Finite Strip Method Research Articles

Configuração de melhor rendimento para telha de aço autoportante submetida à ação de vento de sucção

Construções leves em aço são frequentemente utilizadas como uma solução estrutural apropriada permitindo redução do custo da supra e infraestrutura. Nesse contexto, empregam-se Perfis Formados a Frio (PFF) e que, sendo elementos estruturais esbeltos, tornam-se propícios a condições de flambagem. Assim, este estudo desenvolve uma solução de telha autoportante em PFF do tipo viga-calha que apresente o melhor rendimento tanto à flexão (provocada pela ação do vento) quanto à cobertura obtida. Para a análise de estabilidade, utilizou-se o software CUFSM (Constrained and Unconstrained Finite Strip Method) baseado no Método das Faixas Finitas. Além disso, usou-se o Método da Resistência Direta para a determinação da resistência à flexão de projeto. Logo, este artigo apresenta seis análises numéricas a fim de propor um modelo que apresente a melhor relação entre Momento Resistente Efetivo e taxa de cobertura. Finalmente, sugere-se uma solução de telha do tipo viga-calha autoportante que se mostre eficiente na flexão sob vento de sucção e apresente uma taxa de cobertura satisfatória.

Finite strip method applied to steady heat conduction and thermal radiation in a planar slab: absorbing ̶ emitting gray material and parallel diffuse surfaces

This paper addresses a new finite strip method for the analysis of simultaneous heat conduction and thermal radiation in a planar slab with diffuse surfaces and filled with an absorbing and emitting material considered as a gray medium. The gray material is discretized into a finite number of strips where the temperature is approximated with quadratic expansions in local coordinates whose coefficients are unknowns inside each strip. The finite strip method consists in a set of discrete equations corresponding to energy balance equations united to the compatibility conditions of both temperature and heat flux between consecutive strips. The gray material is articulated with different combinations of thermal and optical properties. Numerical results for the temperature fields and the conductive, radiative and total heat fluxes are presented in graphical and tabular forms and they compared favorably with equivalent results employing standard calculation techniques. The three main features attributable to the finite strip method are simplicity, quick calculation, good convergence and quality results.

An efficient finite strip procedure for initial post-buckling analysis of thin-walled members

An efficient procedure based on the semi-analytical finite strip method with invariant matrices is developed and applied to analyze the initial post-buckling of thin-walled members. Nonlinear strain–displacement equations are introduced in the manner of the von Karman assumption for the classical thin plate theory, and the formulations of the finite strip methods are deduced from the principle of the minimum potential energy. In order to improve the computational efficiency, an analytical integral of the stiffness matrix is transformed into matrix multiple calculation with introducing invariant matrices which can be integrated in advance only once. Three commonly employed benchmark problems are tested with proposed method and other state-of-the-art methods. The corresponding comparison results show that: (1) this finite strip method is proved to be a feasible and accurate tool; (2) compared with the calculation process of the conventional finite strip methods, the proposed procedure is much more efficient since it requires the integration of the stiffness matrix only once no matter how many iterations are needed; and (3) the advantage of time-saving is greatly remarkable as the number of iterations increases.

Plate Bending Spline Finite Strip Models Using Mixed Formulation and Combined Spline Series

As Classical and Spline finite strip method based on stiffness and mixed variational formulation principle become important tool for continuum structural analysis , especially in the field of plate bending problems , a lot of researches has been focused on interpolation functions in order to improve the efficiency and increase the reliability of the method. The main objective of this paper is to introduce and propose a new spline interpolation function in the light of combination techniques of basic splines through introduction and brief review of previous studies in this field. This work which uses abbreviated form of augmented matrix proposed by authors published in past time , reveals a very good accordance results compared with the analytical and published solutions of different plate bending problems.

Plate Bending Spline Finite Strip Models Using Mixed Formulation and Combined Spline Series

As Classical and Spline finite strip method based on stiffness and mixed variational formulation principle become important tool for continuum structural analysis , especially in the field of plate bending problems , a lot of researches has been focused on interpolation functions in order to improve the efficiency and increase the reliability of the method. The main objective of this paper is to introduce and propose a new spline interpolation function in the light of combination techniques of basic splines through introduction and brief review of previous studies in this field. This work which uses abbreviated form of augmented matrix proposed by authors published in past time , reveals a very good accordance results compared with the analytical and published solutions of different plate bending problems.

Calculation of Critical Load for Pure Distortional Buckling of Lipped Channel Columns

This paper presents a method that allows calculating the elastic critical stress for the distortional buckling mode, based on the buckling mode classification of typical lipped channel columns. In our case, Cold-Formed Steel Lipped Channel Columns are subjected to compression. Moreover, in order to consolidate the important findings of this work, a comparative study was carried out to assess the reliability of various distortional buckling models that are provided by different design Standards. It was found that the American and Australian approaches, given in the codes of practice, are closer to the Finite Strip Method than to the European method. An analytical solution was proposed for the determination of the distortional buckling stress on the basis of a statistical method; it corresponds to lipped channel sections with a flange width to web width ratio b/h ranging from 0.1 to 1, and a lip width to web width ratio c/h between 0 and 0.5. After comparison with the results given by the finite strip method for pure distortional buckling, it turned out that the proposed approach provides a reasonable prediction for the elastic distortional buckling stress for lipped channel sections subjected to compression. In fact, this method gives better results than the American approach.

Experimental and numerical investigation of stiffener effects on buckling strength of composite laminates with circular cutout

In the notched structures, to achieve maximum buckling resistance in comparison with structural weight, the optimal design of a stiffener is very important. In this research, after a review of the existing literature, nonlinear buckling behavior of composite plates containing the cutout with three different designs of stringer was investigated. The considered stiffeners are planer, longitudinal, and ring types. The buckling experiments were carried out on the stiffened plates containing a circular notch. Moreover, to achieve an efficient prediction of the buckling in the stiffened laminate with the hole, a finite strip method is developed based on the Airy stress function and von Karman’s large deformation equations. Studies show that there is a good agreement between the postbuckling behaviors derived from developed finite strip method with experimental results. Fast convergence of the considered finite strip method compared with the finite element results shows its efficiency for prediction of buckling behavior in laminated composites. The results show that the buckling load-bearing capacities of perforated plates with a longitudinal and planer stiffener are higher compared with the other stiffener, respectively. The detailed parametric study on the effects of thickness of the plate and stiffener and opening diameter on buckling behavior was performed using experiments and modeling.

An efficient finite strip procedure for initial post-buckling analysis of composite laminated members

An efficient procedure based on the semi-analytical finite strip method with newly introduced invariant matrices is developed to analyze the initial post-buckling of composite laminated members. The nonlinear strain-displacement equations obtained from the Von-Karman assumption and three plate theories, which are classical thin plate theory, first-order shear deformation plate theory, and high-order shear deformation plate theory can be used to evaluate the initial post-buckling performance of the composite laminated members. According to the principle of the minimum potential energy, the formulations of the finite strip method can be deduced. In order to improve the computational efficiency, the pre-integrated invariant matrices are introduced, which can convert the complicated analytical integral calculation of the stiffness matrix into a relatively simple matrix multiplication calculation. Several benchmark problems are tested based on the proposed method and other conventional methods. The corresponding comparison results show that: (1) the proposed method is proved to be feasible and accurate for those three different theories; (2) compared with the other conventional finite strip methods, the proposed method is much more efficient since it requires the integration of the stiffness matrix only once no matter how many iterations are needed, (3) and the advantage of time-saving is increasingly remarkable as the number of iterations increases.

Derivation of Explicit Augmented Spline Finite Strip Matrix Using Mixed Formulation For Plate Bending

Although Spline finite strip method for the analysis of plate bending based on a mixed variational formulation principle , using a variety B-Spline series as interpolation function was widely used in researches , the explicit form of the Augmented Matrix nowhere given. This leads to some difficulties concerning the verification and understanding the published results. The main objective of this paper is to introduce this matrix in abbreviated size through a detailed review of the mixed formulation for different spline finite strip models. The derived matrix will be helpful subject of research future work as it is examined by the time, reveals a very good accordance results compared with the analytical and published solutions of different plate bending problems as the reader can verified.

Derivation of Explicit Augmented Spline Finite Strip Matrix Using Mixed Formulation For Plate Bending

Although Spline finite strip method for the analysis of plate bending based on a mixed variational formulation principle , using a variety B-Spline series as interpolation function was widely used in researches , the explicit form of the Augmented Matrix nowhere given. This leads to some difficulties concerning the verification and understanding the published results. The main objective of this paper is to introduce this matrix in abbreviated size through a detailed review of the mixed formulation for different spline finite strip models. The derived matrix will be helpful subject of research future work as it is examined by the time, reveals a very good accordance results compared with the analytical and published solutions of different plate bending problems as the reader can verified.

Distortional-buckling analysis of channel sections with web stiffened by longitudinal ribs subjected to axial compression or bending

Abstract In the present work, the distortional buckling behaviour of simply supported columns and beams made from channel sections with longitudinal web ribs is investigated when subjected to axial compression and/or pure bending. The effect of stiffening ribs on the critical buckling stress of such members is studied using finite strip method (FSM). An analytical model, namely, the stiffened plate buckling model (SPBM), is developed. Based on this model, the closed form analytical solution is obtained and the formulae for calculating the critical distortional buckling stresses are derived. The analytical solution is then validated by comparing the critical distortional buckling stress with those obtained in finite strip method (FSM). An excellent agreement from the comparison is found. The present model has the potential to be adopted in the development of the designed model of such sections in engineering practices.

Structural behavior of intermediate length cold-formed steel rack columns with C-stitches

This article presents an experimental and numerical investigation on the strength and performance of intermediate length rack column sections with C-stitches under axial compression. The test program consisted of 10 axial concentric compression tests on columns with and without C-stitches under pin end conditions for two different geometric lengths. Finite element (FE) models were developed using commercial FE package ABAQUS considering material and geometric nonlinearities as well as initial geometric imperfections. The elastic buckling properties of the section were calculated using readily available linear elastic buckling analysis tools based on Generalized Beam Theory (GBT) and Finite Strip Method (FSM). Obtained FE results were compared with those obtained experimentally, and once verified the developed FE modeling technique was used to carry out a parametric study to examine changes in structural response due to variations in length, depth and spacing of C-stitches. Observed influences of C-stitches on the behavior and resistance of the considered columns were carefully analyzed, and key design aspects are presented herein.

Modal buckling analysis of thin-walled members with rounded corners by using the constrained finite strip method with elastic corner elements

In this paper modal decomposition of thin-walled structural members with rounded corners is discussed. Modal decomposition is a process which separates the characteristic behaviour types. If modal decomposition is applied in buckling analysis, pure uncoupled buckling modes can readily be analysed, such as pure global buckling, pure distortional buckling or pure local-plate buckling. Ability to calculate critical loads to a pure buckling mode is highly beneficial in the design of thin-walled structural members, for example in the design of cold-formed steel beams or columns. However, cold-formed steel profiles are always produced with rounded corners, and earlier studies showed that the now-used modal decomposition techniques of the constrained finite strip/element method sometimes fail to lead to reasonable results if the rounded corners are directly modelled in the analysis. In this paper a special version of the constrained finite strip method is presented and discussed. The proposed method introduces elastic corner elements, which makes it possible to perform the modal decomposition by the same process used for members with sharp corners, even if the rounded corners are directly modelled, still the results of pure buckling modes satisfy the engineering expectations. The theoretical background of the proposal is briefly summarized, then the elastic-corner approach is discussed by detailed analysis of sample examples as well as by an extended parametric study.

Direct Strength Design of Cold-Formed Steel Members Using Constrained Spline Finite Strip Method

Direct strength method (DSM) for the design of cold-formed steel members recommends finite strip method (FSM) for calculating the elastic buckling stresses corresponding to local, distortional and global buckling, which are considered to be the basic input parameters for design. This paper presents application of constrained spline finite strip method (cSFSM) developed by authors for calculating pure elastic buckling stresses in DSM and hence predicting the ultimate member capacity in uniform flexure and axial compression. The elastic buckling stresses are determined for a specified set of experiments available in literature using cSFSM by considering different end conditions and failure modes and the elastic stress values are applied in DSM for calculating ultimate member capacity. For beams with simply supported-warping free ends and columns with simply supported-warping fixed ends, the DSM evaluated results using cSFSM produces results comparable with experiments. The results obtained by the comparison of DSM with experiments were not satisfactory for fixed columns and beams with simply supported-warping fixed ends.

Buckling Analysis of Toroidal Shell by Rayleigh-Ritz Method

The energy approach is used to analyze the buckling stability of toroidal shells. A closed and an open toroidal shell, as well as a shell segment are considered. Linear strain energy and nonlinear strain energy due to a uniform external pressure are formulated. Variations of the in-surface and normal displacement components in the circumferential and meridional directions are assumed in the form of a double Fourier series. The eigenvalue problem for the determination of the critical pressure is formulated by the Rayleigh–Ritz method (RRM). The proposed procedure is evaluated by numerical examples: one for a closed and another one for a simply supported open toroidal shell. The obtained results are validated by a comparison with results obtained by the finite strip method (FSM) and the finite element method (FEM), which shows a very good agreement.

Exact strip postbuckling analysis of composite plates under compression and shear

ABSTRACTStiffened wing and fuselage panels often have a postbuckling reserve of strength, enabling them to carry loads far in excess of their critical buckling loads. Therefore allowing for postbuckling in design can reduce their weight, hence reducing fuel consumption and environmental impact. The present paper extends the postbuckling analysis in the exact strip software VICONOPT to more accurately reflect the skewed mode shapes arising from shear load and anisotropy. Such mode shapes are represented by a series of sinusoidal responses with different half-wavelengths which are coupled together using Lagrangian multipliers to enforce the boundary conditions. In postbuckling analysis the in-plane deflections involve responses with additional half-wavelengths which are absent from the out-of-plane deflection series. Numerical results are presented and compared with finite element analysis for validation. The present analysis gives close results compared to the finite element and finite strip methods and saves computational time significantly.

Analysis techniques for folded plate roofs and cellular bridges general review and comparisons

Folded plates have attracted profound interest in recent years because of their economic advantages and architectural appearance. In particular, their basic structural response is indeed logical enough, explicit and simple although its required numerical computation procedure is, in a little bit, boring. This type of structures have gained increasing popularity and offers more advantages than more complex structures, such as cylindrical shells, arches and right folded plate frames. Similarly, the thin-walled cellular bridge decks can be treated as a multi-folded plates structure. This study produces an overall review of the historical development of the most popular methods utilized for analysis the folded plate structures which are offered with their applications and how these methods are developed gradually. Four common methods are chosen in this paper to show their highlights of references particularizing in analysis of the above mentioned types of structure; the folded plate elasticity method (FPEM), finite element method (FEM), finite strip method (FSM) and spline finite strip method (SFSM). This investigation covers the elastic behavior, and the experimental researches on the elastic reaction of folded plate structures.

Modal identification of thin-walled members by using the constrained finite element method

Thin-walled structural members have complex behavior. It is usual to interpret the complex behavior as the superposition of simpler behavior components, like global, distortional, local, in-plane shear and transverse extension. When the standard shell finite element method is employed for the analysis, the behavior components are not separated, and the results can be difficult to interpret due to the complexity of the deformations. The results are more meaningful if identified, i.e., if the participations of the behavior components are quantified. Methods for the formal identification of the deformations have already been proposed, by using either the modes of generalized beam theory, or the basis functions of the constrained finite strip method. In this paper a newer and more general method, the constrained finite element method is used. Since this method can handle a wide range of thin-walled members, including members with holes, or members with varying cross-sections, or even stiffened plates, the identification can readily be applied to various thin-walled members. In the paper some particularities of the identification method are highlighted, as well as several sample examples are presented and discussed.

An energy-based approach to buckling modal decomposition of thin-walled members with arbitrary cross sections, Part 1: Derivation

This paper presents the generalisation of an energy-based method for the modal decomposition of buckled shapes of thin-walled members. This comprehensive method is derived and validated for fully decomposing the elastic buckling solution of a thin-walled member into the pure buckling mode classes of global, distortional, local, shear and transverse extension. The first three modes are de-facto prerequisites for buckling capacity predictions found in current design standards for thin-walled structures. In the literature, two main methods, namely the generalised beam theory (GBT) and the constrained finite strip method (cFSM), are widely employed for modal decomposition. Recently, an alternative energy-based approach has been presented for the decomposition of buckling modes into the classical local, distortional and global modes. This method is generalised in the present study to achieve a complete decomposition that also accounts for shear and transverse extensional modes in addition to global, distortional and local modes. In this method, each of the buckling classes is separated by imposing constraints that are defined by enforcing specific criteria on the total strain energy of the member. The adopted criteria are based on the fundamental mechanical assumptions of the GBT which were also implemented in the conventional cFSM and later were further detailed for modal classification in the generalised cFSM. This paper is accompanied by a paper in which derivation of a modified global torsion mode for sections with closed loops is presented and the applicability of the proposed method is demonstrated using a series of numerical examples.

The buckling of CFRP composite plates in compression and shear and thin-walled composite tubes in torsion – The effects of bend-twist coupling and the applied shear direction on buckling performance

The influence of flexural anisotropy or bend-twist coupling on the buckling performance of CFRP composite plates in compression and shear and thin-walled CFRP composite tubes in torsion is examined in this paper using the finite strip method of analysis. The finite strip formulation employed in the analysis procedure is readily able to deal with the many complexities associated with typical laminated composite construction. Lay-up configurations resulting in membrane anisotropy, flexural anisotropy and membrane-flexural coupling are all easily dealt with. The strip perturbation or buckling displacement fields are postulated to vary sinusoidally along the strip length and algebraicly across the strip width and any combination of linearly varying bi-axial tension or compression coupled with in-plane shear loading on the strip can be accommodated. The paper gives an in-depth understanding of the complex buckling mechanics associated with flexural anisotropy in polymer composite construction and highlights the importance of realising the significance of the applied in-plane shear or torque direction on buckling performance. Markedly different stability levels are shown to be in existence for the load cases of positive and negative shear in composite plates and for the clockwise and anticlockwise torsional loading of thin-walled composite tubes. This situation is, of course, not realised in isotropic metal construction or in orthotropic composite construction since such material systems are devoid of the effects of bend-twist coupling.