Finite Strip Model Research Articles

Analysis of horizontal cyclic bearing capacity of pile based on cyclic strain wedge finite element strip method

This paper proposes a cyclic strain wedge finite element strip model to analyze of the cyclic bearing characteristics of pile foundation. First, the strain wedge body is meshed by every soil element, which can assign the stress-strain relationship to each soil element of the wedge body. Then, the equivalent substitution stress‒strain relationship of each wedge layer can be obtained from the stress‒strain relationship of the soil element by the principle of the stress‒strain equivalent substitution method. It can truly reflect the stress-strain relationship of the soil to the stress-strain relationship of the wedge layer and the p-y curve. At the same time, the equivalent cyclic creep constitutive of soil is applied to the strain wedge finite element strip model for the cyclic bearing characteristics of the wedge layer and the cyclic p‒y curve. Finally, the cyclic strain wedge finite element strip model is verified by some tests. The results from the proposed method agree reasonably well with the measured results. It can provide a new method for analyzing the horizontal cyclic bearing characteristics of pile.

Finite strip method based on Carrera unified formulation for the free vibration analysis of variable stiffness composite laminates

AbstractThis work presents a refinement of the finite strip method (FSM) based on the Carrera unified formulation (CUF) and is applied to free vibration analysis of variable stiffness composite laminated (VSCL) plates. VSCL plates considered here are composed of layers with curvilinear fibers in which their orientation angle changes linearly with respect to one of the in‐plane coordinates. The FSM permits the plate to be divided into some finite strips connected along the so‐called nodal lines. The conventional finite strip method involves an approximation of the solution of a plate problem by using continuously harmonic series in the longitudinal direction along the nodal lines and simple polynomial shape functions (the usual beam shape functions) in the transverse direction of the plate. However, refined finite strip model that presented in this paper allows one to express the unknown variables as a set of thickness functions that only depend on the thickness coordinate and the corresponding variable that depends on the in‐plane coordinates which involve continuously harmonic series and polynomial shape functions. Thanks to this new finite strip model, the shape functions used in the transverse direction can be chosen as 1D bar shape functions, and also, all three components of the displacement field are considered in each nodal line. Moreover, based on this approach, three‐dimensional displacement field is approximated in a compact form as a generic N‐order expansion. Therefore, explicit expressions of fundamental nuclei of finite strip matrices are obtained in a compact form and presented here. The results obtained by the present formulation for VSCL plates are compared with those obtained from published data. The results show that this kind of strip is efficient and useful. Further, several numerical examples are presented, and the effect of the order of expansion, the number of strips, curvilinear fiber angle, and various boundary conditions are examined.

Shear lag including axial balance of box beams by finite segment model

A finite segment element including axial balance is formulated to describe shear lag in thin-walled box beams having constant or variable cross sections made from steel or other materials. The axial balance neglected in the conventional finite segment element model (CFSM) is enforced by adding the nodal longitudinal displacements, while shear lag and shear deformation are incorporated using the nodal shear lag functions and rotations, respectively. The homogeneous solutions deduced by the analytical method are utilized for constructing the element shape functions. By invoking the minimum potential energy theorem, the stiffness matrix and the equivalent nodal force vector are then derived for the element. The precision of the proposed finite segment model (PFSM) is verified against the results yielded from the solid finite element model (SFEM), the finite strip model (FSTM), and the experiments. A continuous box beam having varying cross sections is chosen for comparing the neutral axis depth to the centroidal axis depth. Subsequently, the influence of the axial balance on the mechanical behavior is evaluated. Moreover, the effects of three major geometric parameters are discussed for stress analysis. The results reveal that the proposed finite segment model is capable of reproducing the mechanical behavior of box beams having constant or varying cross sections, and that the stress analysis concerning the continuous box beam with variable cross sections is substantially affected by the axial balance condition.

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.

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.

Finite Strip Modeling of the Varying Dynamics of Shell-Like Structures During Machining Processes

The efficiency of the finite strip method (FSM) in modeling the varying dynamics of shell-like structures during machining operations is investigated. The workpiece is modeled as a shallow, helicoidal, cantilevered shell, and the natural modes are computed using FSM. In the FSM solution, the workpiece is discretized only in the chordwise direction, and the membrane and bending displacement fields of the shell in the spanwise direction are approximated by a set of basis functions that satisfy clamped-free boundary conditions. The displacement fields in the chordwise direction are approximated using polynomial functions. The efficiency of the presented FSM is investigated by comparing the computed natural vibration modes against the ones obtained using the finite element method (FEM). The FSM model was found to yield results of greater or comparable accuracy, even with up to 40% fewer degrees-of-freedom (DOFs). Also, the accuracy of the presented model is verified by comparing the predicted frequency response functions (FRFs) against the FRFs that were measured by conducting impulse hammer tests in various stages of machining a generic curved blade.

Development of a viscoelastic spline finite strip formulation for transient analysis of plates

In this study, the forced vibration behavior of viscoelastic plates is investigated using the spline finite strip method (spline FSM). It is assumed that the viscoelastic behavior of materials considered in this research is linear, which means the material constants are independent of load level and are a function of time only. The shear modulus is thus represented as a function of the so-called Prony series. Moreover, it is assumed that the bulk modulus remains constant. For spline FSM, the equilibrium equations are derived using the principle of virtual work and the classical bending plate theory in matrix form. A numerical solution is developed for forced vibration analyses using the Newmark's method. The damping effects corresponding to the viscoelastic nature of materials are incorporated in the analysis by a novel approach that defines a fictitious damping force vector. The convergence of the spline finite strip method for a viscoelastic plate under different loading conditions is studied. Additionally, the fast fourier transform (FFT) of forced vibration responses is applied to evaluate the natural frequencies of plates. The accuracy and efficiency of the proposed spline finite strip model are verified by comparing the simulation outcomes presented in this work with the results obtained from the finite element method using ANSYS. Through a comparison of the results, we found the spline finite strip results to be in good agreement with the finite element results.

Finite strip modeling of the varying dynamics of thin-walled pocket structures during machining

The structural model of the workpiece is required for modeling, analysis, and avoidance of forced and regenerative (chatter) vibrations in machining of thin-walled parts. Finite element models (FEM) provide a versatile means for modeling the workpiece dynamics, but such models need to be updated frequently as the mass and stiffness of the workpiece varies continuously during machining. The computational time and power that is needed for re-meshing the FEM and then re-computing the natural modes of the workpiece is prohibitive. In this paper, a new approach based on Finite strip modeling (FSM) is presented for modeling the structural dynamics of thin-walled structures during pocket milling operations. The substantially higher computational efficiency of the FSM approach in predicting the varying dynamics of thin-walled pocket structures is verified by comparing its performance against FEM and the multi span plate (MSP) approach presented in (J Manuf Sci Eng 133:021014, 2011). Additionally, the accuracy of the presented approach in analyzing the stability of vibrations and determining the extent of dynamic deflections is verified using experimental results.

Finite strip modeling of cementitious laminates reinforced with sisal fibers

The use of natural fibers to reinforce of cementitious matrices permits the development of sustainable materials with many potential applications. However, the improvement of such materials strongly depends on experimental studies, making the process slow and expensive. The numerical methods currently available for modeling composites can adequately describe the behavior of polymeric laminates, but have limited application in cementitious laminates that can have multiple cracking. This paper proposed a numerical model that combines the Finite Strip Method, Classical Theory of Laminates and Damage Mechanics to model the flexural behavior of laminated composites. The method can monitor the stresses developed in each layer and verify the ruptures resulting from traction, compression or shear. To validate the numerical method, flexural tests were carried out on cementitious laminates reinforced with 2 or 3 layers of long sisal fiber, with fiber content of 3% or 6%. Comparisons between the numerical and experimental results demonstrate good agreement, especially for composites reinforced with high fiber content. The adequate prediction of internal stress allows for the use of this numerical method to design cementitious laminates reinforced with sisal fibers that possess properties suitable for various applications.

Inelastic local buckling of curved plates with or without thickness-tapered sections using finite strip method

This paper addresses the inelastic local buckling of the curved plates using finite strip method in which buckling modes and displacements of the curved plate are calculated using sinusoidal shape functions in the longitudinal direction and polynomial functions in the transverse direction. A virtual work formulation is employed to establish the stiffness and stability matrices of the curved plate whilst the governing equations are then solved using a matrix eigenvalue problem. The accuracy and efficiency of the proposed finite strip model is verified with finite element model using ABAQUS as well as the results reported elsewhere while a good agreement is achieved. In order to illustrate the proposed model, a comprehensive parametric study is performed on the steel and aluminium curved plates in which the effects of curvature, the length of the curved plate as well as circumferential boundary conditions on the critical buckling stress are investigated. The developed finite strip method is also used to determine the buckling loads of the curved plates with thickness-tapered sections as well as critical stresses of the aluminium cylindrical sectors that are subjected to uniform longitudinal stresses.

Finite strip modeling for optimal design of reinforced concrete folded plate structures

The optimal design of reinforced concrete folded plate structures under multiple loading conditions is presented. The design variables include geometrical quantities, like the thickness, dimensions of the structural members (plates), and topological parameters, which define the locations and the connectivity of such elements. The structural analysis required during the design process is performed by using the classical finite strip method and complex harmonic coupled finite strip method for the solution of the corresponding geometric nonlinear design problem. Some applications to the optimal design of prismatic folded plates show the effectiveness of the proposed procedures.

Optimal Design of Piezolaminated Structures Using B-Spline Finite Strip Models and Genetic Algorithms

In this work, a set of numerical models is developed using the B-spline finite strip approach for linear analysis of piezolaminated plates and shells with particular focus to box girder type structures. These models are linked to global optimization techniques, such as genetic algorithms, which may consider either binary or floating point encoding of design variables, along with the inherent particularities of genetic operators at implementation level. Examples are discussed to illustrate the performance of these models.

Optimal design of piezolaminated structures using B-spline strip finite element models

A package of B-spline finite strip models is developed for the linear analysis of piezolaminated plates and shells. This package is associated to a global optimization technique in order to enhance the performance of these types of structures, subjected to various types of objective functions and/or constraints, with discrete and continuous design variables. The models considered are based on a higher-order displacement field and one can apply them to the static, free vibration and buckling analyses of laminated adaptive structures with arbitrary lay-ups, loading and boundary conditions. Genetic algorithms, with either binary or floating point encoding of design variables, were considered to find optimal locations of piezoelectric actuators as well as to determine the best voltages applied to them in order to obtain a desired structure shape. These models provide an overall economy of computing effort for static and vibration problems.

Buckling mode decomposition of single-branched open cross-section members via finite strip method: Derivation

This paper provides the first detailed presentation of the derivation for a newly proposed method which can be used for the decomposition of the stability buckling modes of a single-branched, open cross-section, thin-walled member into pure buckling modes. Thin-walled members are generally thought to have three pure buckling modes (or types): global, distortional, and local. However, in an analysis the member may have hundreds or even thousands of buckling modes, as general purpose models employing shell or plate elements in a finite element or finite strip model require large numbers of degrees of freedom, and result in large numbers of buckling modes. Decomposition of these numerous buckling modes into the three buckling types is typically done by visual inspection of the mode shapes, an arbitrary and inefficient process at best. Classification into the buckling types is important, not only for better understanding the behavior of thin-walled members, but also for design, as the different buckling types have different post-buckling and collapse responses. The recently developed generalized beam theory provides an alternative method from general purpose finite element and finite strip analyses that includes a means to focus on buckling modes which are consistent with the commonly understood buckling types. In this paper, the fundamental mechanical assumptions of the generalized beam theory are identified and then used to constrain a general purpose finite strip analysis to specific buckling types, in this case global and distortional buckling. The constrained finite strip model provides a means to perform both modal identification relevant to the buckling types, and model reduction as the number of degrees of freedom required in the problem can be reduced extensively. Application and examples of the derivation presented here are provided in a companion paper.

Finite strip modeling for optimal design of prestressed folded plate structures

The optimal limit state design of prestressed thin-walled folded plate structures under multiple loading conditions is presented. The design variables include (a) geometrical quantities, like the thickness and the dimensions of the structural members, (b) topological parameters, which define the location and the connectivity of such elements, and (c) the characteristics of the eventual prestressing system, described by the prestressing forces and the cables profile. Besides the physical and technological limits on such variables, the design constraints account for given limit states on both the stress and the displacement states which define the structural behavior. The objective of the design process is to find the structural layout which minimizes the structural volume and/or the total prestressing force according to the mentioned side and behavioral constraints. The solution of the corresponding non-linear optimization problem is achieved by using a numerical procedure based on the complex method. The structural analyses required during the optimization process are performed by using the finite strip method. Some applications to the optimal design of beams, vaults and box-girder bridges show the effectiveness of the proposed procedure.

Finite strip modeling for optimal design of prestressed folded plate structures

The optimal limit state design of prestressed thin-walled folded plate structures under multiple loading conditions is presented. The design variables include (a) geometrical quantities, like the thickness and the dimensions of the structural members, (b) topological parameters, which define the location and the connectivity of such elements, and (c) the characteristics of the eventual prestressing system, described by the prestressing forces and the cables profile. Besides the physical and technological limits on such variables, the design constraints account for given limit states on both the stress and the displacement states which define the structural behavior. The objective of the design process is to find the structural layout which minimizes the structural volume and/or the total prestressing force according to the mentioned side and behavioral constraints. The solution of the corresponding non-linear optimization problem is achieved by using a numerical procedure based on the complex method. The structural analyses required during the optimization process are performed by using the finite strip method. Some applications to the optimal design of beams, vaults and box-girder bridges show the effectiveness of the proposed procedure.

Comparison of numerical techniques for 3D flutter analysis of cable-stayed bridges

This paper presents the results of a comparison study of the numerical techniques of structural and aerodynamic force models developed based on the spline finite strip method with the conventional finite element approach in three-dimensional flutter analysis of cable-stayed bridges. In the new formulation, the bridge girder is modelled by spline finite strips. The mass and stiffness properties of the torsional behaviour of complex bridge girder, which have a significant influence on the wind stability of long-span bridges, are modelled accurately in the formulation. The effects of the spatial variation of the aerodynamic forces can be taken into account in the proposed numerical model by distributing the loads to the finite strips modelling the bridge deck. The numerical example of a 423 m long-span cable-stayed bridge is presented in the comparison study. The accuracy and effectiveness of the proposed finite strip model are compared to the results obtained from the equivalent beam finite element models. The advantages and disadvantages of these different modelling schemes are discussed.

A model for deformable roll coating with negative gaps and incompressible compliant layers

A soft elastohydrodynamic lubrication model is formulated for deformable roll coating involving two contra-rotating rolls, one rigid and the other covered with a compliant layer. Included is a finite-strip model (FSM) for the deformation of the layer and a lubrication model with suitable boundary conditions for the motion of the fluid. The scope of the analysis is restricted to Newtonian fluids, linear elasticity/viscoelasticity and equal roll speeds, with application to the industrially relevant highly loaded or ‘negative gap’ regime. Predictions are presented for coated film thickness, inter-roll thickness, meniscus location, pressure and layer deformation as the control parameters – load (gap), elasticity, layer thickness and capillary number, – are varied. There are four main results: Hookean spring models are shown to be unable to model effectively the deformation of a compliant layer when Poisson's ratio and qualitive agreement for flow rate. It is shown that this difference in the latter case may be due to viscoelastic effects in the compliant layer.