Showing papers on "Direct stiffness method published in 1998"
TL;DR: In this article, a new element for geometrically nonlinear analysis of frame structures is presented, which is flexibility based and uses force interpolation functions for the bending moment variation that depend on the transverse displacements and strictly satisfy equilibrium in the deformed configuration.
Abstract: The paper presents a new element for geometrically nonlinear analysis of frame structures. The proposed formulation is flexibility based and uses force interpolation functions for the bending moment variation that depend on the transverse displacements and strictly satisfy equilibrium in the deformed configuration. The derivation of the governing equations and their consistent linearization are substantially more involved than for stiffness-based elements. Nonetheless, the element offers significant advantages over existing stiffness-based approaches, since no discretization error occurs and all governing equations are satisfied exactly. Consequently, fewer elements are needed to yield results of comparable accuracy. This is demonstrated with the analysis of several simple example structures by comparing the results from flexibility and stiffness-based elements.
197 citations
TL;DR: In this paper, an extension to the available direct methods of model updating to estimate both the damping and stiffness matrices of a structure is presented, with the constraint that the measured modal data is reproduced.
Abstract: This note has outlined an extension to the available direct methods of model updating to estimate both the damping and stiffness matrices of a structure. The method minimizes the change in the damping and stiffness matrices, with the constraint that the measured modal data is reproduced
156 citations
TL;DR: In this paper, the authors developed an exact dynamic stiffness matrix of a composite beam with the effects of axial force, shear deformation and rotatory inertia taken into account, for an axially loaded composite Timoshenko beam.
122 citations
TL;DR: In this article, the stiffness of a rail pad is measured as a function of the excitation frequency for known loading conditions, where the resilient element is placed between two large blocks, the vibrations of which are measured.
99 citations
TL;DR: In this paper, a perturbation of the healthy eigenvalue problem is performed to yield the relationship between the changes in eigenvalues and in the global stiffness matrix, where stiffness change is represented as a sum over every structural member by a product of a stiffness reduction factor and a stiffness submatrix.
Abstract: A method is presented to improve the robustness of current damage detection methodologies. Measured statistical changes in natural frequencies and mode shapes along with a correlated analytical stochastic finite element model are used to assess the integrity of a structure. The approach accounts for variations in the modal properties of a structure (due to experimental errors in the test procedure). A perturbation of the healthy eigenvalue problem is performed to yield the relationship between the changes in eigenvalues and in the global stiffness matrix. This stiffness change is represented as a sum over every structural member by a product of a stiffness reduction factor and a stiffness submatrix. The determination of damaged stiffness statistics permits the comparison of probability density functions between the healthy and estimated damaged stiffnesses. A set of graphical and statistical probability damage quotients are then found that indicate a confidence level on the existence of damage. The effectiveness of the proposed technique is illustrated using simulated data on a three-degree-of-freedom spring-mass system and on an Euler-Bernoulli cantilever aluminum beam.
84 citations
TL;DR: In this article, a linear least squares problem is used to identify the local stiffness of a structure from vibration test data, based on a projection of the experimentally measured flexibility matrix onto the strain energy distribution in local elements or regional superelements.
Abstract: A new method is presented for identifying the local stiffness of a structure from vibration test data. The method is based on a projection of the experimentally measured flexibility matrix onto the strain energy distribution in local elements or regional superelements. Using both a presumed connectivity and a presumed strain energy distribution pattern, the method forms a well-determined linear least squares problem for elemental stiffness matrix eigenvalues. These eigenvalues are directly proportional to the stiffnesses of individual elements or superelements, including the cross-sectional bending stiffnesses of beams, plates, and shells, for example. An important part of the methodology is the formulation of nodal degrees of freedom as functions of the measured sensor degrees of freedom to account for the location offsets which are present in physical sensor measurements. Numerical and experimental results are presented which show the application of the approach to example problems.
79 citations
TL;DR: In this article, it was shown that the Cartesian stiffness matrix associated with a linear elastic coupling between two rigid bodies is, in general, asymmetric if the resulting forces and moments do not sum to zero.
73 citations
TL;DR: In this article, a viscoelastic material approach for steady-state rolling structures has been developed based on the generalized Maxwell-model, where the final state is attained in a few load increments and just one time step.
Abstract: Based on the generalized Maxwell-model, a viscoelastic material approach for steady-state rolling structures has been developed. Unlike a transient finite element formulation the final state is attained in a few load increments and just one time step. The consistent linearization of the steady-state viscoelastic constitutive formulation leads to additional coupling matrices so that the number of non-zero entries in the global stiffness matrix is increased. The steady-state formulation of the viscoelastic material approach as well as the transient formulation allow the addition of so-called Prandtl-elements to consider elastoplastic effects, too. Numerical results confirm the robustness, reliability and capability of the steady-state viscoelastic material formulation.
62 citations
TL;DR: In this article, a test specimen geometry for the direct measurement of the four in-plane stiffness components of orthotropic materials is defined based on a suitable use of the principle of virtual work, which leads to a system of equations that links the stiffness components to the global force applied and geometry parameters.
Abstract: This paper deals with the definition of a new test specimen geometry for the direct measurement of the four in-plane stiffness components of orthotropic materials. The technique is based on a suitable use of the principle of virtual work. The choice and application of four different types of virtual kinematic fields leads to a system of equations that links the our stiffness components to the global force applied and geometry parameters. A numerical simulation based on finite lement modelling is used to validate the approach. The stability of the process is also demonstrated.
54 citations
TL;DR: In this article, the exact stiffness matrix for a curved beam element with constant curvature is derived for a plane two-node six degree-of-freedom element in which effects of flexural, axial and shear deformations are taken into account.
54 citations
TL;DR: In this article, a generalization of the classical structural flexibility matrix is presented, where the flexibility of an individual element or substructure is directly obtained as a particular generalized inverse of the free-free stiffness matrix.
TL;DR: In this paper, a stochastic finite element method has been proposed in the frequency domain for analysis of structural dynamic problems involving uncertain parameters, where the harmonic forces as well as earthquake-induced ground motion are treated as random process defined by respective power spectral density function.
TL;DR: In this paper, a beam-to-column connection classification system was proposed, in which the stiffness and strength characteristics of the connections are considered simultaneously, and a connection is classified into a unique category, thereby clarifying the position for design engineers.
TL;DR: In this article, the authors demonstrate how to collect in situ field data and solve for stiffness (scaled shear) and damping values by a method consistent with this constitutive model.
Abstract: Determination of in situ dynamic soil properties is fundamental to the prediction of the seismic behavior of foundations and soil embankment structures. Both elastic (stiffness) and inelastic (damping) values are required for computational analysis. To be of value to engineers, the geophysical inversion should employ the same soil model as used in the dynamic analysis software. Current engineering practice employs a Kelvin-Voigt model (spring in parallel with dashpot). The relevant wave equation is a third-order partial differential equation. This paper demonstrates how to collect in situ field data and solve for stiffness (scaled shear) and damping values by a method consistent with this constitutive model. Measurements of seismic wave amplitude decay and velocity dispersion are simultaneously inverted for the required stiffness and damping values. These in situ stiffness and damping values are directly comparable to those obtained by resonant column measurements in the laboratory. Furthermore, the results may be directly input into currently available engineering software to provide values of stiffness and viscous damping. This paper includes both synthetic (finite difference) and field data examples that illustrate the method.
TL;DR: In this article, a method that estimates mass and stiffness matrices of shear building from modal test data is presented, which depends on only measurable points that are less in number than the total structural degrees of freedom, and on the first two orders of structural mode measured.
Abstract: A method that estimates mass and stiffness matrices of shear building from modal test data is presented in this paper. The method depends on only measurable points that are less in number than the total structural degrees of freedom, and on the first two orders of structural mode measured. So it is applicable to most of the general test. Based on this method modal data of unmeasurable points are estimated, then global mass and stiffness matrices of structure are obtained by using the first two orders of modal data. Taking advantage of iteration the optimum global mass and stiffness matrices are gained. Finally, an example is studied in this paper. Its result shows that this method is reliable. © 1998 John Wiley & Sons, Ltd.
TL;DR: In this paper, an optimum design has been performed to maximize the specific energy density (SED) of a composite flywheel rotor for an energy storage system, which consists of multiple rings, and the interferences and ply angles vary in the radial direction.
Abstract: An optimum design has been performed to maximize the specific energy density (SED) of a composite flywheel rotor for an energy storage system. The flywheel rotor consists of multiple rings, and the interferences and ply angles vary in the radial direction. For the structural analysis the rotor is assumed to be an axisymmetric thick laminated shell with a plane strain state. Considering the ring-by-ring variation of fiber orientations, a symmetric local stiffness matrix was derived for each ring. Using the stiffness matrix, the continuity conditions of radial stresses and displacements between the rings with a consideration of the interferences can be easily incorporated. A symmetric global stiffness matrix is then obtained assembling the local stiffness matrices. Displacements are obtained by solving the global stiffness matrix, and the stresses in each ring are then calculated. Three-dimensional intra-laminar quadratic Tsai-Wu criterion for the strength analysis is used yielding the strength ratio for ea...
TL;DR: In this article, a manufacturing complexity index is proposed to assess manufacturing complexity without undertaking a detailed cost analysis, which interprets numerically qualitative issues such as simple and complex layups.
Abstract: Design criteria are essential for describing the objectives of optimization. Strength, stiffness, and manufacturing are addressed.The mechanical criteria, for strength and stiffness, provide with the magnitude by which the thickness of a given laminate must be scaled in order to just meet all requirements. For first-ply-failure strength, a quartic failure criterion was derived from the quadratic Tsai-Wu criterion, for unsymmetric and symmetric laminates subject to mixed loadsets. For stiffness, maximum displacement constraints can be selectively set on all components and modulus. Combined strength and stiffness control is also analyzed. While developed for single elements, these criteria are also suited for designing entire laminated plates.Assessing manufacturing complexity without undertaking a detailed cost analysis is achieved by an index which interprets numerically qualitative issues such as simple and complex layups. The new manufacturing complexity index takes into account variations in thickness,...
TL;DR: In this article, a matrix formulation is used to estimate the maximum deflection of composite beams with web openings and an expression for calculating the deflection across a web opening is given.
Abstract: Procedures for calculating the deflections of composite beams with web openings are described. Initially, a matrix formulation is used. Modeling assumptions are verified by comparison with experimental data, and recommendations for practical application of the matrix analysis procedures are made. The results of the comparison are used to develop a design aid for estimating the maximum deflection of beams with web openings and an expression for calculating the deflection across a web opening. The work demonstrates that, in most cases, a single web opening often has little effect on the total deflection of a composite beam. There are, however, important cases where the effect can be significant. The effects of an opening and of shear deflections are of the same order. Ignoring both the web opening and shear deformation can lead to significant error. The matrix stiffness method, the design aid, and closed form equations provide reasonable estimates of both total deflection and deflection across an opening.
TL;DR: In this article, the authors derived consistent tangent moduli for two models of unified theory of viscoplasticity, proposed by Anand and Estrin, and Robinson's potential viscasticity are derived.
Book•
22 Oct 1998
TL;DR: Finite Element Method Prerequisites as discussed by the authors The Finite Element Method is a direct method to derive global stiffness equation by direct methods, and it can be used in many virtual work applications.
Abstract: Finite Element Method Prerequisites. The Finite Element Method. Element Stiffness Equations by Direct Methods. Global Stiffness Equations. Element Stiffness Equations by Displaced State Virtual Work Applications. General Approach to Element Stiffness Equations. Plane Stress and Plane Strain. Plane Stress Structural Triangular Finite Elements. Isoparametric Plane Stress Structural Quadrilateral Finite Elements. Flat Plate Flexural Finite Elements. Axisymmetric Structural Finite Elements. Structural Finite Elements in Perspective. Appendix. Answers to Selected Problems. Index.
TL;DR: In this paper, the authors examined the role of the integrated force method in analysis, animation and design of aerospace and other products and concluded that it is advisable to use both methods to calculate stress and eliminate errors through comparison.
21 Jun 1998
TL;DR: In this article, an energy-based argument is used to derive the dynamic equation of a mechanical impedance at the end effector of a robot manipulator, both for its translational part and for its rotational part.
Abstract: In this paper an energy-based argument is used to derive the dynamic equation of a mechanical impedance at the end effector of a robot manipulator, both for its translational part and for its rotational part. The adoption of unit quaternions to describe orientation displacements leads to a geometrically consistent definition of the stiffness in the impedance equation. Remarkably, off-diagonal elements in the equivalent stiffness matrix are considered; namely, coupling forces with orientation displacements and coupling moments with position displacements. The equilibrium and the stability of the impedance equation are discussed as well as the geometric properties of the stiffness matrix.
TL;DR: Closed form solutions for the element stiffness matrices for four commonly used hybrid finite elements, namely, the 5-β-I, 5β-II, RGH4 and RGH8 elements are given in detail as discussed by the authors.
TL;DR: In this article, a finite element method formulated on the assumption of uniform bending stiffness within each element is used in the deflection analysis of the shafts, where differences between measured and theoretically predicted deflections at any two points on a shaft are used to construct an error function for deflection.
TL;DR: In this article, the problem of identifying a positive semi-definite symmetric stiffness matrix for a stable elastic structure from measurements of its displacement in response to some set of static loads is addressed.
TL;DR: In this paper, a finite element method based on exact inverse of stiffness matrix is proposed for beam bending problems with stochastic stiffness, which avoids the error due to truncating the expansion series of random stiffness matrix.
TL;DR: In this article, an approach for extension of the optimal design method to include the structural uncertainty with the random parameters is presented, where the stiffness parameter and external load are treated as random variables.
TL;DR: In this paper, a six degree-of-freedom high-accuracy manipulator with four revolute and two prismatic joints is presented, where a finite element model is used to validate the theory for calculating torsional stiffness of such joints.
TL;DR: In this article, the authors propose a method to find the best solution for the following problems: 1) ǫ: 1.直動ガイドの剛性解析が可能な理論式を整理した.
Abstract: 直動ガイドの剛性解析についてボールガイドとローラガイドシステムの負荷分布式をたて, 剛性解析が可能な理論式を整理したが, レールやガイドブロックに加工誤差やミスアライメントがある場合ならびにテーブルの曲げ変形を考慮した剛性解析等は割愛せざるを得なかった.機会を得て, いずれ整理して読者の参考にできればと思う.