Finite Element-transfer Matrix Method Research Articles

A Method for Determining the Fundamental Site Period and the Average Shear Wave Velocity

The soil–structure interaction plays a crucial role in determining the displacement and internal forces of multi-story buildings subjected to strong ground motion. One of the critical dynamic characteristics influencing soil–structure interaction is the fundamental site period and the average shear wave velocity associated with it. This study introduces an original equation to determine these parameters. In addition, for the first time in the literature, the version of the Rayleigh method used for finding the fundamental periods of buildings is used to find the fundamental site period. The soil is modeled as an equivalent shear beam to obtain the proposed equation. The peak displacement is obtained by acting the soil mass as an external load on the equivalent shear beam. For single-layer soil, the fundamental site period is proportional to the square root of the peak displacement of the equivalent shear beam. The least squares method generalizes the proposed relation for single-layer soils to multi-layer soil profiles. Modified Finite element Transfer matrix method is used for calibration in the least squares method. The equations used in the literature and earthquake codes for determining the fundamental site period and average shear velocity are tested on various examples, and it is shown that the method proposed in this study, along with the Rayleigh method, gives better results than these equations. The performances of these two methods and the five commonly used equations are tested and compared on different soil profiles. Transfer functions, Finite Element Method (SAP200) and Modified Finite Element Transfer Matrix Method are used for verification. For all soil profiles, the results obtained from the transfer function, Finite Element Method (SAP200) and Modified Finite Element Transfer Matrix Method are found to be in agreement. The true percent relative error found in the results obtained with the proposed method is 4.47%.

Time-harmonic analysis of acoustic pulsation in gas pipeline systems using the Finite Element Transfer Matrix Method: Theoretical aspects

Structural vibration of gas pipeline systems can be strongly affected by the response of the acoustic domain represented by the gas being transported through pressurized pipes, cylinders and other related components. The resultant Acoustically Induced Vibration (AIV) can be a cause of failure, for example, in reciprocating compressor systems, where the discharge and suction pulsations are the main source of excitation. The objective of this work is to explore and enhance the use of the Finite Element Transfer Matrix Method (FETM) for solving time-harmonic acoustic problems related to AIV, whose results can be used to analyze pulsation in piping systems. Four different damping models are explored and implemented (apart from the classical undamped model) resulting in five different acoustic elements for the quiescent fluid case. In addition, two different damping models are analyzed for the case of a fluid with mean flow, and implemented through two flow-acoustic elements. The physical behavior of certain typical junctions is also investigated, represented by acoustic and flow-acoustic length corrections, and an FETM formulation is proposed to account for local non-linear effects in transfer impedance elements. Also, a discussion related to the minimum and maximum FETM element sizes is presented. A critical analysis of the effectiveness of the whole FETM strategy is performed using a variety of representative gas pipeline geometries as application examples with a particular set of boundary conditions for quiescent and moving fluid medium. Nodal pressure frequency plots of cases considering all the presented acoustic and flow-acoustic elements, and related damping models, are presented. Coherent results were achieved using the procedure when frequency plots are compared with experimental data and 3D FEM equivalent models.

Obtaining the Transfer Function in One Dimensional Soil Amplification Analysis with Modified Finite Element Transfer Matrix Method

Bu çalışmada tek boyutlu zemin büyütme analizlerinde kullanılan Transfer fonksiyonlarının elde edilmesi için bir yöntem önerilmiştir. Çalışma kapsamında daha önce literatürde zemin hâkim periyodunun bulunması için kullanılan Değiştirilmiş Sonlu Elemanlar Taşıma Matrisi (DSETM) yöntemi zemin büyütme analizlerinde kullanılan transfer fonksiyonlarının bulunması problemine uyarlanmıştır. Klasik sonlu elamanlar yönteminde eleman sayısına bağlı olarak artan sistem matrisi DSETM yönteminde eleman sayısından bağımsızdır. Çalışmanın sonunda önerilen yöntemin uygunluğu iki örnek üzerinde gösterilmiştir. Ele alınan örnekler hem bu çalışmada sunulan DSETM yöntemiyle hem de literatürde yer alan yöntemle çözülerek sonuçlar karşılaştırılmıştır. Sunulan yöntemin uygulanması için Scilab ortamında bir program yazılmıştır.

Hybrid finite element transfer matrix method and its parallel solution for fast calculation of large-scale structural eigenproblem

Vibration characteristics play a fundamental role in structural analysis and dynamics design. The determination of vibration characteristics requires the solution of an eigenproblem. In this work, a novel parallel hybrid finite element (FE) transfer matrix method (TMM) is studied for a large-scale structural eigenproblem. The full structure is divided into some substructures, and the vibration characteristics of each substructure are calculated with their proper solution method (FE or TMM). Then by using the order-reduction transformation of the full structure based on an improved fixed interface modal synthesis, the reduced global equation of the full structure is obtained easily, and it can be used to solve the vibration characteristics of the full structure efficiently. To overcome the numerical instability of the ordinary transfer matrix technology in a large-scale structural analysis, the Riccati transform is also adopted. This hybrid method has good parallelism, and the corresponding parallel algorithms are presented. Finally, this method is applied to a vacuum vessel structure of the China fusion engineering test reactor, which has cyclic symmetry conditions. The simulation results demonstrate that this method has low computational cost and satisfactory accuracy.

AN APPLICATION OF THE MODIFIED FINITE ELEMENT TRANSFER MATRIX METHOD FOR A HEAT TRANSFER PROBLEM

The Transfer Matrix Method is an effective method which is used in mechanics and provides a great advantage especially in solving some mechanical problems. The most important advantage of the Transfer Matrix Method is reducing the dimensions of the matrix used in the analysis. The most important consequence of this is the saving the time. In this study, firstly studies in recent years in relation with the Transfer Matrix Method have been briefly summarized. Then the Modified Finite Element Transfer Matrix Method is explained briefly. At the end of the study, the application of the Modified Finite Element Transfer Matrix Method to the heat transfer problem has been demonstrated.

Free vibration analysis of axisymmetric shells with various shapes using Sylvester-transfer stiffness coefficient method

We developed a computational method for effectively conducting the free vibration analysis of axisymmetric shells with various shapes. This paper describes a computational algorithm for the free vibration analysis of axisymmetric shells using the Sylvester-transfer stiffness coefficient method (S-TSCM). From the free vibration analyses of three axisymmetric shells (joined conical-cylindrical shell, hermetic capsule and built-up shell), we verified the applicability of the S-TSCM. We then confirmed that the computational power of the S-TSCM is much better than both the finite element-transfer matrix method and finite element-transfer stiffness coefficient method, in terms of computational accuracy and time. In particular, when axisymmetric shells are modeled into a large number of conical shell elements, the S-TSCM is superior to both the bisection method using Sturm sequence property and Jacobi method, in terms of computational time and storage.

Free vibration analysis of asymmetric shear wall-frame buildings using modified finite element-transfer matrix method

In this study, the modified finite element- transfer matrix methods are proposed for free vibration analysis of asymmetric structures, the bearing system of which consists of shear wall-frames. In the study, a multi-storey structure is divided into as many elements as the number of storeys and storey masses are influenced as separated at alignments of storeys. The shear walls and frames are assumed to be flexural and shear cantilever beam structures. The storey stiffness matrix is obtained by formulating the governing equation at the center of mass for the shear walls and the frames in the i.th floor. The system transfer matrix is constructed in the dimension of 6x6 by transforming the obtained stiffness matrix. Thus, the dimension, which is 12nx12n in classical finite elements, is reduced to the dimension of 6x6. To study the suitability of the method, the results are assessed by solving two examples taken from the literature.

Modified finite element-transfer matrix method for the static analysis of structures

In this paper the Modified Finite Element-Transfer Matrix Method, which is the combination of Transfer Matrix Method and Finite Element Method, is applied to the static analysis of the structures. In the method, the structure is divided into substructures thus the number of unknowns that need to be worked out is reduced due to the transformation process. The static analysis of the structures can be performed easily and speedily by the proposed method. At the end of the study examples are presented for ensuring the agreement between the proposed method and classic Finite Element Method.

Perturbation Finite Element Transfer Matrix Method for Random Eigenvalue Problems of Uncertain Structures

The rapid computation of random eigenvalue problems of uncertain structures is the key point in structural dynamics, and it is prerequisite to the efficient dynamic analysis and optimal design of structures. In this paper, by combining finite element-transfer matrix method (FE-TMM) with perturbation method, a new method named as perturbation FE-TMM is presented for random eigenvalue problems of uncertain structures. By using the proposed method, the rapid computation of random eigenvalue problems of uncertain structures with complicated shapes and boundaries can be achieved, and the repeated eignvalues and characteristic vectors can be solved conveniently. Compared with stochastic finite element method, this method has the low memory requirement, high computational efficiency and high computational stability. It has more advantages for dynamic design of uncertain structures. Formulations as well as some numerical examples are given to validate the method.

Dynamic modeling and H ∞ independent modal space vibration control of laminate plates

In this paper, combining the transfer matrix method and the finite element method, the modified finite element transfer matrix method is presented for high efficient dynamic modeling of laminated plates. Then, by constructing the modal filter and the disturbance force observer, and using the feedback and feedforward approaches, the H ∞ independent modal space control strategy is designed for active vibration control of laminate plates subjected to arbitrary, immeasurable disturbance forces. Compared with ordinary dynamic modeling and control methods of laminated plate structures, the proposed method has the low memory requirement, high computational efficiency and robust control performance. Formulations as well as some numerical examples are given to validate the method and the control performance.

Modified Finite Element Transfer Matrix Method for Eigenvalue Problem of Flexible Structures

The speedy computation of eigenvalue problems is the key point in structure dynamics. In this paper, by combining transfer matrix method and finite element method, the modified finite element-transfer matrix method and its algorithm for eigenvalue problems are presented. By using this method, the speedy computation of eigenvalue problem of flexible structures can be realized, and the repeated eignvalue problem can be solved simply and conveniently. This method has the low order of system matrix, high computational efficiency, and stability. Formulations of this method, as well as some numerical examples, are given to validate the method.

Development of high speed computation algorithm for transient analysis of rectangular plates

A new transient analysis method for a rectangular plate structure comprised of a large number of plate elements was developed in order to significantly reduce computational time and memory. This algorithm was derived from the combination of the transfer technique of the transfer mass coefficient method, the modeling technique of the finite element method, and the numerical integration technique of Newmark’s method. In this paper, the algorithm for the transient analysis of a rectangular plate structure is formulated by the proposed method. In order to verify the computational accuracy and efficiency of the proposed method, the results obtained by the proposed method were compared with those obtained by the finite element method and the finite element-transfer matrix method. The proposed method, the finite element-transfer mass coefficient method, could considerably reduce the computation time without the loss of accuracy, in spite of using small computation memory, by using the transfer rules successively.

A stiffness equation transfer method for transient dynamic response analysis of structures

A stiffness equation transfer method is proposed for transient dynamic response analysis of structures under various excitations. This method is a development and refinement of the combined finite element-transfer matrix (FE-TM) method. In the present method, the transfer of state vectors from left to right in the FE-TM method is changed into the transfer of general stiffness equations of every section from left to right. This method has the advantages of reducing the order of the ordinary transfer equation systems and minimizing the propagation of round-off errors occurring in recursive multiplication of transfer and point matrices. Furthermore, the drawback that the number of degrees of freedom on the left boundary must be the same as that on the right boundary in the ordinary FE-TM method, has now been avoided. The Newmark generalized acceleration formulation for time discretization is employed for a solution of the time problem. At the end, numerical examples are presented to demonstrate the accuracy as well as the potential of the proposed method for transient dynamic response analysis of structures.

A stiffness equation transfer method for natural frequencies of structures

A stiffness equation transfer method is proposed for obtaining vibration frequencies of structures. This method is an extension of the finite element-transfer matrix (FE-TM) method. In the present method, the transfer of state vectors from left to right in the ordinary FE-TM method is changed into the transfer of stiffness equations of every section from left to right. This method reduces the propagation of round-off errors produced in the ordinary transfer matrix method. Furthermore, the drawback that the number of degrees of freedom on the left boundary must be the same as that on the right boundary in the ordinary FE-TM method, is now avoided. Besides, this method finds out the values of the frequency by Newton–Raphson iteration method, so no plotting of the value of the determinant versus assumed frequency is necessary. An IFETM—W program based on this method for use on an IBM PC586 microcomputer is developed. Finally, numerical examples are presented to demonstrate the accuracy as well as the potential of the proposed method for free vibration analysis of structures.

A combined finite element–stiffness equation transfer method for steady state vibration response analysis of structures

An extended finite element transfer matrix method, in combination with stiffness equation transfer, is applied to dynamic response analysis of the structures under periodic excitations. In the present method, the transfer of state vectors from left to right in a combined finite element-transfer matrix (FE-TM) method is changed into the transfer of general stiffness equations of every section from left to right. This method has the advantages of reducing the order of standard transfer equation systems, and minimizing the propagation of round-off errors occurring in recursive multiplication of transfer and point matrices. Furthermore, the drawback that in the ordinary FE-TM method, the number of degrees of freedom on the left boundary be the same on the right boundary, is now avoided. A FESET program based on this method using microcomputers is developed. Finally, numerical examples are presented to demonstrate the accuracy as well as the potential of the proposed method for steady state vibration response analysis of structures.

Large deflection analysis of structures by an improved combined finite element-transfer matrix method

An improved combined finite element-transfer matrix (IFE-TM) method is applied to the static analysis of structures with large displacement. In the present method, the transference of the state vectors from the left to the right in the combined finite element-transfer matrix method is changed into the transference of incremental stiffness equations of every section from the left to the right, in order to overcome the fault that the FE-TM method is generally applied to structures with a regular boundary. Furthermore, in the present method, the propagation of round-off errors occurring in recursive multiplications of the transfer and point matrices is avoided. A load incremental method is combined with modified Newton-Raphson method for the non-linear equations. A program ITNONDL-J based on this method is developed on the microcomputer IBM-PC/AT. Finally, numerical examples are presented to demonstrate the accuracy as well as the capability of the proposed method for geometrically non-linear static analysis of structures with a random boundary.

Geometrically non-linear dynamic analysis of plates by an improved finite element-transfer matrix method on a microcomputer

An improved finite element-transfer matrix method is applied to the transient analysis of plates with large displacement under various excitations. In the present method, the transfer of state vectors from left to right in a combined finite element-transfer matrix method is changed into the transfer of generally incremental stiffness equations of every section from left to right. Furthermore, in this method, the propagation of round-off errors occurring in recursive multiplications of transfer and point matrices is avoided. The Newmark-<TEX>${\beta}$</TEX> method is employed for time integration and the modified Newton-Raphson method for equilibrium iteration in each time step. An ITNONDL-W program based on this method using the IBM-PC/AT microcomputer is developed. Finally numerical examples are presented to demonstrate the accuracy as well as the potential of the proposed method for dynamic large deflection analysis of plates with random boundaries under various excitations.

A Finite Element-Transfer Matrix Method For Dynamic Analysis Of Frame Structures

A combined finite element-transfer matrix method is applied to transient dynamic analysis of plane and space frame structures under harmonic and impulsive excitations. The transfer matrix relating the state vectors on the lower and upper boundaries of a substructure at a certain time is derived from the system of equations of motion for a substructure. Some numerical examples of plane and space frame structures subjected to ground accelerations are proposed, and their results and computation times are compared with those obtained by the finite element method to demonstrate the accuracy and efficiency of this method.

A modified finite element-transfer matrix for control design of space structures

The Finite Element-Transfer Matrix (FETM) method was developed for reducing the computational efforts involved in structural analysis. While being widely used by structural analysts, this method does, however, have certain limitations, particularly when used for the control design of large flexible structures. In this paper, a new formulation based on the FETM method is presented. The new method effectively overcomes the limitations in the original FETM method, and also allows an easy construction of reduced models that are tailored for the control design. Other advantages of this new method include the ability to extract open loop frequencies and mode shapes with less computation, and simplification of the design procedures for output feedback, constrained compensation, and decentralized control. The development of this new method and the procedures for generating reduced models using this method are described in detail and the role of the reduced models in control design is discussed through an illustrative example.

Control of Flexible Structures by Finite Element-Transfer Matrix Approach

For a flexible structure to meet its mission objectives successfully, a close interaction between structural analysis and control group is needed at both the modelling and control design phases. For such an interaction to be beneficial, an integration of suitable methods from both the groups is essential. The finite element-transfer matrix (FETM) approach and the method of decentralized control using optimal control theory are ideally suited for this integration: the FETM method has been developed by structural analysts to overcome the ‘dimension-problem’, which problem is also encountered by control engineers; the decentralized control strategy is being adopted by control engineers to control large flexible structures. This paper presents the development of this method and demonstrates its applicability to the control of distributed parameter systems. Specifically, as an illustration, the control of a simply-supported beam is investigated