Showing papers on "Direct stiffness method published in 2000"

Stiffness--an unknown world of mechanical science?

Abstract: "Stiffness" is a term used to describe the force needed to achieve a certain deformation of a structure. In the biomechanical world, several different definitions of stiffness are used, but not all of them are explained adequately to those readers who are less familiar with biomechanical terminology. This paper gives examples for specific definitions which are based on the basic definition of stiffness of a loaded structure

Calculation of the Stiffness Matrix of Angular Contact Ball Bearings by Using the Analytical Approach

Abstract: The stiffness matrix of angular contact ball bearings is calculated by using the analytical approach in which the summation of ball-race loads is replaced by an integration. The matrix connected to the conventional model in two degrees of freedom is first presented. A practical application of this formulation is illustrated through the common problem of sizing a two bearings-shaft arrangement. Variations of displacements, axial forces, and bearing fatigue life related to preload are shown to be easily obtained. Then, the matrix connected to the model in five degrees of freedom is given. This may be coupled with finite elements which are generally used to model the shaft or the housing.

The eigenscrew decomposition of spatial stiffness matrices

Abstract: A manipulator system is modeled as a kinematically unconstrained rigid body suspended by elastic devices. The structure of spatial stiffness is investigated by evaluating the stiffness matrix "primitives"-the rank-1 matrices that compose a spatial stiffness matrix. Although the decomposition of a rank-2 or higher stiffness matrix into the sum of rank-1 matrices is not unique, one property of the set of matrices is conserved. This property, defined as the stiffness-coupling index, identifies how the translational and rotational components of the stiffness are related. Here, we investigate the stiffness-coupling index of the rank-1 matrices that compose a spatial stiffness matrix. We develop a matrix decomposition that yields a set of rank-1 stiffness matrices that identifies the bounds on the stiffness-coupling index for any decomposition. This decomposition, referred to as the eigenscrew decomposition, is shown to be invariant in coordinate transformation. With this decomposition, we provide some physical insight into the behavior associated with a general spatial stiffness matrix.

Matrix Structural Analysis, 2nd Edition

Abstract: Matrix Structural AnalysisAdvances in Ready Mixed Concrete TechnologyMatrix Analysis of StructuresMatrix Methods of Structural AnalysisStructural Engineering and Geomechanics Volume 1Structural AnalysisStructural Analysis with the Finite Element Method. Linear StaticsMatrix Structural Analysis Using SpreadsheetsStructural Stability And Dynamics, Volume 1 (With Cd-rom) Proceedings Of The Second International ConferenceMatrix Analysis of StructuresMatrix Structural AnalysisProblems in Structural Analysis by Matrix MethodsAn Introduction to Matrix Structural Analysis and Finite Element MethodsEarthquake EngineeringMatrix Methods of Structural AnalysisComputer Methods in Advanced Structural AnalysisMatrix Analysis of Structures, SI EditionStructural Analysis SystemsIntroduction to Structural AnalysisChallenges, Opportunities and Solutions in Structural Engineering and ConstructionMatrix Analysis Framed StructuresMatrix Analysis of StructuresComputer Analysis of StructuresMatrix Methods of Structural AnalysisMatrix Analysis of Structures SI VersionProceedings of the Second International Conference on Structural Stability and DynamicsVibrations, Dynamics and Structural Systems 2nd editionMATRIX METHODS OF STRUCTURAL ANALYSISStructural Analysis : a Matrix ApproachEnergy Principles and Variational Methods in Applied MechanicsHandbook of Structural EngineeringFUNDAMENTALS OF STRUCTURAL ANALYSIS, 2ND EDMATRIX METHODS OF STRUCTURAL ANALYSISOptimal Structural AnalysisMatrix Structural AnalysisMatrix Methods of Structural AnalysisTheory of Matrix Structural AnalysisMatrix Structural AnalysisMatrix Structural AnalysisMatrix Structural Analysis

Shear Effect in Beam Finite Element on Two-Parameter Elastic Foundation

Abstract: A formulation leading to an explicit free-of-meshing stiffness matrix for the beam finite element on the two-parameter elastic foundation model is presented. Considering the shear deformation contribution, the formulation is based on the exact solution of the governing differential equation. Two numerical examples are presented. The first one, a short beam on elastic foundation, is used to validate the new stiffness matrix. The second example examines a structure-foundation interaction problem of a seven-story frame supported by a foundation beam on a two-parameter foundation model.

The continuum of connection rigidity in timber structures

Abstract: The use of timber in rigid frames has been hampered by the debate surrounding the rigidity of the moment connections. Joint stiffness is a function of beam flexural stiffness, as well as of the rotational stiffness of the connection. The level of joint rigidity, which is predictable from joint stiffness, significantly affects the bending moments and forces that are transferred through the connection. We used joint-test data from the literature and computer models to assess the effect of various parameters on joint stiffness. There is a continuum of joint stiffness for moment-resisting connections where the deformed shapes of the beams in beam-to-column connections are described by pinned, semi-rigid, and rigid behavior. Engineers can assess the level of joint rigidity during the design process so that the resulting connections and frames meet performance expectations. It seems unlikely that a fully rigid joint can be designed for use in timber portal frames because of stiffness orthotropy. However, moment-resisting joints that are less than 50% rigid can be used in timber frames to develop frame-like behavior.

On progressive damage phenomena of structures

Abstract: For more than 50 years, the technology of linear damage processes has been known and mastered. Strong, progressive damage processes have recently been discovered on various types of structures, for which a uniform theory has been unavailable. A common feature of these processes is the wide-band excitation of the dominant forces (ocean waves, storm, traffic), a shift of the structural response spectrum into domains of higher excitation caused by degrading structural stiffness, as well as a damage-controlled self-adaptation phenomenon. Any numerical investigation of progressive damage phenomena should be based on the load- or time-evolution of the global stiffness matrix. The eigenvalues or natural frequencies of this stiffness matrix offer a decision basis regarding the damage-induced change of structural features.

The spatial stiffness matrix from simple stretched springs

Abstract: Looks at the stiffness matrix of some simple but very general systems of springs supporting a rigid body. The stiffness matrix is found by symbolically differentiating the potential function. After a short example attention turns to the general structure of the stiffness matrix and in particular the principal screws introduced by Ball (1900).

Analysis of dynamic characteristics of structural joints using stiffness influence coefficients

Abstract: This paper proposes a new modeling method for joints in mechanical structures in order to reduce the errors in eigenvalue analysis due to joint modeling. The new modeling method uses both a stiffness influence method and a condensation method to obtain the dynamic characteristic matrix of the joint region. It also employs the displacement and reaction of finely modeled finite element analysis in the calculation of stiffness influence coefficients. In order to check the validity of the proposed method, natural frequencies and mode shapes of a simple structure with a bolted joint are investigated by the proposed method and by experiments. The eigenvalue analysis using the proposed method shows more accurate results than that using rigid joints modeling, when the natural frequencies are compared with the experimental results. In addition, the differences between the natural frequencies obtained by the proposed method and those by the rigid joints modeling are notable in the modes where the joint has elastic deformation.

Geometrical method for modeling of asymmetric 6/spl times/6 Cartesian stiffness matrix

Abstract: In this paper, we study the 6/spl times/6 Cartesian stiffness matrices of conservative systems using the method of changing basis in differential geometry of the motion of the rigid body. We show that the stiffness matrix is symmetric at the unloaded equilibrium configuration. When the system is subjected to external loads, the 6/spl times/6 Cartesian stiffness matrix becomes asymmetric. The skew-symmetric part of the stiffness matrix is equal to the negative one-half of the cross-product matrix formed by the externally applied load, referenced to the inertial frame. This method presented in this paper provides a systematic way of constructing 6/spl times/6 stiffness matrix in robotic grasping/manipulation and stiffness control.

Complex stiffness measurement of vibration-damped structural elements

Abstract: As vibration suppression technology has matured, the application of viscoelastic materials in passive damping mechanisms has proven to be a reliable means toward improved structural dynamics This paper discusses general steps required in characterization of viscoelastic damping elements and presents several successful passive damping devices as examples of the approach Sample devices include a damper for the Hubble Space Telescope Solar Array 3, a damped strut built for the FORTE satellite, a viscoelastic isolator, and a cocured viscoelastic/composite strut When damping is built into a structure with a damped element, it is necessary to measure the element stiffness to understand its effect on the system dynamics The stiffness measurement is complex because of the level of damping The complex stiffness function, with both real and imaginary components, characterizes the behavior of a damping device, a damped structural element, or a sample of viscoelastic material Stiffness characterization of structural elements with viscoelastic damping is presented in terms of real stiffness and loss (imaginary stiffness/real stiffness)

Accelerated initial stiffness schemes for elastoplasticity

Abstract: Iterative methods for the solution of non-linear finite element equations are generally based on variants of the Newton–Raphson method. When they are stable, full Newton–Raphson schemes usually converge rapidly but may be expensive for some types of problems (for example, when the tangent stiffness matrix is unsymmetric). Initial stiffness schemes, on the other hand, are extremely robust but may require large numbers of iterations for cases where the plastic zone is extensive. In most geomechanics applications it is generally preferable to use a tangent stiffness scheme, but there are situations in which initial stiffness schemes are very useful. These situations include problems where a nonassociated flow rule is used or where the zone of plastic yielding is highly localized. This paper surveys the performance of several single-parameter techniques for accelerating the convergence of the initial stiffness scheme. Some simple but effective modifications to these procedures are also proposed. In particular, a modified version of Thomas' acceleration scheme is developed which has a good rate of convergence. Previously published results on the performance of various acceleration algorithms for initial stiffness iteration are rare and have been restricted to relatively simple yield criteria and simple problems. In this study, detailed numerical results are presented for the expansion of a thick cylinder, the collapse of a rigid strip footing, and the failure of a vertical cut. These analyses use the Mohr–Coulomb and Tresca yield criteria which are popular in soil mechanics. Copyright © 2000 John Wiley & Sons, Ltd.

Analysis of frames with non-prismatic members

Abstract: This paper presents a more realistic and comprehensive static analysis technique for structures having non-prismatic members. In the proposed method a general stiffness matrix for non-prismatic members that is applicable to Timoshenko beam theory has been derived. The stiffness coefficients have been determined for constant, linear, and parabolic height variations of members, employing analytical and (or) numerical integration techniques. Uniform, triangular, and trapezoidal distributed loads over the entire member or along any part of it, concentrated loads, moments at points on the member, and any of these load combinations are taken into consideration to determine the fixed-end forces. A computer program has been coded in Fortran which analyses two-dimensional frames using the proposed stiffness matrix and fixed-end forces for a wide range of external loads. The fixed-end forces may include the effect of shear deformations. The importance of the shear deformations in non-prismatic members with high dep...

Geometric design tools for stiffness and vibration analysis of robotic mechanisms

Abstract: We present a methodology for the first-order stiffness and vibration analysis of general robotic systems including parallel mechanisms, based on geometric methods for kinematics and elasticity analysis. We exploit the uniformity and structure typically extant in parallel mechanisms to develop an accurate and computationally tractable method of stiffness and vibration analysis that is amenable 60 design iterations and optimization. By way of our analysis we formalize the notion of a mechanism's structural compliance matrix and derive an associated set of dynamic equations that model elastic effects without resorting to assumed modes or finite element models. Our methodology is illustrated with a case study involving the Eclipse, a novel six degree-of-freedom parallel mechanism designed for rapid machining.

Precise stability analysis of telescopic boom

Abstract: The beam element stiffness matrix on plane problem can be got from the equilibrium equation of a beam -column which is built according to the theory of Ⅱ order. On condition that the deformation of element is small, the stiffness matrix consists of linear stiffness matrix and geometrically nonlinear stiffness precisely. The precise critical force of a system can be deduced from the fact that the determinant of stiffness matrix of the system is equal to zero in the critical condition. As an example, the stability analysis of a multistepped column is discussed, and a precise recurrence formula is offered to solve the problems of critical force of any telescopic boom in crame.

Design of a Tendon-Driven Articulated Finger-Hand Mechanism and Its Stiffness Adjustability

Abstract: This paper describes design of a tendon-driven articulated finger hand that has similar properties to those of a Remote Compliance Center (RCC) device, i.e., it generates resolved displacements for disturbance forces applied to a grasped object and it can also adjust the elastic coefficients semiactively using the nonlinear elasticity of tendons. After introducing some basic results with respective to a tendon-driven mechanism, the stiffness matrix which relates the restriction forces applied to a grasped object to the small displacements of the object is derived. It is shown that more than six tendons are necessary, for each finger to adjust all elements of the stiffness matrix using only the nonlinear mechanical elasticity of tendons. After that, the wiring and pulley system is designed that cannot only drive the fingers freely without loosing the tension forces but also can diagonalize the stiffness matrix and adjust the elements. It is also shown that the hand can grasp different sized objects without losing the property using the tendon redundancy.

Statics and inverse dynamics solvers based on strain-mode disassembly

Abstract: The finite element method is widely used in design engineering for modeling and analyzing structural systems Two approaches have been developed: the force-based method that exploits the equilibrium of forces and moments at nodal joints of the mesh to formulate the assembly of element-level matrices into master mass and stiffness matrices and its dual counterpart, the flexibility-based method An alternative formulation of stiffness-based finite element assembly is proposed that decomposes element-level matrices even further into strain mode contributions This decomposition (referred to as finite element disassembly here) allows the derivation of an efficient numerical solver It is shown that a single matrix factorization is required for analyzing all models characterized by the same topology This makes finite element disassembly and the associated inverse solver ideal in cases where multiple design analyzes are performed In the first part, this publication derives a framework for an alternat

Modifying stiffness matrix method of elastic foundation beam

Abstract: In this paper, a new method - modifying stiffness matrix method is presented. In the method, the Winkler hypothesis is proposed, the parameters of elastic line function are determined with node displacements of beam element. According to Winkler hypothesis, the reaction of soil is described as a function of beam element node displacement, which is applied to beam element as distributive loads. By the fundamental solution of beam, the relationship between node forces and node displacement is developed in matrix form, which is called as the soil reaction matrix. The soil reaction matrix is added to beam element stiffness matrix, and modified beam element stiffness matrix is formed. At last, the matrix equation for analyzing elastic foundation beam is held up by the equilibrium of node forces.

A Lagrangian Quadratic Triangular Fluid Finite Element for Fluid-Structure Interaction Problems.

Abstract: A quadratic triangular fluid element based on Lagrangian frame of reference is formulated for solving coupled fluid-structure interaction problems. The mesh-locking behavior due to simultaneous enforcement of the incompressibility and the irrotational constraints are studied in detail. In addition, their relationship to the number of active degrees of freedom and the number of integration points used to evaluate the stiffness matrix is established. It is found that the order of numerical integration used in the evaluation of stiffness matrix has pronounced effect on the element behavior. It is found that for a given mesh the formulated element does not lock in the absence of irrotationality constraints when the stiffness matrix is fully integrated. The same mesh locks when the stiffness matrix is fully integrated and both the constraints are enforced simultaneously. However, when the volumetric stiffness matrix is fully integrated and the rotational stiffness matrix is reduced integrated, the twin constraints are satisfied giving superior performance. The utility of the derived element to solve some coupled fluid-structure interaction problems is demonstrated and the solutions are compared with the available results.

Structural stiffness identification using maximum likelihood estimate method

Abstract: Various structural parameter (mass, damping and stiffness) identification techniques are under active development This paper is intended to develop a structural parameter estimation algorithm in the time-domain based on the maximum likelihood estimation (MLE), which manipulates directly on the physical parameters of the structural systems A finite element model of the structural system is transformed into a state space matrix format The solution of the dynamic matrix equation can be readily obtained numerically by matrix exponential method that eliminates the awesome complex eigenproblem The maximum likelihood estimate algorithm and corresponding iteration process are derived to achieve the best matching between the model responses and measured responses Assume that the mass and damping properties of the structure are known a priori by any means and keep unchanged, numerical example has shown that the proposed algorithm gives the ideal estimation of the stiffness parameters The iteration process converges very fast due to some optimum properties of the maximum likelihood estimate