Showing papers on "Direct stiffness method published in 1976"

Fluid-Structure Finite Element Vibrational Analysis

Abstract: A liquid finite element formulation which includes the potential energy due to compression but neglects the density change has been developed. Both kinetic and potential energy are expressed as functions of nodal displacements. Thus, the formulation is similar to that used for structural elements, with the only differences being that 1) the fluid can possess gravitational potential, and 2) the constitutive equations for fluid contain no Shear coefficients. Using this approach, structural and fluid elements can be used interchangeably in existing efficient sparse matrix structural computer programs such as SPAR. The theoretical development of the element formulations and the relationships of the local and global coordinates are shown. Solutions of fluid slosh, liquid compressibility, and coupled fluid-shell oscillation problems which were completed using a temporary digital computer program are shown. The frequency correlation of the solutions with classical theory is excellent.

A new finite element scheme for instability analysis of thin shells

Abstract: This paper describes a new finite element scheme for the analysis of instability phenomena of arbitrary thin shells. A computationally efficient procedure is proposed for calculating the non-linear stiffness and tangential stiffness matrices for a doubly-curved quadrilateral element defined by co-ordinate lines. The essential feature is the explicit addition of the non-linear terms into the rigid-body motion of the element. Thus the non-linear and tangential element stiffness matrices can easily be generated by transforming the generalized element stiffness matrix for linear analysis, and the non-linear terms of these matrices are separated into a number of component terms multiplied by the rigid-body rotations. These component terms can be stored permanently and used to calculate efficiently the non-linear and tangential stiffness matrices at each iteration. Illustrative examples are presented which confirm the validity of the present approach in the analysis of instability phenomena of thin plates and shells.

Stiffness matrix for a non-prismatic beam-column element

Abstract: An algorithm is presented which generates an element stiffness matrix for non-prismatic beam-column members using Newmark's numerical procedure of successive approximations. The resulting element stiffness matrix on element co-ordinates is fond to be in excellent agreement with those available for limiting cases. An approximate stability analysis conducted on the covergence of the numerical scheme shows that the proposed algorithm is stable. The critical buckling loads for various and conditions are computed as part of the computational scheme. A computer program listing in FORTRAN IV is included which will handle essentially and order and/or kind of non-prismaticity of beam elements. The results are presented in the conventional and convenient coefficient format.

Convergence of an iterative procedure for large-scale static analysis of structural components

Abstract: The paper proves convergence of an iterative procedure for calculating the deflections of built-up component structures which can be represented as consisting of a dominant, relatively stiff primary structure and a less stiff secondary structure, which may be composed of one or more substructures that are not connected to one another but are all connected to the primary structure. The iteration consists in estimating the deformation of the primary structure in the absence of the secondary structure on the assumption that all mechanical loads are applied directly to the primary structure. The j-th iterate primary structure deflections at the interface are imposed on the secondary structure, and the boundary loads required to produce these deflections are computed. The cycle is completed by applying the interface reaction to the primary structure and computing its updated deflections. It is shown that the mathematical condition for convergence of this procedure is that the maximum eigenvalue of the equation relating primary-structure deflection to imposed secondary-structure deflection be less than unity, which is shown to correspond with the physical requirement that the secondary structure be more flexible at the interface boundary.

A comparison of the two NASTRAN differential stiffness techniques

Abstract: NASTRAN contains two techniques to solve the differential stiffness problems. One is incorporated in a new static analysis rigid format and the other is contained in a new normal modes analysis rigid format. The two techniques relative to computational accuracy and time of execution are compared.

Efficient reanalysis of structures by a direct modification method

Abstract: A procedure for the local stiffness modifications of large structures is described. It enables structural modifications without an a priori definition of the changes in the original structure and without loss of efficiency due to multiple loading conditions. The solution procedure, implemented in NASTRAN, involved the decomposed stiffness matrix and the displacement vectors of the original structure. It solves the modified structure exactly, irrespective of the magnitude of the stiffness changes. In order to investigate the efficiency of the present procedure and to test its applicability within a design environment, several real and large structures were solved. The results of the efficiency studies indicate that the break-even point of the procedure varies between 8% and 60% stiffness modifications, depending upon the structure's characteristics and the options employed.

Iterative Analysis Method for Structural Components with Diverse Stiffnesses

Abstract: An iterative solution scheme is presented for the static and dynamic analysis of built-up structures in which the stiffness of one relatively rigid component is a dominant factor in governing the overall response. In complex problems, where each structural component is represented by finite-elemen t models with many degrees of freedom, application of the standard direct-stiffness method requires equation solutions involving large numbers of unknowns. Also, the direct stiffness method may lead to numerical precision problems when combining the terms of components with diverse stiffnesses. This paper presents a technique which, under certain conditions to be discussed, overcomes these problems through an efficient iterative procedure. The method requires treatment of only a single structural component at any given time and the convergence rate is shown to depend upon the relative impedances of the components. Results are presented for the static, dynamic, and thermal stress analysis of the space-shuttle thermal-protection system. This problem is ideally suited to this application and results reveal a rapid rate of convergence.