DQFEM Analyses of Static and Dynamic Nonlinear Elastic-Plastic Problems Using a GSR-Based Accelerated Constant Stiffness Equilibrium Iteration Technique

2001 ◽  
Vol 123 (3) ◽  
pp. 310-317 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Finite Element ◽  
Numerical Technique ◽  
Time Integration ◽  
Differential Quadrature ◽  
Element Discretization ◽  
Constant Stiffness ◽  
Structural Problems ◽  
Nonlinear Structural ◽  
Numerical Time Integration ◽  
Nonlinear Elastic

An integrated numerical technique for static and dynamic nonlinear structural problems adopting the equilibrium iteration is proposed. The differential quadrature finite element method (DQFEM), which uses the differential quadrature (DQ) techniques to the finite element discretization, is used to analyze the static and dynamic nonlinear structural mechanics problems. Numerical time integration in conjunction with the use of equilibrium iteration is used to update the response history. The equilibrium iteration can be carried out by the accelerated iteration schemes. The global secant relaxation-based accelerated constant stiffness and diagonal stiffness-based predictor-corrector equilibrium iterations which are efficient and reliable are used for the numerical computations. Sample problems are analyzed. Numerical results demonstrate the algorithm.

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.

scholarly journals A Validation of FEM3MP with Joint Urban 2003 Data

2007 ◽  
Vol 46 (12) ◽  
pp. 2127-2146 ◽  
Author(s):  
Stevens T. Chan ◽  
Martin J. Leach
Keyword(s):  
Finite Element ◽  
Homeland Security ◽  
Urban Areas ◽  
Stokes Equations ◽  
Time Integration ◽  
Element Model ◽  
Department Of Energy ◽  
Parallel Computer ◽  
Urban Dispersion ◽  
Element Discretization

Abstract Under the sponsorship of the U.S. Department of Energy and U.S. Department of Homeland Security, a computational fluid dynamics (CFD) model for simulating airflow and dispersion of chemical/biological agents released in urban areas has recently been developed. This model, the Finite Element Model in 3-Dimensions and Massively Parallelized (FEM3MP), is based on solving the three-dimensional, time-dependent Navier–Stokes equations with appropriate physics submodels on massively parallel computer platforms. It employs finite-element discretization for effective treatment of complex geometries and a semi-implicit projection scheme for efficient time integration. A simplified CFD approach, using both explicitly resolved and virtual buildings, was implemented to improve further the model’s efficiency. Results from our model are continuously being verified against measured data from wind-tunnel and field studies. Herein, this model is further evaluated using observed data from intensive operation periods (IOP) 3 and 9 of the Joint Urban 2003 field study conducted in Oklahoma City, Oklahoma, in July 2003. The model simulations of wind and concentration fields in the near and intermediate regions, as well as profiles of wind speed, wind direction, friction velocity, and turbulent kinetic energy (TKE) in the urban wake region, are generally consistent with and compared reasonably well to field observations. In addition, this model was able to reproduce the observed split plume of IOP 3 and the end vortices along Park Avenue in IOP 9. The dispersion results and TKE profiles at the crane station indicate that the effects of convective mixing are relatively important for the daytime release of IOP 3 but that the stable effects are relatively unimportant for the nighttime release of IOP 9. Results of this study also suggest that the simplified CFD approach implemented in FEM3MP can be a cost-effective tool for simulating urban dispersion problems.

scholarly journals A Robust and Efficient Composite Time Integration Algorithm for Nonlinear Structural Dynamic Analysis

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Lihong Zhang ◽  
Tianyun Liu ◽  
Qingbin Li
Keyword(s):  
Finite Element ◽  
Time Integration ◽  
Computational Cost ◽  
Nonlinear Problems ◽  
Central Difference ◽  
Integration Algorithm ◽  
Structural Dynamic ◽  
Nonlinear Structural ◽  
Time Integration Algorithm ◽  
Difference Formula

This paper presents a new robust and efficient time integration algorithm suitable for various complex nonlinear structural dynamic finite element problems. Based on the idea of composition, the three-point backward difference formula and a generalized central difference formula are combined to constitute the implicit algorithm. Theoretical analysis indicates that the composite algorithm is a single-solver algorithm with satisfactory accuracy, unconditional stability, and second-order convergence rate. Moreover, without any additional parameters, the composite algorithm maintains a symmetric effective stiffness matrix and the computational cost is the same as that of the trapezoidal rule. And more merits of the proposed algorithm are revealed through several representative finite element examples by comparing with analytical solutions or solutions provided by other numerical techniques. Results show that not only the linear stiff problem but also the nonlinear problems involving nonlinearities of geometry, contact, and material can be solved efficiently and successfully by this composite algorithm. Thus the prospect of its implementation in existing finite element codes can be foreseen.

scholarly journals Finite Element Analysis of Diffusion Processes in White Dwarfs

1989 ◽  
Vol 114 ◽  
pp. 249-252
Author(s):  
C. Pelletier ◽  
G. Fontaine ◽  
F. Wesemael
Keyword(s):  
Finite Element ◽  
White Dwarf ◽  
White Dwarfs ◽  
Diffusion Processes ◽  
Numerical Technique ◽  
Time Integration ◽  
Spectral Evolution ◽  
Element Analysis ◽  
Theoretical Understanding ◽  
Diffusion Problems

The spectral evolution of white dwarfs is governed by diffusion processes which enter into competition with mechanisms such as mass loss, convective mixing, and accretion from the interstellar medium in various phases of the evolution. Until recently, our theoretical understanding of the chemical evolution of these stars has been limited by the very severe numerical difficulties which plague a time-dependent description of the problem. Indeed, diffusion problems in white dwarf interiors and envelopes are particularly demanding from a computational standpoint: they involve relative chemical abundances spanning many orders of magnitude, time integration length of a few billion years, and many physical processes operating with greatly different time constants. We have already introduced in the field a robust numerical technique based on an implicit finite difference scheme designed for nonlinear two-point boundary value problems (Pelletier 1986). This method has been used to investigate a number of problems related to the spectral evolution of white dwarfs (Pelletier 1986; Pelletier et al. 1986; Dupuis et al. 1987). As requirements for further progress in the field become more exacting and in the interest of improving the efficiency, we have sought to develop even more powerful numerical techniques. We briefly introduce here an efficient computational approach to diffusion problems in white dwarfs based on a Galerkin finite element method to solve the convective-diffusion equation in an evolving white dwarf model. As an illustrative example, we discuss some sample results of a detailed investigation of the problem of chemical sedimentation (H, He, and C) in the envelopes of hot white dwarfs and the formation of DA stars.

scholarly journals A Survey in Mathematics for Industry An efficient method for the numerical simulation of magneto-mechanical sensors and actuators

2007 ◽  
Vol 18 (2) ◽  
pp. 233-271 ◽  
Author(s):  
M. SCHINNERL ◽  
M. KALTENBACHER ◽  
U. LANGER ◽  
R. LERCH ◽  
J. SCHÖBERL
Keyword(s):  
Finite Element ◽  
Vector Potential ◽  
Time Integration ◽  
Test Problems ◽  
Computational Domain ◽  
Finite Element Discretization ◽  
Sensors And Actuators ◽  
Element Discretization ◽  
Multigrid Solvers ◽  
Mechanical Sensors

The dynamic behaviour of magneto-mechanical sensors and actuators can be completely described by Maxwell's and Navier-Lamé's partial differential equations (PDEs) with appropriate coupling terms reflecting the interactions of these fields and with the corresponding initial, boundary and interface conditions. Neglecting the displacement currents, which can be done for the classes of problems considered in this paper, and introducing the vector potential for the magnetic field, we arrive at a system of degenerate parabolic PDEs for the vector potential coupled with the hyperbolic PDEs for the displacements.Usually the computational domain, the finite element discretization, the time integration, and the solver are different for the magnetic and mechanical parts. For instance, the vector potential is approximated by edge elements whereas the finite element discretization of the displacements is based on nodal elements on different meshes. The most time consuming modules in the solution procedure are the solvers for both, the magnetical and the mechanical finite element equations arising at each step of the time integration procedure. We use geometrical multigrid solvers which are different for both parts. These multigrid solvers enable us to solve quite efficiently not only academic test problems, but also transient 3D technical magneto-mechanical systems of high complexity such as solenoid valves and electro-magnetic-acoustic transducers. The results of the computer simulation are in very good agreement with the experimental data.

Vibration of a Simple Beam Subjected to a Moving Sprung Mass with Initial Velocity and Constant Acceleration

2016 ◽  
Vol 16 (03) ◽  
pp. 1450109 ◽  
Author(s):  
Shih-Hsun Yin
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Initial Velocity ◽  
Time Integration ◽  
Dynamic Responses ◽  
Constant Acceleration ◽  
Element Discretization ◽  
Integration Schemes ◽  
Average Acceleration ◽  
Time Integration Schemes

In this paper, a semi-analytical solution to the problem of a simply supported beam subjected to a moving sprung mass with initial velocity and constant acceleration or deceleration was presented, which serves as a benchmark for checking the performance of other numerical methods. Herein, a finite element modeling procedure was adopted to tackle the vehicle–bridge interaction, and the responses of the vehicle and bridge were computed by time integration schemes such as the Newmark average acceleration, HHT-[Formula: see text], and Wilson-[Formula: see text] methods. In comparison with the semi-analytical solution, the acceleration response of the beam solved by the Newmark average acceleration method shows spurious high-frequency oscillations caused by the finite element discretization. In contrast, the HHT-[Formula: see text] and Wilson-[Formula: see text] methods can dissipate these oscillations and show more accurate results. Moreover, we found that the dynamic responses of the beam and sprung mass were mainly determined by the initial velocity of the sprung mass, but not by the acceleration or deceleration.

Sign in / Sign up

Export Citation Format

Share Document