Number Of DOF Research Articles

Grid Convergence Study of Spectral Volume Method for Hybrid Unstructured Mesh

Grid convergence characteristics of the spectral volume (SV) method is explored for hybrid unstructured meshes. In this study, the SV method originally developed for tetrahedral computational cells is extended to use prismatic and hexahedral cells. The extended SV method (hereafter SV+) for hybrid unstructured mesh is first applied to solve the linear advection and diffusion problems. The formal spatial accuracy is rigorously kept in both problems. Then, the SV+ is applied to solve the turbulent boundary layer flow over a flat plate. It is shown that the SV+ can obtain grid convergence even for using tetrahedral cells in the turbulent boundary layer, where the mesh aspect ratio becomes as large as 20,000. Convergence toward steady solutions using prismatic layers with the same number of DOFs becomes about two times faster than that using tetrahedral cells in the turbulent boundary layer. Finally, the SV+ is applied to compute the flowfield around the NASA-CRM. It is shown that the present SV+ gives mesh converged solutions which quantitatively agree with the corresponding experimental data regardless of mesh type.

Numerical study of ITZ contribution on diffusion of chloride and induced rebar corrosion: A discussion of three-dimensional multiscale approach

Modeling approach for mesoscopic model of concrete depicting mass transportation and physicochemical reaction is important since there is growing demand for accuracy and computational efficiency of numerical simulation. Mesoscopic numerical simulation considering binder, aggregate and interfacial transition zone (ITZ) generally produces huge number of DOFs, which is inapplicable for full structure. In this paper, a three-dimensional multiscale approach describing three-phase structure of concrete was discussed numerically. An effective approach generating random aggregate in polygon based on checking centroid distance and intersection of line segment was introduced. Moreover, ITZ elements were built by parallel expanding the surface of aggregates on inner side. By combining mesoscopic model including full-graded aggregate and macroscopic model, cases related to diffusivity and thickness of ITZ, volume fraction and grade of aggregate were studied regarding the consideration of multiscale compensation. Result clearly showed that larger analysis model in multiscale model expanded the diffusion space of chloride ion and decreased chloride content in front of rebar. Finally, this paper addressed some worth-noting conclusions about the chloride distribution and rebar corrosion regarding the configuration of, rebar diameter, concrete cover and exposure period.

Numerical Study on Diffusion of Chloride and Induced Rebar Corrosion by Two-Dimensional Multiscale Approach

Modeling approach for mesoscopic model of concrete depicting mass transportation and physicochemical reaction is important since there is growing demand for accuracy and computational efficiency of numerical simulation. Mesoscopic numerical simulation considering binder, aggregate, and interfacial transition zone (ITZ) generally produces huge number of DOFs, which is inapplicable for full structure. In this paper, a two-dimensional multiscale approach describing three-phase structure of concrete was discussed numerically. An effective approach generating random aggregate in polygon based on checking centroid distance and intersection of line segment was introduced. Moreover, ITZ elements were built by parallel expanding the edge of aggregates on inner side. By combining mesoscopic model including full-graded aggregate and macroscopic model, cases related to diffusivity and width of ITZ, volume fraction, and grade of aggregate were studied regarding the consideration of multiscale compensation. Result clearly showed that larger analysis model in multiscale model expanded the diffusion space of chloride ion and decreased chloride content in front of rebar. Finally, this paper addressed some noteworthy conclusions about the chloride distribution and rebar corrosion regarding the configuration of rebar diameter, concrete cover, and exposure period.

Robot Lengan Pemindah Barang Otomatis Berbasis Arduino Menggunakan Sensor Warna

Robot arm transporter using Arduino-based sensor auto color, a tool designed to this aim to reduce human role in a grouping or sorting goods with the sort tool so that it can minimize the influence of inconsistencies humans in the event. This tool as well as a simulation as well as the media of instruction. Methods of data analysis used IE needs analysis that includes software that is the OS, and the Arduino Software, and hardware in the form of a Laptop, Arduino, Sensor, RGB, and Servo Motor. From the results of testing that has been done can be inferred that this Robot can run well at a time when reading the color box and put the table by the location of their vessels. The conclusion of the tool is designed as a common transport good; the robotic arm can be applied using several servos in the number of dof.

An adaptive space-time shock capturing method with high order wavelet bases for the system of shallow water equations

PurposeThis paper aims to propose an adaptive method for the numerical solution of the shallow water equations (SWEs). The authors provide an arbitrary high-order method using high-order spline wavelets. Furthermore, they use a non-linear shock capturing (SC) diffusion which removes the necessity of post-processing.Design/methodology/approachThe authors use a space-time weak formulation of SWEs which exploits continuous Galerkin (cG) in space and discontinuous Galerkin (dG) in time allowing time stepping, also known as cGdG. Such formulations along with SC term have recently been proved to ensure the stability of fully discrete schemes without scarifying the accuracy. However, the resulting scheme is expensive in terms of number of degrees of freedom (DoFs). By using natural adaptivity of wavelet expansions, the authors devise an adaptive algorithm to reduce the number of DoFs.FindingsThe proposed algorithm uses DoFs in a dynamic way to capture the shocks in all time steps while keeping the representation of approximate solution sparse. The performance of the proposed scheme is shown through some numerical examples.Originality/valueAn incorporation of wavelets for adaptivity in space-time weak formulations applied for SWEs is proposed.

Analysis of isotropic and composite laminated plates and shells using a differential quadrature hierarchical finite element method

A p-version curved composite laminated shell element has been developed using the modified high order bases of a differential quadrature hierarchical finite element method (DQHFEM). The theoretical model of the shell is based on a layerwise theory with linear expansion in each layer. Exact geometry is established using the CAD technique of Non-Uniform Rational B-splines. As a result, the FEM discretization errors of geometry are eliminated. To solve the coupling difficulty of elements with different parameterization that commonly exists in complicated models, a novel method based on interpolation on arc length coordinates is proposed in this work. Even though the computational efficiency based on a layerwise theory is not as fast as those based on the equivalent single-layer theory, it produces as accurate results as the 3D theory and uses less DOFs as well as less input data than the 3D model. Additionally, because of the high convergence rate of the p-version FEM and the exact representation of the geometric model, the present elements are expected to produce more accurate results than the conventional h-version flat shell elements with the same number of DOFs. Numerical examples are provided to illustrate the accuracy as well as versatility of the present elements.

Hybrid Isogeometric-Finite Element Discretization Applied to Stress Concentration Problems

Isogeometric analysis (IGA) employs non-uniform rational B-splines (NURBS) or other B-spline-based variants to represent both the geometry and the field variable. Exact geometry representation and higher order global continuity (at least [Formula: see text] even on elements’ boundaries) are two favorable properties that would make IGA an appropriate discretization technique in problems with responses associated with the derivatives of the primary field variable. As a category of these problems, in this paper, 2D elastostatic problems involving stress concentration sites are analyzed with a hybrid isogeometric-finite element (IG-FE) discretization. To exploit higher order continuity of NURBS basis functions, IGA discretization is applied selectively at pre-identified locations of high displacement gradients where the stress concentration occurs. In addition, considering computational efficiency, the rest of problem domain is discretized by means of linear Lagrangian finite elements. The connection of NURBS and Lagrangian domain is carried out through employing specially devised elements [Corbett, C. J. and Sauer, R. A. [2014] “NURBS-enriched contact finite elements”, Computer Methods in Applied Mechanics and Engineering 275, 55–75]. The methodology is applied in some 2D elastostatic examples. Increasing the number of DOFs and comparing convergence of the concentrated stress value using different discretizations, it is shown that the hybrid IG-FE discretizations generally have faster and more stable convergence response compared with pure FE discretizations especially at lower DOFs.

On the Comprehensive Kinematics Analysis of a Humanoid Parallel Ankle Mechanism

In this paper, we present a thorough kinematics analysis of a humanoid two degrees-of-freedom (DoF) ankle module based on a parallel kinematics mechanism. Compared with the conventional serial configuration, the parallel kinematics ankle permits the distribution of the torque/power of the actuators to the two DoF of the ankle taking full advantage of available power/torque capacity of the two actuators. However, it complicates the kinematics study in return. In this work, a complete study of a parallel ankle mechanism is performed that permits the full characterization of the ankle module for the purpose of its design study, control, and performance evaluation. Screw theory is employed for mobility analysis to first determine the number and properties of the mechanism's DoFs. Then the inverse kinematics is solved analytically and the Jacobian matrix for describing the velocity relation between the ankle joints and motors is found. Based on these results, the forward kinematics of the parallel mechanism can be numerically computed using the Newton–Raphson method. The workspace of the ankle is also analyzed and the motor limits are decided accordingly. Finally, an experimental demonstration consisting of four tests is carried out to evaluate the proposed methods and ankle module.

Mesh convergence study and estimation of discretization error of hub in clutch disc with integration of ANSYS

Structural analysis is an essential tool for design engineers. Mesh generation is the basic step in any simulation. In practice of finite-element stress analysis, the engineer first needs to know if key stresses are converging, and second if they have converged to a reasonable level of accuracy. In order to achieve results that are reliable when using the finite element method, it must be ensured that an acceptable mesh is used with respect to the shape and size of the elements. Mesh quality and mesh density values are directly linked with the solution accuracy. This paper presents a mesh convergence study on the hub which is the most challenging part in the automotive clutch disc assembly. Finite element analysis convergence defines the relationship between the number of elements or DOF and the analysis accuracy. Discretization error is key concept for the study of mesh convergence study, also discretization is function of number of degree of freedom of model. A detailed comparison of different results is carried out using convergence test based on displacement and energy norms. Error between exact and ANSYS results are compared in this study.

Subspace exclusion zones for damage localization

If a subdomain of a structural system is introduced to a perturbation, the resulting shifts in any field quantity outside the boundary of some closed region encompassing the perturbation can be generated from stress fields acting on the aforementioned boundary. In the present paper, this is exploited in the context of structural damage localization to cast the Subspace Exclusion Zone (SEZ) scheme, which locates damage by inspecting the feasibility of generating the observed shifts from actions acting at the boundary of the postulated zones in a model of the structure in question. As such, the SEZ scheme is a forward interrogation that allows for a user-defined localization resolution and, under certain input conditions, operates without the use of system identification. The approach is most conveniently implemented in the Laplace domain and holds at s-values for which the load vector in the reference and the damaged states are proportional. The constraint that ensures exact results in an idealized model context is that the number of measurements outside any considered exclusion zone (EZ) exceeds the number of DOF on its boundary. It is shown, however, that useful results can be obtained with notably smaller sensor counts. The paper illustrates application of the SEZ scheme in simulations and in an experimental setting using a beam subjected to harmonic input.

An isogeometric formulation of the Koiter’s theory for buckling and initial post-buckling analysis of composite shells

Numerical formulations of the Koiter theory allow the efficient prediction, through a reduced model, of the behavior of shell structures when failure is dominated by buckling. In this work, we propose an isogeometric version of the method based on a solid-shell model. A NURBS interpolation is employed on the middle surface of the shell to accurately describe the geometry and the high continuity typical of the displacement field in buckling problems and to directly link the CAD model to the structural one. A linear interpolation is then adopted through the thickness together with a modified generalized constitutive matrix, which allows us to easily eliminate thickness locking and model multi-layered composites. Reduced integration schemes, which take into account the continuity of the shape functions, are used to avoid interpolation locking and make the integration faster. A Mixed Integration Point strategy makes it possible to transform the displacement model into a mixed (stress–displacement) one, required by the Koiter method to obtain accurate predictions, without introducing stress interpolation functions. The result is an efficient numerical tool for buckling and initial post-buckling analysis of composite shells, characterized by a low number of DOFs and integration points and by a simple and quick construction of the reduced model.

A multiscale numerical simulation approach for chloride diffusion and rebar corrosion with compensation model

Refined analysis depicting mass transportation and physicochemical reaction and reasonable computing load with acceptable DOFs are the two major challenges of numerical simulation for concrete durability. Mesoscopic numerical simulation for chloride diffusion considering binder, aggregate and interfacial transition zone is unable to be expended to the full structure due to huge number of DOFs. In this paper, a multiscale approach of combining both mesoscopic model including full-graded aggregate and equivalent macroscopic model was introduced. An equivalent conversion of chloride content at the Interfacial Transition Layer (ITL) connecting both models was considered. Feasibility and relative error were discussed by analytical deduction and numerical simulation. Case study clearly showed that larger analysis model in multiscale model expanded the diffusion space of chloride ion and decreased chloride content in front of rebar. Difference for single-scale simulation and multiscale approach was observed. Finally, this paper addressed some worth-noting conclusions about the chloride distribution and rebar corrosion regarding the configuration of rebar placement, rebar diameter, concrete cover and exposure period.

Non-symmetric forms of non-linear vibrations of flexible cylindrical panels and plates under longitudinal load and additive white noise

Parametric non-linear vibrations of flexible cylindrical panels subjected to additive white noise are studied. The governing Marguerre equations are investigated using the finite difference method (FDM) of the second-order accuracy and the Runge-Kutta method. The considered mechanical structural member is treated as a system of many/infinite number of degrees of freedom (DoF). The dependence of chaotic vibrations on the number of DoFs is investigated. Reliability of results is guaranteed by comparing the results obtained using two qualitatively different methods to reduce the problem of PDEs (partial differential equations) to ODEs (ordinary differential equations), i.e. the Faedo-Galerkin method in higher approximations and the 4th and 6th order FDM. The Cauchy problem obtained by the FDM is eventually solved using the 4th-order Runge-Kutta methods. The numerical experiment yielded, for a certain set of parameters, the non-symmetric vibration modes/forms with and without white noise. In particular, it has been illustrated and discussed that action of white noise on chaotic vibrations implies quasi-periodicity, whereas the previously non-symmetric vibration modes are closer to symmetric ones.

Nonlinear time-varying dynamic analysis of a spiral bevel geared system

In this paper, a nonlinear time-varying dynamic model of a drivetrain composed of a spiral bevel gear pair, shafts and bearings is developed. Gear shafts are modeled by utilizing Timoshenko beam finite elements, and the mesh model of a spiral bevel gear pair is used to couple them. The dynamic model includes the flexibilities of shaft bearings as well. Gear backlash and time variation of mesh stiffness are incorporated into the dynamic model. Clearance nonlinearity of bearings is assumed to be negligible, which is valid for preloaded rolling element bearings. Furthermore, stiffness fluctuations of bearings are disregarded. Multi-term harmonic balance method (HBM) is applied on the system of nonlinear differential equations in order to obtain a system of nonlinear algebraic equations. Utilizing receptance method, system of nonlinear algebraic equations is grouped in nonlinear and linear sets of algebraic equations where the nonlinear set can be solved alone decreasing the number of equations to be solved significantly. This reduces the computational effort drastically which makes it possible to use finite element models for gear shafts. In the calculation of Fourier coefficients, continuous-time Fourier transform as opposed to the gear dynamics studies that utilize discrete Fourier Transform is used. Thus, convergence problems that arise when the number of nonlinear DOFs is large are avoided. Moreover, analytical integration is employed for the calculation of Fourier coefficients rather than numerical integration in order to further reduce the computational time required. Nonlinear algebraic equations obtained are solved by utilizing Newton’s method with arc-length continuation. Direct numerical integration is employed to verify the solutions obtained by HBM. Several case studies are carried out, and the influence of backlash amount, fluctuation of gear mesh stiffness and variation of bearing stiffness are investigated. In addition to these, the response of the coupled gear system model is compared with that of gear torsional model in order to study the influence of the coupling on dynamics of the system.

A Reconfigurable Gripper for Dexterous Manipulation in Flexible Assembly

In this paper, a high-speed multi-fingered reconfigurable gripper is presented. The aim is to create a robotic end effector that is capable of handling parts of different geometries and weight. It consists of three fingers, accounting for a total of eight Degrees of Freedom (DoFs). The paper discusses the design, control, and reconfiguration aspects of the gripper, and demonstrates its applicability to different manipulation tasks. The gripper has the ability of high-force movement and its high number of DoFs enables it to grasp a large variety of geometries, while retaining the design simplicity. The preliminary grasping experiments highlight its potential in robotic handling applications in both research and production environments.

ALGORITHM OF EULER-LAGRANGE METHOD FOR DEISGNING OF DYNAMIC MODEL

Urgency of the research. Nowadays robotics and mechatronics come to be mainstream. With development in these areas also grow computing fastidiousness. Since there is significant focus on numerical modeling and algorithmization in kinematic and dynamic modeling. Target setting. By automation of whole process of dynamic model design the errors are eliminated as well as the time of designing significantly decreases. Actual scientific researches and issues analysis. Designing of dynamic model by analytical way is very difficult especially in the cases considering high number of DOF. For hyperredundant manipulators it is practically impossible. From this reason whole process is automatized. Uninvestigated parts of general matters defining. The theory of Euler – Lagrange method is automatized by means of robotic view on this issue. The research objective. In the paper, an algorithm for design of dynamic model was introduced. The statement of basic materials. The paper deals with automatic design process of dynamic model for serial kinematic structure mechanisms. In the paper Euler – Lagrange formula is discussed. Analytical way of dynamic modeling should be difficult problem especially for mechanisms with high number of degrees of freedom. From this reason the paper shows the way of automatically designing of dynamic modeling in MATLAB. Our study shows dependence of computing time on increasing DOF. The relation is expressed by function of 3rd order. Subsequently the paper presents automatically generated inverse dynamic model in cooperation with inverse kinematic model as well as trajectory planning task. Conclusions. The paper introduces automatically generated dynamic model for mechanisms with serial kinematic structure. The paper also established the time for designing of dynamic model for several mechanisms with changing DOF.

A lean and efficient snapshot generation technique for the Hyper-Reduction of nonlinear structural dynamics

Model Order Reduction based on subspace projection can lead to impressive speedups, as the number of dofs can be drastically reduced. However, the computation of the nonlinear forces, which is performed in the unreduced physical domain, becomes the dominating bottleneck for nonlinear systems. This issue is addressed by Hyper-Reduction, which is the approximate but inexpensive computation of the nonlinear forces in a reduced basis model.The established Hyper-Reduction methods require training sets which are usually obtained by a training simulation of the full, unreduced model resulting in immense offline costs. To reduce the offline-costs, so-called Nonlinear Stochastic Krylov Training Sets (NSKTS) are proposed in this paper. These training sets are obtained by solving a number of nonlinear static problems where the force is constructed by stochastically weighted forces of a Krylov force subspace. The feasibility of NSKTS as training sets for the Energy Conserving Mesh Sampling and Weighting (ECSW) Hyper-Reduction method is demonstrated on a geometrically nonlinear rubber boot example exhibiting excellent results in terms of accuracy, speedup and robustness.

A fast biem algorithm to evaluate seismic ground response in 2d elastic time domain

Since the topography and surface irregularities of the terrain have a significant effect on the seismic response of the earth's surface, the numerical analysis using boundary element method in elastodynamics, which leads to a significant increase in the number of DOF and stiffness matrix dimension, as well as the sparse and unsymmetrical structure of stiffness matrix, indicates the inefficiency of the conventional method. This paper presents a fast boundary element algorithm in seismic analysis of two-dimensional elastic media for the first time. In the proposed method, instead of the usual node-to-node, a method of cell-to-cell relation method is implemented by hierarchy tree structure. In addition, the Plane Wave Time Domain algorithm and the Iterative method has been used to solve a system of equations which increases the speed of network convergence, especially in high degrees of freedom that has not been used in the study of the seismic waves’ response yet. Nowadays, this new algorithm adopts for investigating the response wave fields of electrical, magnet [1], acoustic and thermal conductivity which are discussed in details in various articles and books.

A new frequency matching technique for FRF-based model updating

Frequency Response Function (FRF) residues have been widely used to update Finite Element models. They are a kind of original measurement information and have the advantages of rich data and no extraction errors, etc. However, like other sensitivity-based methods, an FRF-based identification method also needs to face the ill-conditioning problem which is even more serious since the sensitivity of the FRF in the vicinity of a resonance is much greater than elsewhere. Furthermore, for a given frequency measurement, directly using a theoretical FRF at a frequency may lead to a huge difference between the theoretical FRF and the corresponding experimental FRF which finally results in larger effects of measurement errors and damping. Hence in the solution process, correct selection of the appropriate frequency to get the theoretical FRF in every iteration in the sensitivity-based approach is an effective way to improve the robustness of an FRF-based algorithm. A primary tool for right frequency selection based on the correlation of FRFs is the Frequency Domain Assurance Criterion. This paper presents a new frequency selection method which directly finds the frequency that minimizes the difference of the order of magnitude between the theoretical and experimental FRFs. A simulated truss structure is used to compare the performance of different frequency selection methods. For the sake of reality, it is assumed that not all the degrees of freedom (DoFs) are available for measurement. The minimum number of DoFs required in each approach to correctly update the analytical model is regarded as the right identification standard.

Robust adaptive beamforming using multi-snapshot direct data domain approach

For the realistic case where there is no secondary snapshot that does not contain the desired signal and exhibits the statistical characteristics similar to the snapshot under test, direct data domain (D3) beamforming approaches have been proposed to estimate a desired signal in the presence of interference. However, the basic idea of the D3 methods is realized by making significant sacrifices with respect to the number of degrees of freedom (DoFs). In this paper, we present a multi-snapshot approach for D3 beamforming. Using the least-squares method with multiple snapshots, we can eliminate the interference without causing a severe reduction in the number of DoFs. In addition, to consider a mismatch between nominal and actual target steering vectors, we propose a D3 approach combined with a probability constraint to prevent the self-nulling effect, and the relationship between the probability constraint and norm constraint is discovered. The simulations verify that the proposed method provides better performance and robustness than the conventional D3 approaches.