Showing papers on "Direct stiffness method published in 2016"

Stiffness analysis of parallelogram-type parallel manipulators using a strain energy method

Abstract: Although stiffness analyses of specific parallelogram-type parallel manipulators (PTPMs) have been presented by several researchers, an algebraic expression is still needed to obtain the stiffness of a general PTPM. To address this issue, this paper uses a strain energy method considering the compliances of the mobile platform, the limb and the actuator of a PTPM. In this method, the deformation of the mobile platform, which has typically been ignored by many researchers, is integrated in the total deformation of the PTPM. After comparison with a FEA method, it is found that the proposed algebraic method is a comparable alternative to the FEA method to be used in the pre-design stage. Additionally, a new stiffness index is proposed to evaluate the stiffness property. Compared with other stiffness indices, the new index uses virtual work to unify the units of translation and orientation and relates the index value to the direction of the wrench experienced by a parallel manipulator in a task. With this index, the resistance of a PTPM to deformation under a given wrench can be measured easily. Stiffness analysis of a general PTPM using an algebraic method.Result comparison between the proposed method and a finite element analysis method.A new stiffness index relating the stiffness property to the wrench experienced in a task.

Kinetostatic-model-based stiffness analysis of Exechon PKM

Abstract: As a comparative newly-invented PKM with over-constraints in kinematic chains, the Exechon has attracted extensive attention from the research society Different from the well-recognized kinematics analysis, the research on the stiffness characteristics of the Exechon still remains as a challenge due to the structural complexity In order to achieve a thorough understanding of the stiffness characteristics of the Exechon PKM, this paper proposed an analytical kinetostatic model by using the substructure synthesis technique The whole PKM system is decomposed into a moving platform subsystem, three limb subsystems and a fixed base subsystem, which are connected to each other sequentially through corresponding joints Each limb body is modeled as a spatial beam with a uniform cross-section constrained by two sets of lumped springs The equilibrium equation of each individual limb assemblage is derived through finite element formulation and combined with that of the moving platform derived with Newtonian method to construct the governing kinetostatic equations of the system after introducing the deformation compatibility conditions between the moving platform and the limbs By extracting the 6×6 block matrix from the inversion of the governing compliance matrix, the stiffness of the moving platform is formulated The computation for the stiffness of the Exechon PKM at a typical configuration as well as throughout the workspace is carried out in a quick manner with a piece-by-piece partition algorithm The numerical simulations reveal a strong position-dependency of the PKM's stiffness in that it is symmetric relative to a work plane due to structural features At the last stage, the effects of some design variables such as structural, dimensional and stiffness parameters on system rigidity are investigated with the purpose of providing useful information for the structural optimization and performance enhancement of the Exechon PKM It is worthy mentioning that the proposed methodology of stiffness modeling in this paper can also be applied to other overconstrained PKMs and can evaluate the global rigidity over workplace efficiently with minor revisions An kinetostatic model for Exechon is established with substructure synthesisThe compliances of all joints and limb bodies are considered in the modelThe stiffness matrix of moving platform is formulated conciselyThe stiffness distributions throughout the workspace are predicted efficientlyThe effects of variables on stiffness are studied to provide design guidances

Development of an efficient algorithm to analyze the elastic wave in acoustic metamaterials

Abstract: A novel modified edge-based smoothed finite element method (modified ES-FEM) is developed to compute the band gap of acoustic metamaterials. The stiffness in the modified ES-FEM is created by the edge-based smoothed finite element method (ES-FEM) which is aimed at softening the overly stiffness of standard finite element method (FEM). On the other hand, the mass matrix is constructed by mass-redistributed method to tune the balance between the smoothed stiffness and mass matrix. The present modified ES-FEM adopts linear triangular elements generated automatically, which enables automation in computation and saving computational cost in mesh generation. Two numerical examples are presented to verify the computational efficiency of the modified ES-FEM. The numerical results have clearly demonstrated that the modified ES-FEM is very effective to minimize the dispersion errors in the simulation of band gap of acoustic metamaterials.

Ultra-efficient wound composite truss structures

Abstract: This paper presents the design, analysis, manufacturing, experimental testing, and multiobjective optimization of a new family of ultra-efficient composite truss structures. The continuously wound truss concept introduced here is a versatile, low cost and scalable method of manufacturing truss structures based on a simple winding process. A prototype truss configuration is shown and experimentally characterized under torsion and three point bending loads. A large deformation implementation of the direct stiffness method is shown to provide good prediction of the stiffness properties of the prototype truss. This model is extended to include strength prediction with multiple failure modes. The design space achievable with these truss structures is then explored through multiobjective optimization using the NSGA II genetic algorithm. These continuously wound truss structures have the potential to provide between one and two orders of magnitude increase in structural efficiency compared to existing carbon fiber composite tubes.

Train-Track-Bridge Interaction by Coupling Direct Stiffness Method and Mode Superposition Method

Abstract: In this study, a track-bridge model was proposed by combining the direct stiffness method (DSM) and the mode superposition method (MSM) for analysis of the train-track-bridge interaction. The tracks were modeled by applying DSM, which can effectively display the nonlinear contact spring and the dynamic behavior of the tracks. The bridge was modeled by applying MSM, a method that can efficiently show dynamic behavior with a small number of modes. The analysis model was built based on a previously proposed train-track analysis model. Consequently, the train, track, and bridge were modeled as a coupled system that was interconnected by nonlinear Hertzian springs between the train and track, and springs and dampers between the track and bridge. Thus, the convergence is greatly improved as a result of the stabilization of the analytical system. Using the proposed train-bridge-track interaction analysis model, the impacts of the vertical displacements of the bridge resulting from thermal load on the dyn...

A new top-down design method for the stiffness of precision machine tools

Abstract: This work describes a new top-down design method for the stiffness of precision machine tools that considers the entire machine stiffness to guarantee the stiffness requirements in the initial design stage A stiffness modelling method and a stiffness matching design method are presented to achieve the top-down design of the stiffness A new stiffness characterisation using the stiffness coefficients for characterising the stiffness of the structural parts and the functional units is proposed The deformation model of the entire machine is established based on multi-body system theory, and the equations of the stiffness coefficients for the deformations of the components are established based on the simultaneous equations of the static equilibrium equations, the deformation compatibility equations and the physical equations The three-direction (3D) stiffness model is obtained by substituting the equations into the deformation model that reflects the stiffness characteristics of the machine tool Thus, the reliability of the stiffness model is verified by experiments Next, the stiffness matching design is performed to confirm the reasonable stiffness values of the parts based on the stiffness model The finite element method (FEM) is used to validate the proposed method The contribution rate of the stiffness of the parts to the stiffness of the entire machine is analysed

Jacobian-based stiffness analysis method for parallel manipulators with non-redundant legs:

Abstract: Stiffness is an important element in the model of a parallel manipulator. A complete stiffness analysis includes the contributions of joints as well as structural elements. Parallel manipulators po...

Aeroelastic response of a selectively compliant morphing aerofoil featuring integrated variable stiffness bi-stable laminates

Abstract: Distributed compliance systems with integrated variable stiffness elements show great promise for reconciling the conflicting requirements of morphing. The distinct structural properties of each equilibrium configuration allow bi-stable laminates to provide stiffness variability in a purely elastic, energy-efficient manner. This article presents a novel morphing concept based on a distributed arrangement of embeddable variable stiffness bi-stable composites inside a 500 mm chord NACA 0012 profile (where ‘NACA’ is the National Advisory Committee for Aeronautics). The structural response of the aerofoil is assessed numerically and experimentally, with a particular focus on the global stiffness modification potential via the snap-through of the component laminates. Extending the validated finite element models to include a weak static aeroelastic coupling permits evaluation of the aerodynamic adequacy of the final, passively morphed shapes. This concurrent aero-structural methodology is finally employed to d...

Discrete approaches for the nonlinear analysis of in plane loaded masonry walls: Molecular dynamic and static algorithm solutions

Abstract: The aim of the paper is to present and validate a non commercial discrete element model (DEM) code for the nonlinear analysis of in plane loaded masonry panels, with dry or mortar joints. Such model is based on the hypothesis of rigid blocks and joints modeled as interfaces, that turn out to be both suitable for representing the behavior of ancient masonry, characterized by joint size negligible with respect to block size and block stiffness larger than joint stiffness. Hence, the elastic and inelastic behavior of a masonry assemblage is concentrated at joints by defining their stiffness and adopting a Mohr-Coulomb law as a restraint for interfacial actions. The proposed strategy is based on two approaches: a static solution method and a molecular dynamics algorithm. The static solution method allows to determine the stiffness matrix of a masonry panel and to update such matrix accounting for actual joint stiffness and blocks arrangement. Such method turns out to be computationally faster and equally effective with respect to the molecular dynamics one for performing incremental analysis of in plane loaded masonry panels. On the other hand, the molecular dynamics method is computationally less onerous than the static solution method, since it does not require to define and update panel stiffness matrix and to invert it for determining displacements. Both approaches are used and critically compared for solving several case studies of masonry panels modeled by DEM. In addition, it must be pointed out that results in terms of ultimate loads and collapse mechanisms are in good agreement with existing experimental data and numerical solutions.

In situ determination of dynamic stiffness for resilient elements

Abstract: An in situ method for the measurement of a resilient lements dynamic transfer stiffness is outlined and alidated. Unlike current methods, the proposed in situ approach allows for the characterisation of a resilient element whilst incorporated into an assembly, and therefore under representative mounting conditions. Potential advantages of the proposed method include the simultaneous attainment of both translational and rotational transfer stiffness components over a broad frequency range without the need for any cumbersome test rigs. These rotational components are obtained via the application of a finite difference approximation. A further advantage is provided via an extension to the method allowing for the use of remote measurement positions. Such an extension allows for the possible characterisation of hard-to reach elements, as well as the over-determination of the problem. The proposed method can thus be broken into two sub-methods: direct and remote. Preliminary results are shown for the direct method on a simple mass-isolator-mass laboratory test rig along with a more realistic beam-isolator-plate system. Validation of this method is provided for by a transmissibility prediction, in which an obtained dynamic stiffness value is used to predict the transmissibility of a separate system. Further results are presented for the remote case using a beam-isolator-plate system. In all cases the results are obtained over a substantial frequency range and are of a sufficient quality to be used as part of structure borne sound and vibration predictions.

Analytical layer-element approach for wave propagation of transversely isotropic pavement

Abstract: Asphalt pavements have been recognised as transversely isotropic multi-layered structures. In this paper, an analytical layer-element approach is utlised to solve the wave propagation of transversely isotropic multi-layered pavement structures under the falling weight deflectometer impact load. After the application of Fourier–Hankel transform, the Navier's equation for transversely isotropic layer by impulsive force are solved analytically. The global stiffness matrix equation of multilayered structures is further obtained by assembling the interrelated layer-elements, and the actual solution is achieved by numerical inversion of the Fourier–Hankel transform after the solution in the transformed domain is obtained. The layer-element of a single layer and the global stiffness matrix only contain negative exponential functions, which leads to a considerable improvement in computation efficiency and stability. Numerical examples are presented to demonstrate the accuracy of this method and to inversitgate the...

Second-Order Direct Analysis of Domelike Structures Consisting of Tapered Members with I-Sections

Abstract: A new and advanced beam-column element, namely the curved tapered-three-hinges (TTH) beam-column element, is proposed in this paper. The present element can perform large deformation analysis and explicitly simulate the initial member curvature, which is essential for the second-order direct analysis using one-element-per-member models. Another distinct feature of the element is to analytically express the flexural rigidity of tapered I-sections in the stiffness matrix through a series of tapered stiffness factors such as the αi and βi factors. Unlike the conventional models using the approximated distributions (e.g., linear, parabolic, or cubic) or stepped-elements modeling approaches in an analysis, the present study gives an accurate simulation solution on nonprismatic beam-column elements. Herein, the element derivations and formulations are given in detail. To consider the large deflection effect in the analysis, the incremental tangent stiffness method is adopted and the kinematic descriptio...

Research on the low frequency band gap properties of periodically composite stiffened thin-plate with fillers

Abstract: In this paper, a new composite stiffened thin-plate (CSTP) is developed, the filler is distributed periodically in the viscoelastic damping material (VDM), and the simplified-super-finite-element (SSFM) is employed in the analysis. According to the periodical properties of the CSTP, a primitive cell is extracted, which is divided into six parts according to n-order Lagrangian element (LgE). After each parts’ mass, stiffness and damping matrices are obtained, the global matrices are assembled by standard direct stiffness method (SDSM). The filler's mass is considered as lump mass loaded on the defined LgE's nodes, and the filler's number is determined by the LgE's order. Then, the element matrices are simplified and compressed by Bloch's theorem. Finally, the band gap properties of the CSTP are determined according to the eigenvalues problems, and the parameters of the structures (such as the filler's mass, the VDM's damping ratio and the lattice constant, etc.) which affect the band gaps are examined thoroughly. The results show the existence of full band gap (FBG) in low frequency. Meanwhile, the results are validated by the finite element method (FEM), which show good consistency.

Dynamic blocked transfer stiffness method of characterizing the magnetic field and frequency dependent dynamic viscoelastic properties of MRE

Abstract: Magneto rheological elastomer (MRE) is a potential resilient element for the semi active vibration isolator. MRE based isolators adapt to different frequency of vibrations arising from the source to isolate the structure over wider frequency range. The performance of MRE isolator depends on the magnetic field and frequency dependent characteristics of MRE. Present study is focused on experimentally evaluating the dynamic stiffness and loss factor of MRE through dynamic blocked transfer stiffness method. The dynamic stiffness variations of MRE exhibit strong magnetic field and mild frequency dependency. Enhancements in dynamic stiffness saturate with the increase in magnetic field and the frequency. The inconsistent variations of loss factor with the magnetic field substantiate the inability of MRE to have independent control over its damping characteristics.

Interactively Cutting and Constraining Vertices in Meshes Using Augmented Matrices

Abstract: We present a finite-element solution method that is well suited for interactive simulations of cutting meshes in the regime of linear elastic models. Our approach features fast updates to the solution of the stiffness system of equations to account for real-time changes in mesh connectivity and boundary conditions. Updates are accomplished by augmenting the stiffness matrix to keep it consistent with changes to the underlying model, without refactoring the matrix at each step of cutting. The initial stiffness matrix and its Cholesky factors are used to implicitly form and solve a Schur complement system using an iterative solver. As changes accumulate over many simulation timesteps, the augmented solution method slows down due to the size of the augmented matrix. However, by periodically refactoring the stiffness matrix in a concurrent background process, fresh Cholesky factors that incorporate recent model changes can replace the initial factors. This controls the size of the augmented matrices and provides a way to maintain a fast solution rate as the number of changes to a model grows. We exploit sparsity in the stiffness matrix, the right-hand-side vectors and the solution vectors to compute the solutions fast, and show that the time complexity of the update steps is bounded linearly by the size of the Cholesky factor of the initial matrix. Our complexity analysis and experimental results demonstrate that this approach scales well with problem size. Results for cutting and deformation of 3D linear elastic models are reported for meshes representing the brain, eye, and model problems with element counts up to 167,000; these show the potential of this method for real-time interactivity. An application to limbal incisions for surgical correction of astigmatism, for which linear elastic models and small deformations are sufficient, is included.

Fast MATLAB assembly of FEM matrices in 2D and 3D using cell-array approach

Abstract: We propose a MATLAB implementation of the P1 finite element method for the numerical solutions of the Poisson problem and the linear elasticity problem in two-dimensional (2D) and three-dimensional (3D). The code consists of vectorized (and short) assembling functions for the matrices (mass and stiffness) and the right-hand sides. Since for the P1 finite element, the element mass matrix and right-hand side are simple, the implementation uses only the MATLAB function sparse on the elements volume. For the stiffness matrix, to obtain a MATLAB implementation close to the standard form, cell-arrays are used to store the gradients of the element basis functions. The assembling procedure can then use matrix/vector products on small size cell-arrays. Numerical experiments show that our implementation is fast, scalable with respect to time, and outperforms existing vectorized MATLAB FEM codes.