Showing papers on "Direct stiffness method published in 2003"
TL;DR: In this paper, a method for determining the nonlinear modal stiffness coefficients for an arbitrary finite element model is presented, which is suitable for use with commercial finite element codes having a geometrically nonlinear static capability.
279 citations
TL;DR: In this article, a method is developed to systematically remove and reintroduce low density elements from and into the finite element mesh on which the structural topology optimization problem is defined, and the material density field which defines the topology and the local stiffness of the structure is optimally distributed via non-linear programming techniques.
Abstract: A method is developed to systematically remove and reintroduce low density elements from and into the finite element mesh on which the structural topology optimization problem is defined. The material density field which defines the topology and the local ‘stiffness’ of the structure is optimally distributed via non-linear programming techniques. To prevent elements from having zero stiffness, an arbitrarily small lower bound on the material density is typically imposed to ensure that the global stiffness matrix does not become singular. While this approach works well for most minimum compliance problems, the presence of low density elements can cause computational problems, particularly in structures that exhibit geometric non-linearities, e.g. in compliant mechanisms. To resolve this problem, a systematic approach for removing and reintroducing low density elements is presented, and the substantial performance improvements both in design and computational efficiency of the method over current methods are discussed. Several structures and compliant mechanisms are designed to demonstrate the method. Copyright © 2003 John Wiley & Sons, Ltd.
196 citations
TL;DR: In this paper, a direct method using a strain energy-based RVE-procedure was proposed for the determination of the effective plate stiffness matrix for composite shells with microheterogeneous layers.
Abstract: The present study is concerned with the numerical determination of the effective plate stiffness matrix for composite shells with microheterogeneous layers. Contrary to the standard two-step procedure, where the effective plate or shell stiffness matrix is derived by a projection of the effective elasticity tensor onto the plate or shell reference surface, a direct method is proposed. This method uses a strain energy based RVE-procedure which assumes mechanical equivalence of a representative volume element for the given microstructure and a corresponding plate element if the strain energy in both elements is equal, provided that the effective deformation is equal in an average sense. In parametric studies concerning sandwich plates with hexagonal honeycomb cores, it is observed that the direct method and the two-step procedure are equivalent for the determination of the in-plane and the transverse shear properties while a significant deviation of the results obtained by both methods is found in case of the effective bending properties.
82 citations
TL;DR: The stiffness synthesis problem of variable geometry double planar parallel robots is addressed through the use of Gröbner bases that determine the solvability of the stiffness synthesis polynomial systems and by transforming these systems into corresponding eigenvalue problems using multiplication tables.
Abstract: In this paper, we address the stiffness synthesis problem of variable geometry double planar parallel robots. For a desired stiffness matrix, the free geometrical variables are calculated as a solution of a corresponding polynomial system. Since in practice the set of free geometrical variables might be deficient, the suggested solution addresses also the case where not all stiffness matrix elements are attainable. This is done through the use of Grobner bases that determine the solvability of the stiffness synthesis polynomial systems and by transforming these systems into corresponding eigenvalue problems using multiplication tables. This method is demonstrated on a novel variable geometry double planar six-degrees-of-freedom robot having six free geometric variables. A solution of the double planar stiffness synthesis problem is obtained through decomposing its stiffness matrix in terms of the stiffness matrices of its planar units. An example of this procedure is presented in which synthesizing six el...
59 citations
Book•
01 Jan 2003
TL;DR: The Finite Element Method for Stochastic Structures (FEM) as mentioned in this paper is based on the exact inverse of stiffness matrix (INF) matrix, which is used to measure stiffness.
Abstract: 1. Fundamentals of Finite Element Method 2. Finite Element Method for Stochastic Structures - A Review and Improvement 3. Finite Element Method for Stochastic Structures Based on Exact Inverse of Stiffness Matrix 4. FEM Based on Direct Exact Inverse of Stiffness Matrix 5. Variational Principles-Based FEM for Stochastic Beams 6. Element-Level Flexibility-Based Finite Element Method for Stochastic Structures 7. A Comparison of Stochastic and Interval Finite Elements Biblography Appendices
58 citations
TL;DR: In this article, a closed-form formulation and geometrical interpretation of the derivatives of the Jacobian matrix of fully parallel robots with respect to the moving platforms' position/orientation variables are presented.
Abstract: This paper presents a closed-form formulation and geometrical interpretation of the derivatives of the Jacobian matrix of fully parallel robots with respect to the moving platforms' position/orientation variables. Similar to the Jacobian matrix, these derivatives are proven to be also groups of lines that together with the lines of the instantaneous direct kinematics matrix govern the singularities of the active stiffness control. This geometric interpretation is utilized in an example of a planar 3 degrees-of-freedom redundant robot to determine its active stiffness control singularity.
52 citations
TL;DR: In this article, a non-linear analysis of beam-type structures with a thin-walled cross-section is presented using updated Lagrangian formulation and the nonlinear displacement field of asymmetric crosssection accounting for large rotation effects.
49 citations
TL;DR: In this article, a matrix formulation for the solution of frictionless contact problems on arbitrarily multilayered piezoelectric half-planes is presented, in which a local stiffness matrix relating the stresses and electric displacements to the mechanical displacements and electrical potentials is formulated for each layer.
Abstract: A matrix formulation is presented for the solution of frictionless contact problems on arbitrarily multilayered piezoelectric half-planes. Different arrangements of elastic and piezoelectric materials with hexagonal symmetry within the layered medium are considered. A generalized plane deformation is used to obtain the governing equilibrium equations for each individual layer. These equations are solved using the infinite-Fourier-transform technique. The problem is then reformulated using the local/global stiffness method, in which a local stiffness matrix relating the stresses and electric displacements to the mechanical displacements and electrical potentials in the transformed domain is formulated for each layer. Then it is assembled into a global stiffness matrix for the entire half-plane by enforcing interfacial continuity of traction forces and displacements. This local/global approach not only eliminates the necessity of explicitly finding the unknown Fourier coefficients, but also allows the use of efficient numerical algorithms, many of which have been developed for finite-element analysis. Unlike finite-element methods, the local/global stiffness approach requires minimal input. Application of the mixed boundary conditions reduces the problem to a singular integral equation. This integral equation is then numerically solved for the unknown contact pressure using a collocation technique. Knowledge of the contact pressure and electrostatic distributions is very important for applications where piezoelectric layers are used as sensors and/or actuators. One example includes the active deformation and shape control of support surfaces.
44 citations
TL;DR: In this article, a weighted-averaging frequency-domain finite-element method for 2D elastic wave modeling is presented. But the method is not suitable for the simulation of large-scale seismic inversion.
Abstract: We present a weighted-averaging frequency-domain finite-element method for an accurate and efficient 2D elastic wave modeling technique. Our method introduces three kinds of supplementary element sets in addition to a basic element set that is used in the standard finite-element method. By constructing global stiffness and mass matrices for four kinds of element sets and then averaging them with weighting coefficients, we obtain a new global stiffness and mass matrix. With optimal weighting coefficients determined by a Marquardt–Levenberg method to minimize grid dispersion and grid anisotropy, we can reduce the number of nodal points per shear wavelength from 33.3 (using the standard finite-element method) and 20 (using the eclectic method) to 5, with the errors of group velocities no larger than 1%. By reducing the number of grid points per wavelength, we achieve a 97% and 75% reduction of computer memory required to store the complex impedance matrix for a band-type matrix solver and a nested dissection method, respectively, compared with those of the eclectic method. Our method gives approximate solutions compatible with exact solutions for an infinite homogeneous, a semi-infinite homogeneous (Lamb9s problem), and a horizontal two-layer model with fewer grid points than the standard and the eclectic method. A major advantage of the weighted-averaging finite-element method for the elastic wave equation is that it provides solutions very close to correct solutions for Lamb9s problem economically, unlike most of the displacement approaches. In addition, our scheme makes the complex impedance matrix symmetric, which satisfies reciprocity. Seismic forward modeling techniques that satisfy reciprocity are of critical importance in seismic imaging and inversion because we can economically calculate a Jacobian matrix using the reciprocity. Successful simulation of a large-size model shows that our method can be used for the simulation of wave propagation in the geological model needed in the reverse-time migration or seismic inversion.
43 citations
TL;DR: In this article, a technique to evaluate the error propagation of the pseudodynamic testing of a nonlinear system is proposed, which mainly relies upon the introduction of the degree of nonlinearity to describe the variation of stiffness for each time step.
Abstract: A technique to evaluate the error propagation of the pseudodynamic testing of a nonlinear system is proposed. This technique mainly relies upon the introduction of the degree of nonlinearity to describe the variation of stiffness for each time step. The commonly used Newmark explicit method is chosen for this study and it is analytically proved that the upper stability limit is enlarged for the case of stiffness softening and is reduced for the case of stiffness hardening. These theoretical results are thoroughly confirmed with numerical examples. It is also theoretically and numerically verified that for each time step stiffness softening encounters less error propagation while stiffness hardening experiences more severe error propagation than for the stiffness invariant case. This is because stiffness softening results in the decrease of the natural frequency and the value of the degree of softening nonlinearity while stiffness hardening leads to the increase of the natural frequency and the value of the degree of hardening nonlinearity.
37 citations
TL;DR: In this article, a mesh superposition technique is presented for an efficient finite element analysis, which allows local refinement of the mesh without introducing transition region or multi-point constraints, by applying appropriate boundary conditions on the local superimposed mesh, singularity in the global stiffness matrix can be avoided and inter-element compatibility conditions can be satisfied.
Book•
01 Jan 2003
TL;DR: In this paper, the authors present a generalization of Matrix Methods for Statically Indeterminate Structures (MIWS) to include three-dimensional or space trusses, as well as three different types of influence lines.
Abstract: Dedication.Preface.PART ONE: STATICALLY DETERMINATE STRUCTURES.Introduction.Structural Loads.System Loading and Behavior.Reactions.Shearing Force and Bending Moment.Introduction to Plane Trusses.Plane Trusses, Continued.Three-Dimensional or Space Trusses.Influence Lines.Introduction to Calculating Deflections.Deflection and Angle Changes-Energy Methods.PART TWO: STATICALLY INDETERMINATE STRUCTURES CLASSICAL METHODS.Introduction to Statically Indeterminate Structures.Energy Method for Statically Indeterminate Structures.Influence Lines for Statically Indeterminate Structures.Slope Deflection: A Displacement Method of Analysis.PART THREE: STATICALLY INDETERMINATE STRUCTURES COMMON METHODS IN CURRENT PRACTICE.Approximate Analysis of Indeterminate Structures.Moment Distribution for Beams.Moment Distribution for Frames.Introduction to Matrix Methods.Generalizing Matrix Methods.Additional Topics in Matrix Methods.Appendix A: The Catenary Equation.Appendix B: Matrix Algebra.Appendix C: Wind and Snow Load Tables and Figures.Appendix D: Beam Fixed-End Moments.Appendix E: Properties of Commonly Used Areas.Appendix F: Elastic Weight and Conjugate Beam Methods.Glossary.Index.
Abstract: In order to execute efficiently the free vibration analysis of 2-dimensional structures like plate structures, the author developed the finite element-transfer stiffness coefficient method. This method is based on the combination of the modeling techniques in the FEM and the transfer technique of the stiffness coefficient in the transfer stiffness coefficient method. Numerical results of the simply supported and the elastic supported rectangular plates showed that the present method can be successfully applied to the free vibration analysis of plate structures on a personal computer. We confirmed that, in the case of analyzing the free vibration of rectangular plate structures, the present method is superior to the FEM from the viewpoint of computation time and storage.
TL;DR: In this paper, the effect of a two-degree-of-freedom system kinematically connected to the beam is represented exactly by replacing it with equivalent stiffness coefficients, which are added to the appropriate stiffness coefficients of the bare beam.
Abstract: This paper is concerned with the dynamic stiffness formulation and its application for a Bernoulli-Euler beam carrying a two degree-of-freedom spring-mass system. The effect of a two degree-of-freedom system kinematically connected to the beam is represented exactly by replacing it with equivalent stiffness coefficients, which are added to the appropriate stiffness coefficients of the bare beam. Numerical examples whose results are obtained by applying the Wittrick-Williams algorithm to the total dynamic stiffness matrix are given and compared with published results. Applications of the theory include the free vibration analysis of frameworks carrying two degree-of-freedom spring-mass systems.
10 Nov 2003
TL;DR: This paper presents systematic methods to approach the conservative congruence transformation, CCT, via the geometrical analysis for the stiffness control transformation of serial manipulators via the CCT theory in the presence of external loads.
Abstract: This paper presents systematic methods to approach the conservative congruence transformation, CCT, via the geometrical analysis for the stiffness control transformation of serial manipulators. Through the strategy of changing basis, the 6/spl times/6 Cartesian stiffness of manipulators is shown to be basis dependent. The generalized formulation and symmetric property of the 6/spl times/6 Cartesian stiffness matrix are presented via the CCT theory in the presence of external loads. Examples of the serial manipulators are conducted to verify the conservative stiffness mapping.
TL;DR: In this article, state-of-the-art finite elements are used to determine the out of plane stiffness of a planar parallel platform for machining operations, and the optimization is carried out by means of two gradient-based methods, namely LFOPC and Dynamic-Q.
TL;DR: In this article, the exact dynamic stiffness matrix for a high-order beam element is derived from the solutions of the differential equations that describe the deformations of the cross-section according to the high order theory, which include cubic variation of the axial displacements over the beam.
Abstract: This work presents the derivation of the exact dynamic stiffness matrix for a high-order beam element. The terms are found directly from the solutions of the differential equations that describe the deformations of the cross-section according to the high-order theory, which include cubic variation of the axial displacements over the cross-section of the beam. The model has six degrees of freedom at the two ends, one transverse displacement and two rotations, and the end forces are a shear force and two end moments. Using the dynamic stiffness matrix exact vibration frequencies for beams with various combinations of boundary conditions are tabulated and compared with results from the Bernoulli-Euler and Timoshenko beam models.
Journal Article•
TL;DR: In this article, the results obtained by finite-element analysis of R/C coupled shear wall systems having several geometries in elastic-plastic space are considered using SPSS (Ver.5.0) statistical package program.
Abstract: Bar frame modelling is a popular method in coupled shear wall systems in structural design. In this process, determining the stiffness of the tie beams is important. In this study, results obtained by finite-element analysis of R/C coupled shear wall systems having several geometries in elastic-plastic space are considered. Using SPSS (Ver.5.0) statistical package program, an equivalent tie beam stiffness modification parameter is provided. The formula which defines the ratio between the plastic and elastic equivalent stiffness modification parameters is also given.
TL;DR: In this paper, an extended finite element transfer matrix (FE-TM) method is applied to dynamic response analysis of the structures under periodic excitations, which has the advantages of reducing the order of standard transfer equation systems, and minimizing the propagation of round-off errors occurring in recursive multiplication of transfer and point matrices.
TL;DR: In this paper, the authors present a method for assessing residual stiffness of a failed reinforced concrete beam structure, through the application of dynamic testing and finite element (FE) model updating.
Abstract: When an under-reinforced concrete beam structure has been loaded to the point where reinforcing steel on the tension side has yielded, it is deemed to have structurally failed and the full load capacity and stiffness can no longer be developed. When unloaded from the point of failure, the residual stiffness of the structure is difficult to estimate. There is a need to establish the serviceability of the structure and ultimately establish the levels of further loading that can be sustained before total collapse. In this paper we present a method for assessing residual stiffness of such a “failed” reinforced concrete structure, through the application of dynamic testing and finite element (FE) model updating. In an experimental study, failed zones in a beam structure were simulated in a FE model. Through a procedure of sensitivity-based updating using the measured modal properties, the stiffness distribution along the failed beam structure was identified.
TL;DR: In this article, the limitations of the mechanical model with lumped mass are discussed by illustrating actual measurement results of the stiffness matrix, where the point stiffness model was mistakenly compared with the transfer stiffness measurement.
Abstract: Several mechanical models with lumped mass were employed in the literature to represent strongly frequency-dependent characteristics of hydraulic engine mounts. Although complex stiffness by the mechanical models showed good agreements with the measured values, there exists a critical pitfall. The fact is that the complex stiffness model was derived at the driving point while measurements were obtained across the mounts. That is, the point stiffness model was mistakenly compared with the transfer stiffness measurement. In this paper, limitations of the mechanical model with lumped mass are discussed by illustrating actual measurement results of the stiffness matrix.
TL;DR: In this paper, the behavior of a beam with stochastic stiffness subjected to either deterministic or non-deterministic loading is studied via finite element method and the results are contrasted with exact solution to check the accuracy of the FEM for the case of large variations.
Abstract: The behavior of beams with stochastic stiffness subjected to either deterministic or stochastic loading is studied via finite element method The results are contrasted with exact solution to check the accuracy of the FEM for the case of large variations It represents a generalization of the previous study in which the stiffness matrix was decomposed as a product of three matrices, two of which are numerical ones and the third matrix involves the uncertain stiffness analytically To illustrate the proposed method, we evaluate the mean and the auto-correlation functions of the displacement of beams under various boundary conditions Two statically determinate beams (clamped-free or simply-supported) and two statically indeterminate beams (clamped–simply-supported or clamped are both ends) are investigated in this study The beams are subjected to a deterministic uniform pressure or a stochastic excitation
TL;DR: A novel algorithm based on transmission-line modeling is proposed to deal both with the nonlinearity and solution in the time domain and demonstrates the efficiency of the method.
Abstract: Nonlinear quasi-static field problems are generally solved by means of the finite-element method coupled with some classical time-stepping technique, such as the Crank-Nicolson iterative scheme, for solution in the time domain At each time step, the nonlinearity must be treated iteratively, and a new linear system must be solved every iteration, which is costly in terms of computation time Here, a novel algorithm based on transmission-line modeling is proposed to deal both with the nonlinearity and solution in the time domain The underlying idea is the analogy that exists between the finite-element matrix and the node-admittance matrix of an equivalent network where resistors and capacitors hold the material properties The nonlinear material is replaced by a fictitious linear and homogeneous one, which permits a global stiffness matrix to remain unchanged throughout the iterative process The emerging time-stepping scheme is precisely the same as the Crank-Nicolson scheme, and so is the accuracy Two numerical examples demonstrate the efficiency of the method
TL;DR: The structural stiffness of a machine tool is one of the main criteria that establishes its ability to produce accurate precision components as discussed by the authors, and the need for high dynamic stiffness is required both statically and dynamically each affecting different aspects of the machming process.
Abstract: The structural stiffness of a machine tool is one of the main criteria that establishes its ability to produce accurate precision components. High stiffness is required both statically and dynamically each affecting different aspects of the machming process. The need for high static stiffness arises from the requirement to produce parts to a desired size and shape [l] and although finish machining often takes place with small depths of cut and correspondingly light cutting forces, the resulting deflections can still be excessively large if the machme has inadequate static stiffness. The resulting deflection can thus produce out of tolerance work-pieces. The need for high dynamic stiffness results from two separate aspects of the machining process. In the first case inadequate dynamic stifhess will result in poor quality surface finish of the machined parts due to relatively low levels of vibration occurring during finish machining operations. In the second case low dynamic stiffness can have more serious consequences when under heavy machining conditions the resulting vibration might be sufficiently high to cause the process to be terminated in-order prevent possible damage to the machine. Traditionally machme tool structures were designed from experience with limited aid from manually carried out calculations using classical theory for such as beam bending, twist and shear. With the advent of powerful desktop computers and the associated Finite Element Software, at costs that are within the grasp of the typical machine tool manufacturer, it is now possible to determine the structural stiffness values for maclvne tools to a hgh order of accuracy and in a relatively short time scale. This paper outlines the static and dynamic structural analyses of a vertical milling machine that were to be subsequently validated against measured results [2, 31.
TL;DR: In this article, the authors used the 3D time-domain finite-element method incorporating the least-squares method to calculate the equivalent foundation mass, damping and stiffness matrices.
Abstract: This paper discusses how to use the three-dimensional (3D) time-domain finite-element method incorporating the least-squares method to calculate the equivalent foundation mass, damping and stiffness matrices. Numerical simulations indicate that the accuracy of these equivalent matrices is acceptable when the applied harmonic force of 1+sine is used. Moreover, the accuracy of the least-squares method using the 1+sine force is not sensitive to the first time step for inclusion of data. Since the finite-element method can model problems flexibly, the equivalent mass, damping and stiffness matrices of very complicated soil profiles and foundations can be established without difficulty using this least-squares method. Copyright © 2003 John Wiley & Sons, Ltd.
TL;DR: In this article, a normalized member stiffness determinant is derived for beams with uncoupled axial and Bernoulli-Euler flexural behaviour, by methods applicable to any member possessing transcendental stiffnesses.
Abstract: Transcendental stiffness matrices are well established in vibration and buckling analysis, having been derived from exact analytical solutions of the differential equations for many structural members without recourse to finite–element discretization. Their assembly into the overall structural stiffness matrix gives a transcendental eigenproblem, solvable with certainty by the Wittrick–Williams (WW) algorithm, instead of the usual linear (algebraic) eigenproblem. This paper establishes a (normalized) member stiffness determinant , being the value of the stiffness matrix determinant if the member were modelled by infinitely many finite elements and its ends were clamped. It is derived for beams with uncoupled axial and Bernoulli–Euler flexural behaviour, by methods applicable to any member possessing transcendental stiffnesses. Multiplying the product of a structure's member stiffness determinants by the determinant of its transcendental overall stiffness matrix gives a determinant, which, unlike the determinant of the transcendental overall stiffness matrix itself, has no poles when plotted against the eigenparameter, leading to a more secure eigenvalue location. Numerical results demonstrate the resulting advantages. In addition, the member stiffness determinant can give exact determinants for members with various standard end conditions and also provides limits for finite–element solutions as the number of elements approaches infinity. Analogous advantages occur in all other disciplines where the WW algorithm is used, e.g. fluid vibrating in pipes, heat and mass diffusion and Sturm–Liouville problems.
20 Jul 2003
TL;DR: This paper designs a modified Delta mechanism, with a well-balanced stiffness, based on the stiffness analysis method proposed, in a compact 6-DOF haptic interface.
Abstract: In our previous work, we developed a compact 6-DOF haptic interface, which contains a modified Delta parallel-link positioning mechanism. This modified Delta mechanism is designed as a compact desktop type and composed of many miniature bearings and small parts. Therefore, the stiffness of the modified Delta mechanism is strongly affected elastic deformations of these components. To design a high stiffness parallel mechanism which is well-balanced for all directions and rotations, we should analyze the stiffness of this parallel mechanism. In our previous paper, we proposed a method to analyze structural stiffness of a parallel mechanism. In this paper, we design a modified Delta mechanism, with a well-balanced stiffness, based on our stiffness analysis method.
TL;DR: In this article, a new method for modelling the stiffness of elastic body with viscoelastic theory is presented, and the parameters of the model set-up by using this method can be determined easily and present the characteristics of the elastic body's static stiffness, dynamic stiffness and shock stiffness.
TL;DR: In this article, simplified formulae for compressive stiffness and tilting stiffness of bonded elastic layers of circular, square and infinite-strip shapes are developed from theoretical solutions, which are used in the design of reinforced elastomeric bearings.
Journal Article•
TL;DR: In this article, the initial stiffness of semi-rigid connections under linear assumption is investigated and the fixed-end moments of semirigid beams under concentrated, uniform and linearly varying loads are obtained.
Abstract: This paper is concerned with the initial stiffness of semi-rigid connections under linear assumption The fixed-end moments of semi-rigid beams under concentrated, uniform and linearly varying loads are obtained The influence of semi-rigid connections on the internal forces of steel frame is discussed It is shown that the initial stiffness of semi-rigid connections is mainly related to the bending stiffness of the joints, thickness and location of bolts The flexibility of the connections affects the behavior of the frame It can decrease the negative end moment of beams and increase the positive moment at the mid-span of beams Thus, it is unreasonable to design under rigid connection assumption It is concluded that the semi-rigid connections should be taken into account in the analysis and design of steel frames