Showing papers on "Direct stiffness method published in 1988"
Book•
01 Feb 1988
TL;DR: This chapter discusses the design Loads, Statics of Structures-Reactions, and Matrix Analysis of Trusses by the Direct Stiffness Method, which guided the development of the TSP.
Abstract: Chapter 1 Introduction Chapter 2 Design Loads Chapter 3 Statics of Structures-Reactions Chapter 4 Trusses Chapter 5 Beams and Frames Chapter 6 Cables Chapter 7 Arches Chapter 8 Live Load Forces: Influence Lines for Determinate Structures Chapter 9 Deflections of Beams and Frames Chapter 10 Work-Energy Methods for Computing Deflections Chapter 11 Analysis of Indeterminate Structures by the Flexibility Method Chapter 12 Analysis of Indeterminate Beams and Frames by the Slope-Deflection Method Chapter 13 Moment Distribution Chapter 14 Indeterminate Structures: Influence Lines Chapter 15 Approximate Analysis of Indeterminate Structures Chapter 16 Introduction to the General Stiffness Method Chapter 17 Matrix Analysis of Trusses by the Direct Stiffness Method Chapter 18 Matrix Analysis of Beams and Frames by the Direct Stiffness Method
45 citations
01 Apr 1988
TL;DR: In this paper, a finite element computer program is developed, incorporating this concept, for the crash simulation of general 3-dimensional structures, using step-by-step solution procedures for the inelastic analysis and the constant-energy incremental loading method for loading increments.
Abstract: The structural analysis for crashworthiness, presented in this paper, consists of three parts: thin-walled element modeling, stiffness formulation and numerical solution. In thin-walled elements the stresses rarely reach the yield level and the element's force- deformation relationship is usually controlled by local buckling and subsequent collapse of the section. This relationship can be generally divided into four regimes: linear, post-buckling, crippling and deep collapse. In the post-buckling regime only a part of the section contributes to its load carrying capacity and it is this effective part that is being used to calculate the section properties. In the deep collapse regime the stiffness is calculated by considering an appropriate mechanism of section collapse. The element stiffness is then assembled into the structural stiffness matrix. A finite element computer program is developed, incorporating this concept, for the crash simulation of general 3-dimensional structures. The program uses step-by-step solution procedures for the inelastic analysis and the constant-energy incremental loading method for loading increments. The analytical results show a promising agreement with the test data. (A) For the covering abstract see IRRD 863693.
16 citations
TL;DR: In this article, minimum-weight designs of statically indeterminate beams subject to strength and stiffness constraints are presented under a given load system consisting of external loads and self-weight, the normal and shear stresses and maximum deflection in the beams are restricted from above.
12 citations
TL;DR: In this paper, the general shape functions and stiffness matrix of a Timoshenko beam are derived and used to establish the stiffness equations for an entire structural system, which can then be easily modified to account for the influences from the concentrated dynamic properties.
Abstract: The general dynamic shape functions and stiffness matrix of a Timoshenko beam are derived and used to establish the stiffness equations for an entire structural system. All the effects of rotary inertia of the mass, shear distortion, mass and structural dampings, axial force, elastic-spring and dashpot foundation are included in this formulation. These stiffness equations can then be easily modified to account for the influences from the concentrated dynamic properties. Both the low-and high-frequency dynamic responses are discussed generally, with special emphasis on the latter case. The problem of structure-borne noise on ships is also studied as an example for application.
11 citations
TL;DR: In this article, a simple technique for finite element mesh refinement is presented based on maximizing strain energy in the elements and the implementation of the technique in a general purpose program is facilitated by the fact that all calculations can be made at the element level.
11 citations
TL;DR: In this article, the finite strip method is employed to model the girder of a cable-stayed bridge, where the entire girder is treated as a substructure with only a few degrees of freedom, corresponding to the points of cable attachments.
10 citations
Book•
24 Nov 1988
TL;DR: In this article, the authors describe a number of methods of structural analysis application of computer programs to structural analysis, including stiffness, matrix stiffness, moment distribution, and virtual work flexibility.
Abstract: Equilibrium analysis and determinacy of structures basic concepts of stiffness method matrix stiffness method moment distribution method principle of virtual work flexibility method approximate methods of structural analysis application of computer programs to structural analysis.
9 citations
TL;DR: In this article, the results of a numerical/experimental study on the dynamic characteristics (natural frequencies and corresponding mode shapes) of a milling machine structure are reported. But, due to forced vibrations, dynamic deformations take place in the machine-tools which contribute to the inaccuracies in the item machined.
5 citations
01 Jan 1988
TL;DR: In this article, an efficient algorithm for computing the response sensitivity of finite element problems based on a mixed-iterative formulation is proposed, which can be used with formulations for which a consistent tangent stiffness is not readily available.
Abstract: An efficient algorithm for computing the response sensitivity of finite element problems based on a mixed-iterative formulation is proposed. This method does not involve explicit differentiation of the tangent stiffness array and can be used with formulations for which a consistent tangent stiffness is not readily available. The method has been successfully applied to probabilistic finite element analysis of problems using the proposed mixed formulation, and this exercise has provided valuable insights regarding the extension of the method to a more general class of problems to include material and geometric nonlinearities.
5 citations
TL;DR: In this paper, minimum-weight designs of statically indeterminate beams under multiple load systems are presented and the solutions of the resulting nonlinear programming problems are attempted by several methods.
5 citations
TL;DR: In this paper, the body of the vehicle is considered as distributed parameter system wich can be described by partial differential equations and the parameters represent mass, stiffness, and damping distributions.
Abstract: SUMMARY The paper deals with some important problems of determination of mass, damping and stiffness matrices using identification of linear vehicle dynamic models. The body of the vehicle is considered as distributed parameter system wich can be described by partial differential equations and the parameters represent mass, stiffness and damping distributions. Using finite elements method the body dynamics can be modelled as concentrated parameter system given by second order vector differential equations. For this case the directly identified parameters of discrete models are sophisticated functions of physical parameters of continuous models. Therefore, it is very important to choose the suitable discrete model class for an effective and reliable solution of the above problem. In the paper special time-domain maximum likelihood method is applied to estimate the coefficients in the transfer matrix of the body and to ensure a direct relationship between the transfer matrix, the modal and physical paramete...
TL;DR: In this paper, a simplified method for determining the J-integral for elastic-plastic conditions using the stiffness gradient method is described, which is based on external displacement and forces, and not directly dependent on the stresses.
Abstract: A simplified method for determining the J-integral for elastic-plastic conditions using the stiffness gradient method is described. Power law hardening material is shown to simplify the J-integral estimation, rendering elastic and fully plastic J solution terms. Numerical results are obtained for an interior complete circumferential crack in a pipe and compared to the analogous EPRI handbook solution. Because the stiffness gradient method is based on external displacement and forces, and not directly dependent on the stresses, it is sufficient to use relatively coarse finite element meshes to determine the J-integral instead of highly refined and costly meshes required in most conventional J-integral computations.
TL;DR: In this paper, a higher order finite strip method for improved accuracy and its application to orthotropic curved bridge decks is discussed, where a quintic polynomial in the radial direction is employed along with a basic function series in the angular direction which satisfy a priori the boundary conditions along the radial edges.
TL;DR: In this article, a new simplified finite element method for the elastic-plastic analysis of plate bending is developed from the general simplified method which the authors have proposed, where plastic nodal displacement increments of an element are derived from the yield condition as plastic potential expressed in terms of the nodal forces based on the flow rule of plasticity.
01 Jan 1988
TL;DR: In this article, two approaches to the analysis of the rock burst phenomena are presented: the first is aimed at determining the limit equilibrium point beyond which the uncontrollable deformation process begins, and the second is more economical as it provides information on the whole dynamic failure process.
Abstract: Two approaches to the analysis of the rock burst phenomena are presented. The first is aimed at determining the limit equilibrium point beyond which the uncontrollable deformation process begins. Finite element discretization is used for incremental elasto plastic analysis with increasing excavation size. By determining the global stiffness matrix (k) for each nodal displacement and force increment, and plotting this against the size parameter, the critical parameter value for which det(k)=0, can be obtained. A less tedious method in which a regular progression condition is assumed is also described. Pillar and seam stability can be studied using this method. Roof strata are simulated as shear beam and the pillar is treated as an elasto plastic softening layer. The second dynamic approach is more economical as it provides information on the whole dynamic failure process. Equations of motion are considered which define force in terms of the stiffness, damping and mass matrices. The static solution is first obtained incrementally for increasing size of excavation. At some stage a small dynamic disturbance is introduced into the system by specifying either initial velocity field of presented total kinetic energy or by initiating a dynamic process by sudden removal of portions of rock. The subsequent dynamic solution will indicate whether growth of the kinetic energy occurs within the system and if so, the associated failure mode can be investigated. (TRRL)
01 Jan 1988
TL;DR: The general basis of the matrix stiffness method was well understood prior to the development of the digital computer, so that analysts were left with having to find the solution to a large number of simultaneous equations by hand calculation, or to avoid them.
Abstract: It is a characteristic of the structural analysis problem that most formulations lead to the need to solve a set of simultaneous equations. Without using a computer or programmable calculator, solving four or more equations is a tedious, if not daunting, task that most people would prefer to avoid. The general basis of the matrix stiffness method as presented in earlier chapters was well understood prior to the development of the digital computer, so that analysts were left with having to find the solution to a large number of simultaneous equations by hand calculation, or to avoid them.
01 May 1988
TL;DR: In this article, a simple two node, linear, finite strip plate bending element based on Mindlin-Reissner plate theory for the analysis of very thin to thick bridges, plates, and axisymmetric shells is presented.
Abstract: A simple two node, linear, finite strip plate bending element based on Mindlin-Reissner plate theory for the analysis of very thin to thick bridges, plates, and axisymmetric shells is presented. The new transverse shear strains are assumed for constant distribution in the two node linear strip. The important aspect is the choice of the points that relate the nodal displacements and rotations through the locking transverse shear strains. The element stiffness matrix is explicitly formulated for efficient computation and ease in computer implementation. Numerical results showing the efficiency and predictive capability of the element for analyzing plates with different supports, loading conditions, and a wide range of thicknesses are given. The results show no sign of the shear locking phenomenon.
01 Jan 1988
TL;DR: In this paper, a general technique applicable to all classes of structure is presented, which uses coordinate transformation and it is first necessary to discuss the axes of reference used to define the structure and its actions.
Abstract: In a final presentation of the matrix stiffness method of structural analysis, a general technique applicable to all classes of structure is outlined. The technique uses coordinate transformation and it is first necessary to discuss the axes of reference used to define the structure and its actions.
TL;DR: In this paper, a study of the effects of the angle condition on the spectral properties of the stiffness matrix has been performed for two plate bending elements: the constant moment triangle (CMT) and the discrete Kirchhoff triangle (DKT).
Abstract: In triangulating a domain to find a finite element approximation for the solution of a specific problem, the so-called angle condition is essential. In this paper, a study of the effects of this condition on the spectral properties of the stiffness matrix has been performed for two plate bending elements: the constant moment triangle (CMT) and the discrete Kirchhoff triangle (DKT). This has been done on the element level and also for the global system. It is shown that as the smallest, rather than the largest, angle of the elements considered herein decreases, the condition number of the global stiffness matrix increases.
01 Jan 1988
TL;DR: In this article, the authors used the direct stiffness method to derive the dynamic stiffness matrix for finding the natural frequencies and joint moments of horizontally circular curved beams having different rectangular cross-sections, and showed the effects of rotatory inertias, shear deformation, warping and opening angle of the arc on the beam.
Abstract: This thesis is devoted to the dynamic analysis of horizontally circular curved beams. The direct stiffness method is used to derive the dynamic stiffness matrix for finding the natural frequencies and joint moments of curved beams having different rectangular cross-sections. Four examples are presented to illustrate the application of the proposed method and to show the effects of rotatory inertias, shear deformation, warping and opening angle of the arc on the beam. First three examples are for the free vibration of the beam. In these examples, beams with different thickness are used for finding effects of warping. In each example, there are three cases; case (a) consider rotatory inertias, shear deformation and warping effects; case (b) consider flexural rotatory inertia, shear deformation and warping effects; and case (c) consider rotatory inertias and shear deformation effects. Example four is for the forced vibration of the beam subjected to a uniformly distributed harmonic load. The results of the last example show the effects of cases (a), (b) and (c) on the joint moment of the beam.