Showing papers on "Direct stiffness method published in 1970"
TL;DR: Structure of flexural members, analyzing torsional and lateral stability by finite element method and matrix formulation is presented in this article, where the authors propose a finite element-based matrix formulation.
Abstract: Structure of flexural members, analyzing torsional and lateral stability by finite element method and matrix formulation
302 citations
TL;DR: In this article, a general procedure for evaluating the stiffness matrix of a cracked element is developed, and numerical results obtained by the simplest elements are compared with those provided by other methods.
Abstract: The calculation of stress intensity factors for complicated crack configurations in finite plates usually presents substantial difficulty. A version of the finite element method solves such problems approximately by means of special cracked elements. A general procedure for evaluating the stiffness matrix of a cracked element is developed, and numerical results obtained by the simplest elements are compared with those provided by other methods.
126 citations
TL;DR: In this article, a computer-oriented method is described for the analysis of frames with partially rigid beam-to-column connections, where the moment-rotation relationship for the partially rigid connections is approximated by a bilinear model.
Abstract: A computer oriented method is described for the analysis of frames with partially rigid beam-to-column connections. The moment-rotation relationship for the partially rigid connections is approximated by a bilinear model. Slopes of these models are graphically determined and used to define connection rigidities. Element stiffness matrices are derived which include the effect of these partial rigidities. The modified element stiffness matrices are then used in a direct stiffness method of solution. Analysis for stability of frames with partial connection rigidity is carried out using the classical method of determining bifurcation states. The modified element stiffness matrices incorporating the effects of partial connection rigidities are directly used in the analysis. Problems ranging from rigid frames to pin connected frames can be solved by the same appproach and examples are presented to show the results.
67 citations
TL;DR: In this article, the stiffness matrix is obtained on the basis of stress assumption, rather than the more usual displacement assumption, and an erroneous addition of the shear-deflection terms to the bending terms can be made if an apparently straightforward approach is utilized.
Abstract: Shear-deflection terms arise naturally in a finite beam element in bending if the stiffness matrix is obtained on the basis of stress assumption, rather than the more usual displacement assumption.If the displacement assumption is used, an erroneous addition of the shear-deflection terms to the bending terms can be made if an apparently straightforward approach is utilized.
47 citations
TL;DR: In this paper, the ground surrounding a deformation zone is replaced mathematically by an idealized material that deforms in accordance with principles of continuum mechanics, and a discrete-element formulation of matrix structural analysis is shown to be adaptable to solutions of nonlinear anisotropic materials, heterogeneously distributed, containing internal discontinuities, and of arbitrary topographic or internal boundary configuration.
Abstract: In the continuum approach to problems of geologic mechanics, the ground surrounding a deformation zone is replaced mathematically by an idealized material that deforms in accordance with principles of continuum mechanics. Studies published to date have been rather few in number and have often followed a methodology characterized by restrictive material property and boundary condition assumptions. In order to avoid these difficulties, emphasis in this paper is given to modern numerical methods. Discrete-element formulations of matrix structural analysis are shown to be particularly useful, inasmuch as they are adaptable to solutions of systems characterized by nonlinear anisotropic materials, heterogeneously distributed, containing internal discontinuities, and of arbitrary topographic or internal boundary configuration.
11 citations
01 Sep 1970
TL;DR: In this paper, the authors presented a theoretical method for the analysis of the behavior of the track structure under static load from which an evaluation of track modulus can be made, using a finite element model.
Abstract: This report presents a theoretical method for the analysis of the behavior of the track structure under static load from which an evaluation of the track modulus can be made. The method simulates the track structure as a finite element model. The behavior of cohesionless soil materials under tensile and shear loading is included in the simulation. A computer solution of the model system by the methods of matrix structural analysis is given. Wheel loads, material constants and boundary conditions are applied to the model and a solution for deflections, stresses and track modulus is obtained. The method is illustrated by an example problem and the results of several determinations of track behavior under load are presented.
11 citations
01 Sep 1970
TL;DR: In this article, the authors present an analysis of CELLULAR STRUCTURES of constant deperturbation with an ARBITRARY GEOMETRY in plan view, where the structure may be subject to a VARIETY of FORCE and DISPLACEMENT Boundedary CONDITIONS, SUCH as DISTRIBUTED DEAD and LIVE-LOADS in addition to CONCENTRATED NODAL LOADS and PRESCRIBED NODal DISplACEMENTS.
Abstract: A COMPUTER PROGRAM IS PRESENTED FOR THE ANALYSIS OF CELLULAR STRUCTURES OF CONSTANT DEPTH WITH ARBITRARY GEOMETRY IN PLAN VIEW. THE DEVELOPMENT IS BASED ON THE FINITE ELEMENT METHOD AND USES TWO DIFFERENT ELEMENT TYPES DESIGNED TO CAPTURE THE MAIN BEHAVIOR OF DECK AND WEB COMPONENTS. THE STRUCTURE MAY BE SUBJECTED TO A VARIETY OF FORCE AND DISPLACEMENT BOUNDARY CONDITIONS, SUCH AS DISTRIBUTED DEAD AND LIVE-LOADS IN ADDITION TO CONCENTRATED NODAL LOADS AND PRESCRIBED NODAL DISPLACEMENTS. THE WELL ESTABLISHED DIRECT STIFFNESS METHOD IS USED FOR THE ELEMENT ASSEMBLY. AFTER SOLVING FOR THE UNKNOWN NODAL DISPLACEMENTS AND REACTIONS, INTERNAL FORCES ARE COMPUTED AT THE CENTER AND AT NODES OF DECK AND WEB ELEMENTS SELECTED BY THE USER. /AUTHOR/
10 citations
TL;DR: In this paper, a stiffness matrix for a non-shallow cylindrical element is developed and a finite-element procedure using this matrix is used to obtain a solution for a barrel vault.
8 citations
01 Feb 1970
TL;DR: In this article, a general computer program was developed which is capable of analyzing any PRISMATIC CELLULAR or OPEN FOLDED PLATE STRUCTURE with TRANSVERSE DIAPHRAGMS and PLANAR FRAMES at any section as well as longitudial beams.
Abstract: A GENERAL COMPUTER PROGRAM WAS DEVELOPED WHICH IS CAPABLE OF ANALYZING ANY PRISMATIC CELLULAR OR OPEN FOLDED PLATE STRUCTURE WITH TRANSVERSE DIAPHRAGMS AND PLANAR FRAMES AT ANY SECTION AS WELL AS LONGITUDINAL BEAMS. THE STRUCTURE MAY BE SUBJECTED TO SURFACE LOADS, LINE LOADS, CONCENTRATED LOADS AS WELL AS KNOWN DISPLACEMENTS. THE SOLUTION IS BASED ON THE FINITE ELEMENT METHOD IN CONJUNCTION WITH THE DIRECT STIFFNESS METHOD. ALL FINAL MODAL DISPLACEMENTS, REACTIONS, AND INTERNAL FORCES AND MOMENTS IN FRAME ELEMENTS AND WITHIN FINITE ELEMENTS ARE PRINTED OUT AT POINTS SELECTED BY THE USER. /AUTHOR/
7 citations
01 Jan 1970
TL;DR: In this article, the authors present a divergence of the Flexibility and Stiffness MatriX of large RECTANGULAR or right-angle TRIANGULAR PLATE ELEMENTS for in-plane deGREES OF FREEDOM.
Abstract: A DERIVATION OF THE FLEXIBILITY AND THE STIFFNESS MATRIX OF LARGE RECTANGULAR OR RIGHT-ANGLE TRIANGULAR PLATE ELEMENTS FOR IN-PLANE DEGREES OF FREEDOM IS PRESENTED. THE FLEXIBILITY MATRIX IS CALCULATED USING FINITE DIFFERENCES. THIS MATRIX IS THEN USED TO DERIVE THE ELEMENT STIFFNESS MATRIX. THE CALCULATIONS INVOLVE SIMPLE MATRIX OPERATIONS AND CAN BE EASILY PROGRAMMED. THE STIFFNESS MATRICES DERIVED BY THIS METHOD ARE INTENDED TO BE USED IN THE ANALYSIS OF STRUCTURES WHICH CAN BE IDEALIZED AS AN ASSEMBLAGE OF LARGE RECTANGULAR OR TRIANGULAR PLATE ELEMENTS, E.G. BOX-GIRDER SKEW BRIDGES. /AUTHOR/
3 citations
01 Jan 1970
TL;DR: In this article, the authors analyze the structure of large RECTANGULAR and TRIANGULAR PLATE ELEMENTS, E. G. Box-Girder SKEW BRIDges.
Abstract: PLATES IN BENDING ARE ANALYZED BY IDEALISING THE CONTINUUM AS AN ASSEMBLAGE OF LARGE RECTANGUALR AND TRIANGULAR ELEMNTS. THE FLEXIBILITY AND STIFFNESS MATRICES OF THESE ELEMENTS CORRESPONDING TO BOUNDARY DISPLACEMENTS ARE DERIVED USING FINITE DIFFERENCES. THE ANALYSIS INVOLVES SIMPLE MATRIX OPERATIONS WHICH CAN BE EASILY COMPUTER PROGRAMMED. THE STIFFNESS MATRICES DERIVED BY THIS METHOD ARE INTENDED FOR USE IN THE ANALYSIS OF STRUCTURES WHICH CAN BE IDEALISED AS AN ASSEMBLAGE OF LARGE RECTANGULAR AND TRIANGULAR PLATE ELEMENTS, E. G. BOX-GIRDER SKEW BRIDGES. /AUTHOR/
01 Feb 1970
TL;DR: In this article, a method is presented for the analysis of Orthotropic Folded Plate StrUCTures with ECCENTRIC Stiffeners, which is based on the discovery of a finite STRIP STIFFness.
Abstract: A METHOD IS PRESENTED FOR THE ANALYSIS OF ORTHOTROPIC FOLDED PLATE STRUCTURES WITH ECCENTRIC STIFFENERS. THE DEVELOPMENT IS BASED ON THE DERIVATION OF A FINITE STRIP STIFFNESS WHICH COUPLES THE PLATE BENDING AND THE IN PLANE ACTION DUE TO THE ECCENTRICITY OF THE RIBS. HARMONIC ANALYSIS IS UTILIZED IN CONJUNCTION WITH THE DIRECT STIFFNESS METHOD PROVIDING A VERY EFFICIENT COMPUTER PROGRAM WHICH CAN HANDLE A VARIETY OF DIFFERENT LOADINGS. AT PRESENT THE PROGRAM IS RESTRICTED TO THE ANALYSIS OF PRISMATIC FOLDED PLATE STRUCTURES WHICH ARE SIMPLY SUPPORTED AT THE TWO END DIAPHRAGMS. /AUTHOR/
15 Oct 1970
TL;DR: Finite element program for determining stiffness and mass matrices of shells of revolution - users manual as discussed by the authors, which can be used to calculate the mass matrix of a shell of revolution.
Abstract: Finite element program for determining stiffness and mass matrices of shells of revolution - users manual
01 Jan 1970
Journal Article•
TL;DR: In this paper, the authors present a computer program designated ZUMIT for the analysis of both two-and three-dimensional framed structures with use of the stiffness method, which is particularly useful for analyzing ship hull structures.
Abstract: Development of computer program designated ZUMIT for the analysis of both two- and three-dimensional framed structures with use of the stiffness method. The present paper outlines the ZUMIT program with an example of its application. The program permits analysis of elastic statically loaded frames, including cases where the influence of shear rigidity has to be considered, and where beams terminating in large brackets are involved, which should be particularly useful for analyzing ship hull structures.