A Finite-Element Based Framework for Transient Rotor Dynamic Simulations

2020 ◽  
Author(s):  
Anurag Rajagopal ◽  
Dilip K. Mandal
Keyword(s):  
Finite Element ◽  
Time Integration ◽  
Integration Scheme ◽  
Test Case ◽  
Computationally Efficient ◽  
Time Step ◽  
Dynamic Simulations ◽  
Adaptive Time Step ◽  
Time Integration Scheme ◽  
Rotor Dynamic

Abstract Transient simulations play a key role in the analysis and subsequent design of structural components with one or more rotating parts. A framework is proposed to this effect, centered around the finite-element solver OptiStruct, consisting of a time integration scheme built on the Newmark family with an appropriate adaptive time-step control. The process accounts for a computationally efficient handling of nonlinearities that might arise through bearings and casings. This solution is detailed starting from the governing equations for transient rotor dynamics to the nuances of the time marching scheme, and this process is applied to a test case from which conclusions are drawn that might be of interest to practicing engineers. These conclusions include insights into enforced motion, operation at or near critical speeds, rotor damping and contact. This work is aimed at producing a user-friendly and robust tool and process for the practicing engineer to perform complex rotor dynamic analysis.

Newmark-Beta Method in Discrete Elastic Rods Algorithm to Avoid Energy Dissipation

2019 ◽  
Vol 86 (8) ◽  
Author(s):  
Weicheng Huang ◽  
Mohammad Khalid Jawed
Keyword(s):  
Energy Dissipation ◽  
Time Integration ◽  
Integration Scheme ◽  
Integration Step ◽  
Elastic Rods ◽  
Computationally Efficient ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Time Integration Scheme

Discrete elastic rods (DER) algorithm presents a computationally efficient means of simulating the geometrically nonlinear dynamics of elastic rods. However, it can suffer from artificial energy loss during the time integration step. Our approach extends the existing DER technique by using a different time integration scheme—we consider a second-order, implicit Newmark-beta method to avoid energy dissipation. This treatment shows better convergence with time step size, specially when the damping forces are negligible and the structure undergoes vibratory motion. Two demonstrations—a cantilever beam and a helical rod hanging under gravity—are used to show the effectiveness of the modified discrete elastic rods simulator.

Studies on the Accuracy Stability and Efficiency of a New Time Integration Scheme for Ballast Modeling Using the Discrete Element Method

2014 ◽  
Author(s):  
G. F. Mathews ◽  
R. L. Mullen ◽  
D. C. Rizos
Keyword(s):  
Particle Interaction ◽  
Time Integration ◽  
Discrete Element ◽  
Critical Discussion ◽  
Implicit Time ◽  
Integration Scheme ◽  
Computationally Efficient ◽  
Time Step ◽  
Central Difference ◽  
Time Integration Scheme

This paper presents the development of a semi-implicit time integration scheme, originally developed for structural dynamics in the 1970’s, and its implementation for use in Discrete Element Methods (DEM) for rigid particle interaction, and interaction of elastic bodies that are modeled as a cluster of rigid interconnected particles. The method is developed in view of ballast modeling that accounts for the flexibility of aggregates and the arbitrary shape and size of granules. The proposed scheme does not require any matrix inversions and is expressed in an incremental form making it appropriate for non-linear problems. The proposed method focuses on improving the efficiency, stability and accuracy of the solutions, as compared to current practice. A critical discussion of the findings of the studies is presented. Extended verification and assessment studies demonstrate that the proposed algorithm is unconditionally stable and accurate even for large time step sizes. It is demonstrated that the proposed method is at least as computationally efficient as the Central Difference Method. Guidelines for the implementation of the method to ballast modeling are discussed.

scholarly journals A finite-element numerical approach for modeling tsunamis

1994 ◽  
Vol 37 (5) ◽  
Author(s):  
S. Tinti ◽  
I. Gavagni ◽  
A. Piatanesi
Keyword(s):  
Finite Element ◽  
Analytical Solutions ◽  
Time Integration ◽  
Model Performance ◽  
Numerical Approach ◽  
Integration Scheme ◽  
Time Step ◽  
Element Space ◽  
Time Integration Scheme ◽  
Step Algorithm

A numerical scheme suitable for modeling tsunamis is developed and tested against available analytical solutions. The governing equations are the shallow water nonlinear nondispersive equations that are known to be appropriate for tsunami generation and propagation in coastal waters. The integration scheme is based on a finite-element space discretization, where the basic elements are triangles and the shape functions are linear. The time integration is a double step algorithm that is accurate to the second order in the time step ?t. The boundary conditions are pure reflectivity and complete transmissivity on the solid and open boundaries respectively and are implemented by modifying the time integration scheme in a suitable way. The model performance is evaluated by comparing the results with the analytical solutions in selected cases and is quite satisfactory, even when the grid has a coarse spatial resolution.

scholarly journals Application of the Generalized Finite Element Method to the acoustic wave simulation in exploration seismology

Geophysics ◽  
2020 ◽  
pp. 1-70
Author(s):  
Edith Sotelo Gamboa ◽  
Marco Favino ◽  
Richard L. Gibson, Jr.
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Acoustic Wave ◽  
Time Integration ◽  
Integration Scheme ◽  
Generalized Finite Element Method ◽  
Time Step ◽  
Time Integration Scheme ◽  
Exploration Seismology ◽  
Element Method

The Generalized Finite Element Method (GFEM) has been applied frequently to solve harmonic wave equations, but its use in the simulation of transient wave propagation is still limited. We apply GFEM to the simulation of the acoustic wave equation in models relevant to exploration seismology. We also perform an assessment of its accuracy and efficiency. The main advantage of GFEM is that it provides an enhanced solution accuracy in comparison to the Standard Finite Element Method (FEM). This is attained by adding user-defined enrichment functions to standard FEM approximations. For the acoustic wave equation,we consider plane waves oriented in different directions as the enrichments, whose argument include the largest wavenumber of the wavefield. We combine GFEM with an unconditionally stable time integration scheme with constant time step. To assess the accuracy and efficiency of GFEM, we present a comparison of GFEM simulation results against those obtained with the Spectral Element Method (SEM). We use SEM because it is the method of choice for wave propagation simulation due to its proven accuracy and efficiency. In the numerical examples, we perform first a convergence study in space and time,evaluating the accuracy of both methods against a semi-analytical solution. Then, we consider two simulations of relevant models in exploration seismology that include low-velocity features, an inclusion with a complex geometrical boundary and topography. Results using these models show that the GFEM presents a comparable accuracy and efficiency to the ones based on SEM. For the given examples, GFEM efficiency stems from the combined effect of local mesh refinement, non-conforming or unstructured, and the unconditionally stable time integration scheme with constant time step. Moreover, these features providegreat flexibility to the GFEM implementations, proving to be advantageous when using, for example, unstructured grids that impose severe time step size restrictions in SEM.

Transonic Flow Computations in Cascades Using Finite Element Method

1981 ◽  
Vol 103 (4) ◽  
pp. 657-664 ◽  
Author(s):  
H. U. Akay ◽  
A. Ecer
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transonic Flow ◽  
Method Development ◽  
Time Integration ◽  
Integration Scheme ◽  
Complex Flow ◽  
Time Integration Scheme ◽  
Naca 0012 ◽  
Element Method

Analysis of transonic flow through a cascade of airfoils is investigated using the finite element method. Development of a computational grid suitable for complex flow structures and different types of boundary conditions is presented. An efficient pseudo-time integration scheme is developed for the solution of equations. Modeling of the shock and the convergence characteristics of the developed scheme are discussed. Numerical results include a 45 deg staggered cascade of NACA 0012 airfoils with inlet flow Mach number of 0.8 and angles of attack 1, 0, and −1 deg.

Time Integration of Impact Phenomena in Solid Mechanics: A One-Dimensional Model Problem

1996 ◽  
Author(s):  
V. Chawla ◽  
T. A. Laursen
Keyword(s):  
Finite Element ◽  
Solid Mechanics ◽  
Exact Analytical Solution ◽  
Time Integration ◽  
Dynamic Contact ◽  
Momentum Conservation ◽  
Integration Scheme ◽  
Mass System ◽  
Element Discretization ◽  
Time Integration Scheme

Abstract 1D impact between two identical bars is modeled as a simple spring-mass system as would be generated by a finite element discretization. Some commonly used time integrators are applied to the system to demonstrate defects in the numerical solution as compared to the exact analytical solution. Using energy conservation as the criterion for stability, a new time integration scheme is proposed that imposes a persistency condition for dynamic contact. Finite element simulation with Lagrange multipliers for enforcing the contact constraints shows exact energy and momentum conservation.

A Newly Developed Algorithm for Treating the Coupled Dynamic Response of Robotic Fixtureless Assembly

1996 ◽  
Author(s):  
Genady Shagal ◽  
Shaker A. Meguid
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Equations Of Motion ◽  
Time Integration ◽  
Integration Scheme ◽  
The Finite Element Method ◽  
Coupled Equations ◽  
Time Integration Scheme ◽  
Implicit Approach ◽  
Cooperating Robots

Abstract The coupled dynamic response of two cooperating robots handling two flexible payloads for the purpose of fixtureless assembly and manufacturing is treated using a new algorithm. In this algorithm, the equations describing the dynamics of the system are obtained using Lagrange’s method for the rigid robot links and the finite element method for the flexible payloads. A new time integration scheme is developed to treat the coupled equations of motion of the rigid links for a given displacement of the flexible payloads. The finite element equations of the flexible payloads are then treated using an implicit approach. The new algorithm was verified using simplified examples and was later used to examine the dynamic response of two cooperating robot arms manipulating flexible payloads which are typical of the automotive industry.

A COMPOSITE TIME INTEGRATION SCHEME FOR DYNAMIC ADHESION AND ITS APPLICATION TO GECKO SPATULA PEELING

2014 ◽  
Vol 11 (05) ◽  
pp. 1350104 ◽  
Author(s):  
SACHIN S. GAUTAM ◽  
ROGER A. SAUER
Keyword(s):  
Nonlinear Response ◽  
Time Integration ◽  
Computational Cost ◽  
Integration Scheme ◽  
Time Step ◽  
Integration Schemes ◽  
Newmark Scheme ◽  
Highly Nonlinear ◽  
Time Integration Schemes ◽  
Time Integration Scheme

Simulation of dynamic adhesive peeling problems at small scales has attracted little attention so far. These problems are characterized by a highly nonlinear response. Accurate and stable time integration schemes are required for simulation of dynamic peeling problems. In the present work, a composite time integration scheme is proposed for the simulation of dynamic adhesive peeling problems. It is shown through numerical examples that the proposed scheme remains stable and also has some gain in accuracy. The performance of the scheme is compared with two collocation-based schemes, i.e., Newmark scheme and Bathe composite scheme. It is shown that the proposed scheme and Bathe composite scheme perform equally. However, the proposed scheme adds very little to the computational cost of Newmark scheme. Through a numerical simulation of the peeling of a gecko spatula from a rigid substrate it is shown that the proposed scheme and the Bathe composite scheme are able to simulate the complete peeling process for given time step whereas the Newmark scheme diverges. It is also shown that the maximum pull-off force is within the range reported in the literature.

Dynamic Behaviour of Delaminated Composite Plate Under Blast Loading

2017 ◽  
Author(s):  
Chetan Kumar Hirwani ◽  
Subrata Kumar Panda ◽  
Siba Sankar Mahapatra ◽  
Sanjib Kumar Mandal ◽  
Apurba Kumar De
Keyword(s):  
Finite Element ◽  
Composite Plate ◽  
Degrees Of Freedom ◽  
Dynamic Behaviour ◽  
Time Integration ◽  
Blast Loading ◽  
Element Model ◽  
Continuity Condition ◽  
Integration Scheme ◽  
Time Integration Scheme

In the present article, the dynamic behaviour of the delaminated composite plate subjected to blast loading has been investigated. For the investigation, a general finite element model using higher-order mid-plane kinematics has been developed. The model has been discretised using nine noded isoparametric Lagrangian elements having nine degrees of freedom at each node. The continuity in the laminated and delaminated section has been established using the intermittent continuity condition. The final governing equation has been solved by applying Newmark’s time integration scheme in conjunction with finite element steps. Further, the said responses have been evaluated by developing an in-house MATLAB code based on the proposed model. In order to illustrate the consistency and accuracy of the present model, convergence and comparison study has been conducted i.e. the responses are evaluated for different mesh sizes and compared them with those of responses of earlier published literature. Finally, various examples have been solved to illustrate the influence of the size and position of debonding, side to thickness ratio, aspect ratio and end condition on the dynamic response of composite structure and discussed in detail.

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