Combined Finite Element-transfer Matrix Method Research Articles

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.

A Combined Finite Element—Transfer Matrix Method

The combined finite element‐transfer matrix method is applied to elastic‐plastic problems with large displacements. In the calculation program developed in this paper, the same procedures as those used in the finite element method based on load increment, are applied except for the estimation of approximate displacements for each specified incremental load. The Prandtl‐Reuss'law obeying the von Mises yield criterion is assumed, and a set of moving coordinate systems is used to take geometric nonlinearity into consideration. Various numerical examples of the geometric and material nonlinear problem are shown to demonstrate the accuracy of this method. These examples' results are in good agreement with those obtained by the finite element method and others.

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.

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.