Semi-analytical Finite Strip Method Research Articles

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.

New transverse extension modes for buckling analysis of thin-walled members by using the constrained finite strip method

In this paper a new way to define transverse extension modes is introduced in the context of modal analysis of thin-walled members. The new transverse extension modes are inspired by the strain distributions of global and distortional modes. The new modes are employed here in the constrained finite strip method. The new modes require some change in the interpolation functions of the semi-analytical finite strip method, and this change is briefly discussed. The practical advantage of the newly proposed transverse extension modes is that the artificial stiffness increase, which is characteristic to pure global and/or distortional deformations in constrained analyses, can be compensated by the consideration of the relevant new transverse extension mode(s), as illustrated by numerous proof-of-concept examples in the paper.

Buckling analysis of orthotropic nanoplates based on nonlocal strain gradient theory using the higher-order finite strip method (H-FSM)

In this paper, a semi-analytical higher-order finite strip method is developed based on the nonlocal strain gradient theory (NSGT) for buckling analysis of orthotropic nanoplates. NSGT contains two material length scale parameters related to the nonlocal and strain gradient effects. To consider the effect of the strain gradient in the governing equation of the plate in the transverse direction, the higher-order polynomial shape functions (higher-order Hermitian shape functions) are utilized to assess the second derivatives, in addition to the displacement and first derivatives. Also, some numerical study is presented on the effects of different factors such as boundary conditions, nonlocal and strain gradient parameters, aspect ratio, and different types of in-plane loading for the isotropic and orthotropic rectangular nanoplate to verify the proposed formulation. In the following, a relation for the nanoplates based on the nonlocal strain gradient theory using the Navier method is extracted and presented for preliminary comparisons. According to the proposed relation, it is shown that in simply supported nanoplates, if the non-local parameter is equal to the second power of the strain gradient parameter, the responses obtained for the nanoplates are equal to the locally available responses.

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).

Explicit approach for elastic local buckling analysis of thin-walled channels under combined bending and shear

For flexural thin-walled section beams, the ultimate strength is significantly affected by the interaction of different local buckling modes associated with combined bending and shear stresses. This paper provides a comprehensive analytical and numerical study of elastic buckling of thin-walled channels subjected to different combinations of bending and shear stresses. The commercial ABAQUS software package using Finite Element Method (FEM) has been used to perform the elastic buckling analyses of the channel sections. The results are benchmarked against those from the Semi-Analytical Finite Strip Method (SAFSM) for the cases of pure bending and shear only. Two typical types of channels with and without lips are selected for investigation. To study the effect of different combinations of bending and shear on the buckling stresses, different normal stress distributions and equilibrating shear stresses are applied at two end cross-sections of the channels to maintain static equilibrium. Different types of interactions which occur during the buckling analyses are studied by varying the ratios of bending moments resulting from the modelled longitudinal stresses. A new concept for the elastic local buckling interaction based on the Average Bending Moment (ABM) at buckling is provided. In addition, an explicit approach for local buckling loads of channels under different combinations of bending and shear is also introduced for the practical design use. The results from this explicit solution for elastic buckling can be used as direct inputs for an explicit Direct Strength Method (DSM) design of members under combined bending and shear.

FREE VIBRATION ANALYSIS OF SINGLY CURVED CLAMPED SHELLS USING THE ISOGEOMETRIC FINITE STRIP METHOD

<jats:p>A hybrid method for the spatial discretization of two-dimensional domains is recently derived and applied to the problem of free vibrations of simply-supported singly curved shells. This new method follows from a tensor product of NURBS functions and a carefully selected series that satisfies boundary conditions a priori. The formulation unifies spatial discretization schemes of the semi-analytical Finite strip method and the Isogeometric analysis. In this paper, the method is improved by implementing the capability to deal with clamped-clamped boundary conditions. The numerical analysis shows that the method has favorable accuracy per DOF, in comparison with the standard finite elements.</jats:p>

Local buckling of thin-walled circular hollow section under uniform bending

This article presents a semi-analytical finite strip method based on Marguerre’s shallow shell theory and Kirchhoff’s assumption. The formulated finite strip is used to study the buckling behavior of thin-walled circular hollow sections (CHS) subjected to uniform bending. The shallow finite strip program of the present study is compared to the plate strip implemented in CUFSM4.05 program for demonstrating the accuracy and better convergence of the former. By varying the length of the CHS, the signature curve relating buckling stresses to half-wave lengths is established. The minimum local buckling point with critical stress and corresponding critical length can be found from the curve. Parametric studies are performed to propose approximative expressions for calculating the local critical stress and local critical length of steel and aluminum CHS.

Buckling Analysis of Variable Stiffness Composite Laminates by Semi-Analytical Finite Strip Method

Buckling Analysis of Variable Stiffness Composite Laminates by Semi-Analytical Finite Strip Method

Correction to: Thermal post-buckling analysis of laminated composite plates embedded with shape memory alloy fibers using semi-analytical finite strip method

Correction to: Thermal post-buckling analysis of laminated composite plates embedded with shape memory alloy fibers using semi-analytical finite strip method

Nonlinear dynamic buckling analysis of imperfect viscoelastic composite laminated plates

The aim of this paper is to study the effects of linear viscoelastic behavior on dynamic buckling response of imperfect composite laminated plates subjected to in-plane dynamic loads by implementing semi-analytical finite strip method (FSM). The semi-analytical FSM converges with a comparatively small number of strips and correspondingly small number of degrees of freedom. Thus, it is usually implemented more easily and faster than many other computational methods. The governing equations are derived by using classical laminated plate theory (CLPT) and the behavior of plate is assumed to be geometrically nonlinear through Von-Karman assumptions. The Newmark's implicit time integration method in conjunction with the Newton-Raphson iteration are employed to solve the nonlinear governing equation. A Kelvin-Voigt viscoelastic model is considered, and the effects of viscosity coefficient, thickness of the layers of the composite plate and boundary conditions on the nonlinear dynamic buckling response are discussed. In order to justify the accuracy of the results, some of them are verified against those available in other sources. It is also shown that the nonlinear dynamic buckling response of an imperfect viscoelastic composite laminated plate is significantly different from the elastic one by considering different viscosity coefficients.

New Transverse Extension Modes for the Constrained Finite Strip Analysis of Thin-walled Members

In this paper a new way to define transverse extension modes is introduced in the context of modal analysis of thin-walled members. The new primary transverse extension modes are inspired by the strain distributions of global and distortional modes. The new modes are employed here in the constrained finite strip method. The new modes require some change in the interpolation functions of the semianalytical finite strip method, which change is briefly discussed. The practical advantage of the proposed new transverse extension modes is that the artificial stiffness increase, which is characteristics to constrained analyses, can be compensated by the consideration of the relevant new transverse extension mode(s), as illustrated by numerous proof-of-concept examples in the paper.

Thermal Post-buckling Analysis of Laminated Composite Plates Embedded with Shape Memory Alloy Fibers Using Semi-analytical Finite Strip Method

The thermal buckling and post-buckling of geometrically perfect and imperfect hybrid laminated composite plates reinforced with shape memory alloys (SMA) subjected to a uniform thermal loading are investigated by a semi-analytical finite strip method. In this method, because of applying trigonometric functions, the energy integrations can be computed analytically. The first-order shear deformation theory in conjunction with von Karman nonlinear strain–displacement formulation is implemented. The solution procedure is based on minimization of the total potential energy and solving the eigenvalue problem or a set of nonlinear equations by using an iterative Newton–Raphson method for linear buckling and post-buckling analysis, respectively. By using 1-D simplified Brinson’s model, the effect of SMA fibers on thermal buckling and post-buckling of composite plates with various boundary conditions is studied.

Free vibration analysis of singly curved shells using the isogeometric finite strip method

A novel method for the spatial discretization of two-dimensional domains is derived and applied to the problem of free vibrations of singly curved shells. This new method utilizes a tensor product of two independent families of lines to discretize the geometry and kinematics of a surface. The first family consists of NURBS functions which are implemented in agreement with the isogeometric approach. The second family of lines is a carefully selected series which satisfies boundary conditions a priori. The present hybrid formulation unifies spatial discretization schemes of the semi-analytical Finite strip method and the Isogeometric analysis. The obtained method inherits many features of both of the underlying techniques, e.g., high continuity in both directions, decoupling of the governing equations, and exact initial geometry. Thorough numerical analysis shows that this novel method is well-suited for the efficient and accurate free vibration analysis of singly curved thin shells.

Inelastic buckling mode interactions and resonance instabilities in thin-walled columns due to the fatigue damage

PurposeThe problems of inelastic instability (buckling) and dynamic instability (resonance) have been the subject of extensive investigation and have received wide attention from the structural mechanics community. This paper aims to tackle these problems in thin-walled structures, taking into account geometrical and/or material non-linearity.Design/methodology/approachThe inelastic buckling mode interactions and resonance instabilities of prismatic thin-walled columns are analysed by implementing the semi-analytical finite strip method (FSM). A scalar damage parameter is implemented in conjunction with a material modelling named rheological-dynamical analogy to address stiffness reduction induced by the fatigue damage.FindingsInelastic buckling stresses lag behind the elastic buckling stresses across all modes, which is a consequence of the viscoelastic behaviour of materials. Because of the lag, the same column length does not always correspond to the same mode at the elastic and inelastic critical stress.Originality/valueThis paper presents the influence of mode interactions on the effective stresses and resonance instabilities in thin-walled columns due to the fatigue damage. These mode interactions have a great influence on damage variables because of the fatigue and effective stresses around mode transitions. In its usual semi-analytical form, the FSM cannot be used to solve the mode interaction problem explained in this paper, because this technique ignores the important influence of interaction of the buckling modes when applied only for undamaged state of structure

A Coupled Improved Element Free Galerkin-Finite Strip (IEFG-FS) Method for Free Vibration Analysis of Plate

In this paper, a coupling of improved element-free Galerkin (IEFG) method and semi-analytical finite strip (FS) method is presented for free vibration analysis of thin plates. This method is very easy to implement and has advantages of both IEFG and FS methods, so that IEFG method is used in sub-domain with complex geometry, and FS method is used for the remaining domains. The use of the FS method considerably reduces the analysis time, and the essential boundary conditions are easily enforced in FS sub-domain. In the IEFG method, the shape function does not have the Kronecker delta function property. Therefore, Lagrange multipliers method is used to satisfy the boundary conditions. Finally, five examples are presented to show the effectiveness of this work.

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.

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.

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.

Free vibration analysis of functionally graded cylindrical shells with different shell theories using semi-analytical method

In this study, the semi-analytical finite strip method is adopted to examine the free vibration of cylindrical shells made up of functionally graded material. The properties of functionally graded shells are assumed to be temperature-dependent and vary continuously in the thickness direction according to a simple power law distribution in terms of the volume fraction of ceramic and metal. The material properties of the shells and stiffeners are assumed to be continuously graded in the thickness direction. Theoretical formulations based on the smeared stiffeners technique and the classical shell theory with first-order shear deformation theory which accounts for through thickness shear flexibility are employed. The finite strip method is applied to five different shell theories, namely, Donnell, Reissner, Sanders, Novozhilov, and Teng. The approximate procedure is compared favorably with three-dimensional finite elements. Finally, a detailed numerical study is carried out to bring out the effects of power-law index of the functional graded material, stiffeners, and geometry of the shells on the difference between various shell theories. Finally, the importance of choosing the shell theory in simulating the functionally graded cylindrical shells is addressed.

Buckling analysis of thin-walled members with open-branched cross section via semi-analytical finite strip transfer matrix method

Thin-walled members with open-branched cross section have been used in many modern engineering structures, and their buckling performance has been widely studied. In this paper, two transfer methods are developed to tackle the transfer problems at the junction of the open-branched cross-section of thin-walled members by using semi-analytical finite strip transfer matrix method (FS-TMM) which is a combined use of semi-analytical finite strip method (SA-FSM) and transfer matrix method (TMM) for the buckling analysis. Compared to traditional SA-FSM, this method has a smaller matrix and higher computational efficiency due to no global stiffness matrix generated. An asymmetric E-section member, a symmetric I-section member and a X-section member with loaded edges simply supported are analyzed by the derived formulation. All the results are compared with SA-FSM's or finite element method's results to prove the reliability and efficiency of this method.