Showing papers on "Direct stiffness method published in 2014"
01 Feb 2014
TL;DR: In this article, the analytical equations of the time-varying mesh stiffness of a planetary gear set using the potential energy method were derived, and three simulations were conducted with a common planetary gear sets under fixed carrier, fixed ring gear, and fixed sun gear.
Abstract: Time-varying mesh stiffness is a periodic function caused by the change of the number of the contact tooth pairs and the contact positions of the gear teeth. In this study, we have derived the analytical equations of the time-varying mesh stiffness of a planetary gear set using the potential energy method. Three simulations are conducted with a common planetary gear set under fixed carrier, fixed ring gear, and fixed sun gear. The results indicate that the obtained time-varying mesh stiffness can reflect the stiffness variation, and the proposed approaches can be extended in the future to model the stiffness of a planetary gear set when faults are introduced.
108 citations
TL;DR: In this paper, the structural stiffness matrix and the total potential energy of the structure are utilized to direct the rapid convergence of the structural configuration to the self-equilibrated and stable state.
91 citations
TL;DR: In this article, a novel type of embeddable variable stiffness elements exploiting thermally-induced multi-stability in unsymmetrically laminated composites is presented.
77 citations
TL;DR: In this paper, the authors introduced the notion of rolling bearing speed-varying stiffnesses introduced and explained by studying the relations of load-deflection through the bearing dynamic model which is based on Jones & Harris's efforts.
74 citations
TL;DR: In this paper, the analytical layer-elements of a finite layer and a half-space are obtained in the transformed domain, and the corresponding solutions in the frequency domain are achieved by taking the inversion of Hankel transform.
64 citations
TL;DR: In this article, the Carrera unified formulation (CUF) is employed to derive the equations of motion through the use of a first-order layer-wise assumption for a plate with a single layer first.
60 citations
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TL;DR: In this article, the concept of zero stiffness is reviewed and categorised by the interpretation that best describes their working principle, and a basic spring-to-spring balancer is analyzed to demonstrate the equivalence of the four different interpretations.
Abstract: Zero-stiffness structures have the remarkable ability to undergo large elastic deformations without requiring external work. Several equivalent descriptions exist, such as (i) continuous equilibrium, (ii) constant potential energy, (iii) neutral stability and (iv) zero stiffness. Each perspective on zero stiffness provides different methods of analysis and design. This paper reviews the concept of zero stiffness and categorises examples from the literature by the interpretation that best describes their working principle. Lastly, a basic spring-to-spring balancer is analysed to demonstrate the equivalence of the four different interpretations, and illustrate the different insights that each approach brings.
58 citations
TL;DR: In this article, the direct stiffness method is used to construct a stiffness model of the roller screw mechanism, which allows for a better understanding of the sensitivities of stiffness and contact stresses in the mechanism with various design parameters.
Abstract: In this paper, the direct stiffness method is used to construct a stiffness model of the roller screw mechanism. This method models the entire roller screw mechanism as a large spring system composed of individual springs representing the various compliances. In addition to predicting the overall stiffness of the mechanism, the direct stiffness method can calculate the distribution of load across the threads of the individual bodies. With the load on the individual threads known, the contact stresses can be calculated. This allows for a better understanding of the sensitivities of stiffness and contact stresses in the mechanism with various design parameters and can ultimately be used to design roller screws that are stiffer and with lower contact stresses.
58 citations
TL;DR: In this article, a simple, robust and efficient stabilization technique for extended finite element (XFEM) simulations is presented, which is useful for arbitrary crack geometries in two or three dimensions that may lead to very bad condition numbers of the global stiffness matrix or even illconditioning of the equation system.
Abstract: In this contribution a simple, robust and efficient stabilization technique for extended finite element (XFEM) simulations is presented. It is useful for arbitrary crack geometries in two or three dimensions that may lead to very bad condition numbers of the global stiffness matrix or even ill-conditioning of the equation system. The method is based on an eigenvalue decomposition of the element stiffness matrix of elements that only possess enriched nodes. Physically meaningful zero eigenmodes as well as enrichment scheme dependent numerically reasonable zero eigenmodes are filtered out. The remaining subspace is stabilized depending on the magnitude of the respective eigenvalues. One of the main advantages is the fact that neither the equation solvers need to be changed nor the solution method is restricted. The efficiency and robustness of the method is demonstrated in numerous examples for 2D and 3D fracture mechanics.
55 citations
TL;DR: A novel approach is proposed for the formulation of the stiffness matrix which exhibits several computational merits, among them its amenability to parallelization and the efficient utilization of the graphics processing units to drastically accelerate computations.
51 citations
TL;DR: In this paper, a 6-degree-of-freedom (dof) parallel kinematic mechanism based on a 3xPPRS topology is proposed to achieve high end-effector tilt angles with enhanced stiffness.
Abstract: Parallel Kinematic Mechanisms (PKMs) are well suited for high-accuracy applications. However, constraints such as end-effector rotation (i.e., platform tilt angle) and configuration-dependent stiffness often limit their usage. A new six degree-of-freedom (dof) PKM architecture based on a 3xPPRS topology that addresses these concerns is presented in this paper - specifically, the proposed PKM can achieve high (end-effector) tilt angles with enhanced stiffness. The mechanism is also compared with similar three known 6-dof architectures, through which it is shown that the proposed PKM indeed exhibits higher stiffness relative to these three reference PKMs. The static stiffness is derived using matrix structural analysis, and the dynamic stiffness is obtained via finite-element analysis. A prototype of the proposed PKM that was designed and built is presented.
TL;DR: In this paper, a comprehensive analytical derivation of the response of transversely isotropic multilayered half-space subjected to time-harmonic excitations is presented in a cylindrical coordinate system.
TL;DR: In this article, the authors used the kinetostatic method for stiffness analysis of Exechon X700 and derived the Jacobian matrices of kinematics, which were used to develop the system stiffness model of the machine.
Abstract: Exechon machines are a new type of parallel kinematic machines, which have been proven experimentally to be competitive in terms of accuracy, reliability, and operation speed. The proven performance is partially contributed by its unique layout of three prismatic legs; its kinematic structure is overconstrained. Higher accuracy is a primary goal for the use of an Exechon machine; accuracy relies on system stiffness and rigidity. However, the works on the stiffness analysis of Exechon machines has been limited to some numerical results from finite element analysis; no correlation between the motions and stiffness change has been studied systematically. To gain a thorough understanding of the impact of the overconstraints on system stiffness, the kinetostatic method is used for stiffness analysis. Jacobian matrices of kinematics have been derived, and they are used to develop the system stiffness model of the machine. The Exechon X700 model has been used as a case study to illustrate the process of stiffness analysis. The stiffness model is established and quantifiable comparison has been made between simulation and test data to verify the effectiveness of the stiffness model. The developed stiffness model can be applied to optimize machine structure or trajectory planning based on the specified task.
TL;DR: A novel direct reanalysis algorithm based on finding updated triangular factorization in sparse matrix solution based on the binary tree characteristics of the global stiffness matrix derived by a graph partitioner as fill-ins’ reducer is proposed.
TL;DR: In this paper, a finite element method is presented for a nonlocal Timoshenko beam model, which relies on the key idea that nonlocal effects consist of long-range volume forces and moments exchanged by non-adjacent beam segments, which contribute to the equilibrium of a beam segment along with the classical local stress resultants.
TL;DR: In this paper, a linear variable-stiffness mechanism (LVSM) is proposed to parallel connect two lateral curved beams with an axial spring to adjust the output force-todisplacement curves.
Abstract: A machine with an internal variable-stiffness mechanism can adapt its output force to the working environment. In the literature, linear variable-stiffness mechanisms (LVSMs) are rarer than those producing rotary motion. This paper presents the design of a class of novel LVSMs. The idea is to parallel connect two lateral curved beams with an axial spring. Through preload adjustment of the curved beams, the output force-todisplacement curves can exhibit different stiffness. The merit of the proposed LVSMs is that very large-stiffness variation can be achieved in a compact space. The stiffness can even be tuned to zero by assigning the appropriate stiffness to the axial spring. LVSMs with pinned curved beams and fixed curved beams are investigated. To achieve the largest stiffness variation with sufficient linearity, the effects of various parameters on the force curves are discussed. Techniques to scale an LVSM and change the equilibrium position are introduced to increase the usefulness of the proposed design. Finally, the LVSMs are experimentally verified through prototypes. [DOI: 10.1115/1.4028705]
TL;DR: In this article, a variable stiffness mechanism is presented, which is capable of achieving an output stiffness with infinite range and an unlimited output motion, i.e., the mechanism output is completely decoupled from the rotor motion, in the zero stiffness configuration.
Abstract: In this paper, a novel variable stiffness mechanism is presented, which is capable of achieving an output stiffness with infinite range and an unlimited output motion, i.e., the mechanism output is completely decoupled from the rotor motion, in the zero stiffness configuration. The mechanism makes use of leaf springs, which are engaged at different positions by means of two movable supports, to realize the variable output stiffness. The Euler–Bernoulli leaf spring model is derived and validated through experimental data. By shaping the leaf springs, it is shown that the stiffness characteristic of the mechanism can be changed to fulfill different application requirements. Alternative designs can achieve the same behavior with only one leaf spring and one movable support pin.
06 Nov 2014
TL;DR: The possibility of using two antagonistic twisted strings actuators as a new type of variable stiffness actuator to control the position and the stiffness of the joint without position and force sensor at the load side is shown.
Abstract: This paper shows the possibility of using two antagonistic twisted strings actuators as a new type of variable stiffness actuator. Variable stiffness model of the twisted string actuator is identified empirically, and the control strategy is proposed for simultaneous position and stiffness control of the actuator. A variable stiffness linear joint actuated by antagonistic twisted string actuators is proposed as a target system. The proposed model and control strategy make it possible to control the position and the stiffness of the joint without position and force sensor at the load side. The developed variable stiffness linear joint can be effectively used in applications where weight distribution is vital, such as exoskeleton systems and low weight manipulators.
TL;DR: A stiffness reduction approach is presented, which utilises Linear Buckling Analysis and Geometrically Nonlinear Analysis in conjunction with developed stiffness reduction functions for the design of columns and beam-columns in steel frames, which provides more accurate capacity predictions than traditional design methods.
TL;DR: A novel optimization method, stiffness spreading method (SSM), is proposed for layout optimization of truss structures, in which stiffness matrices of the bar elements in a truss structure are represented by a set of equivalent stiffnessMatrices which are embedded in a weak background mesh.
Abstract: A novel optimization method, stiffness spreading method (SSM), is proposed for layout optimization of truss structures. In this method, stiffness matrices of the bar elements in a truss structure are represented by a set of equivalent stiffness matrices which are embedded in a weak background mesh. When the proposed method is used, it is unnecessary for the bar elements in a truss structure to be connected to each other during the optimization process, and each of the bar elements can move independently in the design domain to form an optimized design. Another feature of the method is that the sensitivity analysis can be done analytically, making gradient based optimization algorithms applicable in the solution. This method realizes the size, shape and topology design optimization of truss structures simultaneously and allows for more flexibility in topology change. Numerical examples illustrate the feasibility and effectiveness of the proposed method.
TL;DR: In this paper, a mixed-grid finite element method (MGFEM) is proposed to simulate seismic wave propagation in 2D structurally complex media, which divides the physical domain into two subdomains.
Abstract: We have developed a mixed-grid finite element method (MGFEM) to simulate seismic wave propagation in 2D structurally complex media. This method divides the physical domain into two subdomains. One subdomain covering the major part of the physical domain is divided by regular quadrilateral elements, while the other subdomain uses triangular elements to correctly fit a rugged free surface topography. The local stiffness matrix of any quadrilateral element is identical and matrix-vector production is calculated using an element-by-element technique, which avoids assembling a huge global stiffness matrix. As only a few triangular elements exist in the subdomain containing the rugged free surface topography, the memory requirements for storing the assembled subdomain global stiffness matrix are significantly reduced. To eliminate artificial boundary reflections, the MGFEM is also implemented to solve the system equations of PML absorbing boundary conditions (PML ABC). The accuracy and efficiency of the MGFEM is tested in numerical experiments by comparing it with conventional methods, and numerical comparisons also indicate its tremendous ability to describe rugged surfaces.
TL;DR: In this paper, an advanced thin-walled girder theory based on the modified Timoshenko beam theory for flexural vibrations with analogical extension to the torsional problem is used for formulation of the beam finite element for analysis of coupled horizontal and torsion ship hull vibrations.
TL;DR: In this paper, the authors presented a design methodology to determine spring configuration on a statically balanced planar articulated manipulator by formulating similar representation of matrix form, the equilibrium equation is simplified as the summation of gravitational stiffness block matrix and elastic stiffness block matrices remain unchanged.
TL;DR: In this article, a new numerical analysis procedure is presented for the nonlinear analysis of structures, which relies on the natural evolution of localized inelastic quantities within the element, that is, the plastic deformation evaluated at properly defined collocation points rather than the evaluation of global and varying state matrices.
Abstract: A new numerical analysis procedure is presented for the nonlinear analysis of structures. The proposed methodology is developed within the framework of the direct stiffness method and the hysteretic formulation of finite elements. The derived numerical scheme relies on the natural evolution of localized inelastic quantities within the element, that is, the plastic deformation evaluated at properly defined collocation points rather than the evaluation of global and varying state matrices. This is accomplished by considering the additive decomposition of the total strain rate into elastic and plastic parts. Using the principle of virtual work, an equilibrium expression is derived in which the total applied load is equilibrated by an elastic internal force vector and an additional term acting as a nonlinear correction to the elastic component. The evolution of the plastic components is based on a smooth multiaxial hysteretic law that is derived within the framework of classical plasticity. Examples are presented that demonstrate the validity of the proposed method and its computational advantages with respect to existing methods of inelastic analysis.
Patent•
25 Aug 2014
TL;DR: In this paper, a method and system for determining at least one property associated with a selected axis of a manipulator (2) is presented, where the elasticity of the links (4, 6, 9, 10, 13, 14) and joints (3, 5, 7, 8, 11, 12) are modeled and the resulting compliance can be determined.
Abstract: A method and system for determining at least one property associated with a selected axis of a manipulator (2). The elasticity of the links (4, 6, 9, 10, 13, 14) and joints (3, 5, 7, 8, 11, 12) of a manipulator (2) can be modeled and the resulting compliance can be determined. A certain method is used to control the manipulator (2) such that certain quantities related to actuator torque and/or joint position can be determined for a certain kinematic configuration of the manipulator (2). Depending on the complexity of the manipulator (2) and the number of properties that are of interest, the manipulator (2) is controlled to a plurality of different kinematic configurations in which configurations the quantities are determined. Thereafter, a stiffness matrix (K) for each component of the manipulator (2) can be determined, and a global stiffness matrix (MSM) for the total manipulator (2) can be determined in order to determine at least one property of the selected axis.
08 Dec 2014
TL;DR: In this paper, a nonlinear constrained structural optimization is proposed for static damage detection of three-and two-dimensional frames based on the minimization of difference between the measured and analytical static displacements of frames.
Abstract: A new algorithm for static damage detection of three- and two-dimensional frames is presented in this paper. This approach is based on the minimization of difference between the measured and analytical static displacements of frames. The damage detection problem is solved as a nonlinear constrained structural optimization. In this strategy, the global structural stiffness matrix is parameterized. To achieve the goal, a new technique based on the eigen decomposition of the local elemental stiffness matrix is suggested. Structural damage is modeled as a reduction in cross-sectional properties of the elements. It is assumed that the stiffness matrix of the structure is perturbed due to damage. Hence, the damaged structural stiffness matrix is presumed to be the sum of the stiffness matrix of the undamaged structure and the perturbation matrix. Consequently, the sum of these matrices should be inverted in each iteration. Instead of the common ways of inversion, Sherman–Morrison–Woodbury formula is employed. P...
TL;DR: In this article, an explicit numerical manifold method (NMM) was proposed for large-scale rock mass stability analysis, where the accelerations by the corresponding physical covers are solved explicitly without forming a global stiffness matrix.
Abstract: The traditional numerical manifold method (NMM) has the advantage of simulating a continuum and a discontinuum in a unified framework based on a dual cover system. However, since an implicit time integration algorithm is used, the computational efficiency of the original NMM is very low, especially when more contacts are involved. The present study proposes an explicit version of the NMM. Since a lumped mass matrix is used for the manifold element, the accelerations by the corresponding physical covers can be solved explicitly without forming a global stiffness matrix. The open–close iteration is still applied to ensure computational accuracy. The developed method is first validated by two examples, and a highly fractured rock slope is subsequently simulated. Results show that the computational efficiency of the proposed explicit NMM has been significantly improved without losing the accuracy. The explicit NMM is more suitable for large-scale rock mass stability analysis and it deserves to be further developed for engineering computations in rock engineering.
TL;DR: In this article, a dynamic analysis of a stiffened cylindrical shell using the Dynamic Stiffness Method, also known as the Continuous Element Method, is presented, which is based on the determination of the dynamic stiffness matrix of an unmeshed structure.