Showing papers on "Direct stiffness method published in 1971"
TL;DR: Modified Newton-Raphson stiffness matrices and initial value formulations to geometrically nonlinear structural analysis for beam and plane stress triangular elements have been proposed in this article for the first time.
Abstract: Modified Newton-Raphson stiffness matrices and initial value formulations to geometrically nonlinear structural analysis for beam and plane stress triangular elements
39 citations
TL;DR: In this paper, the complete nonlinear equations of joint equilibrium are derived for three dimensional cable and truss structures using the direct stiffness approach for large joint displacements and small member deformations.
Abstract: The complete nonlinear equations of joint equilibrium are derived for three dimensional cable and truss structures using the direct stiffness approach for large joint displacements and small member deformations. The geometric stiffness matrix of the structure is derived solely from the geometrical and statical considerations of a perturbed equilibrium state. Various solution techniques are given for solving the nonlinear problem. Flow charts are given for modification of existing linear programs based on the direct stiffness approach. Several examples are given to illustrate the procedures and to emphasize the importance of nonlinear terms in the stiffness matrix.
37 citations
TL;DR: In this article, a linearized mid-increment stiffness matrix is used in the finite element incremental analysis of nonlinear structures to avoid transformations between local and global axes, and the computational similarity of the incremental and Newton-Raphson iterative processes is pointed out.
32 citations
TL;DR: In this paper, a finite strip method of analysis is presented which can be used to analyze curved folded plate structures simply supported at the two ends and composed of elements that may in general be segments of conical frustra.
Abstract: A finite strip method of analysis is presented which can be used to analyze curved folded plate structures simply supported at the two ends and composed of elements that may in general be segments of conical frustra. The method is based on a harmonic analysis in the circumferential direction, with the loadings expressed by Fourier series, and on a finite element stiffness analysis in the transverse direction. The direct stiffness method is used to assemble the structure stiffness matrix and to determine displacements and element stresses. A description of a general computer program developed for the analysis and the results of several examples are also given.
32 citations
TL;DR: In this paper, the effect of initial truncation in representing the global stiffness matrix on the global solution of a structural analysis has been investigated and an upper bound for this error can be found.
Abstract: Numerical error may destroy the significance of the results of a structural analysis, particularly for certain classes of structures. The initial truncation error originating from representing each value of the structural matrices to constant computer word length approximates the total numerical error in the solution for displacements in medium-sized problems. An upper bound for this error can be readily calculated, and is usually not too conservative when the global stiffness matrix is scaled before solution. When this error appears too large, only consistent higher precision representation and solution of the various structural matrices will ensure a more accurate solution. The varying accuracy of the displacements due to different loading conditions on the same structure is rigorously explained. The normal expression for the a posteriori error bound on the solution is unreliable as it omits the effect of initial truncation in representing the global stiffness matrix. Flexible areas within generally stiff structures and stiff areas within generally flexible structures can both lead to inaccurate solutions for displacements throughout the structure.
27 citations
01 Apr 1971
TL;DR: In this paper, numerical solution procedures evaluation for geometrically nonlinear structural analysis by direct stiffness method, noting capability of self correcting initial value formulation, were presented and evaluated.
Abstract: Numerical solution procedures evaluation for geometrically nonlinear structural analysis by direct stiffness method, noting capability of self correcting initial value formulation
23 citations
21 citations
TL;DR: The basic concepts required to construct a computer code capable of deriving element stiffness matrices are presented and examples are presented for a two-dimensional triangular plate element in which the displacements are represented in terms of area coordinates.
Abstract: This paper presents the basic concepts required to construct a computer code capable of deriving element stiffness matrices. The computer program requires only the displacement functions, transformation matrices, and a few control cards as input. The computer code assembles a complete element stiffness matrix for any type of configuration and displacement functions of any order. The matrix is stored in an alpha-numeric array. The final form is printed in terms of numerical coefficients and material and geometric properties of the element in symbol form. The output is received printed or punched on cards ready for incorporation into existing finite element computer codes. Examples are presented for a two-dimensional triangular plate element in which the displacements are represented in terms of area coordinates. However, the concept is not limited to local coordinate representations of displacement functions or to two-dimensional problems.
19 citations
TL;DR: In this article, a finite element displacement method is used to determine matrices representing the mass and stiffness of the foundation, and a new plate element is derived from the fully compatible element to overcome the difficulty in combining elements for plates and columns.
11 citations
TL;DR: In this paper, the form of the structural stiffness matrix that results from a coupled harmonic type of analysis is examined, and it is shown that such a matrix can be banded, thereby leading toward the practicality of the coupled harmonic finite-element analysis method for complex asymmetrically loaded solids of revolution.
Abstract: The purpose of this note is to examine the form of the structural stiffness matrix that results from a coupled harmonic type of analysis. It is to be shown that such a matrix can be banded, thereby leading toward the practicality of the coupled harmonic finite-element analysis method for complex asymmetrically loaded solids of revolution.
TL;DR: In this paper, a set of stiffness coefficients for isotropic sandwich plates are derived from Reissner's equations for isotropy and a stiffness matrix is derived for homogeneous folded plates.
Abstract: Reissner’s equations for isotropic sandwich plates are used to derive a set of stiffness coefficients which, in conjunction with a stiffness method, can be used to analyze folded plate structures made from sandwich panels. The derivation results in a stiffness matrix which can be used directly in the stiffness formulation outlined by Scordelis for homogeneous folded plates.