average of 21.6%. Thickness had a greater effect on the steel savings, and this variable decreases in the optimal solution, while the height and bend angle increase.

Integral equations in the H-polarized wave scattering from metasurface formed by finite multilayer graphene strip grating inside grounded dielectric slab

Integral equations in the H-polarized wave scattering from metasurface formed by finite multilayer graphene strip grating inside grounded dielectric slab

Novel method for the prediction of load bearing capacity of compressed C channels considering interaction of buckling modes

AbstractThe proposed method focuses on the interaction of global and local buckling. A modified Ayrton‐Perry type buckling curve is proposed to calculate the ultimate compression force resistance of centrically compressed cold‐formed C channel. The new buckling curve incorporates both the effects of global imperfections and shift of the center of gravity caused by local buckling of slender web plate of the considered sections. Distortional buckling usually does not play any role for this configuration.The effective cross‐section properties for the use of the new buckling curve are determined using critical stresses obtained both by finite‐elements analysis and finite strip analysis. The shift of center of effective cross‐section will produce an additional second order bending moment amplified with the corresponding global buckling multiplier.The results are compared with the curve proposed by AISI Direct Strength Method for global‐local interaction and with simulation results, in agreement with the recommendations of the new prEN 1993‐1‐14.

Design of Stainless Steel Cross‐Sections by Inelastic Stability Analysis

AbstractWhile carbon steel cross‐sections are traditionally categorized as Class 1, 2, 3 or 4, depending on when local instability occurs relative to the key stages of yielding, for stainless steel the lack of a well‐defined yield point and the presence of continual strain‐hardening render this approach artificial and superfluous. A new design methodology is therefore needed, which accounts for the effects of both strain‐hardening and local buckling.The proposed method is based on a modified finite strip method, which accounts for the effects of gradual loss of stiffness due to yielding on the stability of thin‐walled members. Extensive verification of the new method against experimental data showed that cross‐sectional capacities are generally well predicted, with average ratios of the measured to the predicted capacity of 1.18 and 1.19 in compression and bending, respectively, and a standard deviation of 0.10 in both cases. This is a significant improvement over the EN 1993‐1‐4 design rules, where the averages over the same dataset were 1.27 and 1.40, respectively, with standard deviations of 0.14 and 0.17. The rotational capacity of stainless steel cross‐sections in bending was also reasonably well predicted, with an average ratio of measured to predicted curvature of 1.79.

Machine learning‐based predictions of buckling behaviour of cold‐formed steel structural elements

AbstractDesigning thin‐walled structural members is a complex process due to the possibility of multiple instabilities. This study aimed to develop machine learning algorithms to predict the buckling behavior of thin‐walled channel elements under axial compression or bending. The algorithms were trained using feed‐forward multi‐layer Artificial Neural Networks (ANNs), with the input variables including the cross‐sectional dimensions, the thickness, the presence and location of intermediate stiffeners, and the element length. The output data included the elastic critical buckling load or moment, as well as a modal decomposition of the buckled shape into the pure buckling mode categories: local, distortional and global buckling. The Finite Strip Method (FSM) and the Equivalent Nodal Force Method (ENFM) were used to prepare the sample output for training. To ensure the accuracy of the developed algorithms, the ANN models were subjected to a K‐fold cross‐validation technique and featured optimized hyperparameters. The results showed that the trained algorithms had a remarkable accuracy of 98% in predicting the elastic critical buckling loads and modal decomposition of the critical buckled shapes.

Buckling analysis of laminated composite elliptical shells using the spline finite strip procedure

According to the first order shear deformation plate assumption, current paper numerically investigates the buckling problem of cylindrical shells with oval cross-section under simply supported boundary condition subjecting to uniform and non-uniform loads via spline finite strip method. Equilibrium governing equations are generated based upon the virtual work's principle. Shell displacement function is assumed to be as dual development of degree 3 spline functions and Lagrange polynomial functions. The analysis method used at any time with any type of loading can calculate deformation and buckling. The step-by-step critical load is calculated using the determinant of the stiffness matrix. In the present paper, it is supposed that the applied linear elastic materials consist of isotropic and non-isotropic materials. Numerical studies are performed to indicate the effects of shell geometry, materials, and layered materials on the buckling load. For the validation purpose, the results of current research are compared with those of previous researches and ABAQUS software.

Elastic critical local buckling stress in cold-formed lipped channel and hat sections under uniform compression

The classical design approach for the elastic critical local buckling load of the cold-formed open section (CFOS) neglects the plate element interaction at the cross-section, which compromises the benefits of CFOSs designed for high performance. To derive a novel formula for the local buckling coefficient, taking into account the plate element interaction at the cross-section, a series of displacement functions for expressing the buckling deformations of the web, flanges, and lips caused by local buckling in CFOSs is proposed in this paper. The effect of cross-sectional geometry on the buckling coefficient was investigated using the proposed formula derived from Timoshenko’s plate buckling theory. Further, simplified formulae were proposed for the buckling coefficient and half wavelength of the elastic critical local buckling for practical use. The reliabilities of the proposed formulae were verified by comparing the results obtained from the proposed formulae with the analysis results based on the finite element method and finite strip method.