Combined Finite Element-transfer Matrix Research Articles

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 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.

Transient analysis of plates by a combined finite element-transfer matrix method

The combined use of the finite element and transfer matrix is applied to the transient analyses of the structures under various excitations. An approximation is also introduced in the equations of motion for the case of in-plane excitations in order to reduce computational efforts. Furthermore, the technique of exchanging the state vectors is, in this paper, proposed to avoid the propagation of round off errors occurred in recursive multiplications of the transfer and point matrices, and the Newmark β method is employed for time integrations. Some numerical examples are presented to demonstrate the accuracy as well as the capability of the proposed method for transient analyses of the plates under out-of-plane and in-plane excitations.

ANALYSIS OF THIN-WALLED MEMBERS BY FINITE ELEMENT-TRANSFER MATRIX METHOD

The combined finite element-transfer matrix method is applied to the linear and nonlinear problems of thin-walled members. The transfer matrix is derived from the tangent stiffness matrix used in the FEM. To deal with complex structures the transfer matrix for the substructure, into which thin-walled members is devided, is introduced. In this method, procedures used in the FEM based on load increment are employed except for the estimation of approximate displacements for each specified increment load. Approximate displacement are estimated by the transfer matrix procedure. Some numerical examples presented in this paper show that for long thin-walled members, this method can be successfully applied to the linear and nonlinear problems by reducing the size of the matrix relative to less than that obtained by the FEM.

Structural analysis by a combined finite element-transfer matrix method

The combined finite element-transfer matrix method has the advantage of reducing the size of a matrix to less than that obtained by the ordinary finite element method. The analytical procedure in this method for bending and buckling problems are described, and techniques for treating the structure with intermediate conditions are proposed. Various numerical examples of these problems are shown to demonstrate the efficiency and accuracy of this method. The results from these examples agree well with those obtained by the finite element method and others.

An Exact Condensation Procedure for Chain-Like Structures Using a Finite Element-Transfer Matrix Approach

The main objective of this study is to describe a new scheme to carry out the static or dynamic analysis of elastic systems using a combined Finite Element-Transfer Matrix Approach. The proposed scheme offers the advantage of automatic matrix size reduction without having to truncate degrees of freedom, and preserving the strain and kinetic energy throughout the condensation. Although limited to chain-like elastic systems, the method is generalized to non-repetitive configurations with substructures having intermediate active degrees of freedom.

Analysis of static and dynamic structural problems by a combined finite element-transfer matrix method

The combined use of the finite element and transfer matrix techniques (FETM) for the study of dynamic problems was proposed a few years ago, in order to overcome the large amount of computer storage and long computation time that the finite element technique often requires. In this paper some interesting applications are emphasized for both static and dynamic problems of structures. A great deal of attention has been paid to the use of shell isoparametric elements for very thin structures, where the usual numerical integration by a two-by-two Gaussian quadrature of the stiffness matrix leads to an ineffective increase of stiffness in the structure. Particularly appealing seems to be the use of quadratic shell elements in the FETM method, because even with a reduction in the total number of elements of the structure it is possible to increase the accuracy of results. Computation time is appreciably reduced by this method, because of the notable lowering of the final matrix order, the manipulation of which gives the solution of the problem. Some results for natural frequencies of a thin plate are finally presented, showing a favourable agreement with those obtained by other proposed methods.

A combined finite element-transfer matrix structural analysis method

A combined finite element-transfer matrix (FETM) method is developed to study the dynamics of orthogonally stiffened structures. Finite element procedures are used in FETM to formulate transfer matrices for structural components which are not one-dimensional. The resulting transfer matrices are used to reduce the large number of unknowns occurring in a standard finite element analysis by obtaining transfer matrix relationships over large units of the structure. A reduction in computer storage and computation time is obtained since the dimension of the final matrix equation to be solved is considerably reduced. The accuracy of the FETM results are verified by comparison with an exact solution to the limiting modes and frequencies of a periodically stiffened structure of infinite length. A reduction of computer time was demonstrated for the FETM by a comparison with the SAP-4 finite element program. The efficiency of the FETM method was further demonstrated by computing the frequency response of a two row-five span orthogonally stiffened plate structure using ordinary transfer matrix procedures.