scholarly journals Nonlinear Structural Dynamic Finite Element Analysis Using Ritz Vector Reduced Basis Method

1996 ◽  
Vol 3 (4) ◽  
pp. 259-268 ◽  
Author(s):  
M.S. Yao
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Finite Amplitude ◽  
Basis Vector ◽  
Reduced Basis ◽  
Ritz Vector ◽  
Element Analysis ◽  
Structural Dynamic ◽  
Nonlinear Equations Of Motion

The large number of unknown variables in a finite element idealization for dynamic structural analysis is represented by a very small number of generalized variables, each associating with a generalized Ritz vector known as a basis vector. The large system of equations of motion is thereby reduced to a very small set by this transformation and computational cost of the analysis can be greatly reduced. In this article nonlinear equations of motion and their transformation are formulated in detail. A convenient way of selection of the generalized basis vector and its limitations are described. Some illustrative examples are given to demonstrate the speed and validity of the method. The method, within its limitations, may be applied to dynamic problems where the response is global in nature with finite amplitude.

Simplified Dynamic Finite-Element Analysis for Three-Dimensional Pile-Grouped-Raft-High-Rise Buildings

2008 ◽  
Vol 400-402 ◽  
pp. 613-619
Author(s):  
Hui Xiong ◽  
Shou Ping Shang ◽  
Liang Huang
Keyword(s):  
Finite Element ◽  
Structural Engineering ◽  
Computational Cost ◽  
Time History ◽  
Pile Group ◽  
Element Analysis ◽  
Structural Dynamic ◽  
Shell Elements ◽  
High Rise ◽  
Mass Spring

Combined with the respective advantages in S-R(Sway-Rocking) impedance concept and finite-element method, a simplified 3D structural dynamic FEM considering composite pile-group-soil effects is presented. The structural members including piles are modeled by spacial beam or shell elements, and raft-base is divided into thick-shell elements with its spring-dashpot boundary coefficient obtained by impedance backcalculated. The mass-spring elements for soil between piles are set to simulate vertical, horizontal pile-group effects by strata-equivalent approach. The soil beside composite body is separated into near-field and far-field parts. The former is modeled by nonlinear spring-dashpot elements based on Winkler’s hypothesis, while the latter is modeled by a series of linear mass-spring-dashpots. With the effects of boundary track forces and energy radiation, the presented model enables researchers to conduct the time-domain nonlinear analysis in a relatively simple manner which avoids sophisticated boundary method and solid-element mesh bringing with tremendous computational cost. The seismic effect on dynamic interaction of pile-soil-complicated structures would be efficiently annotated from two structural engineering and geotechnical engineering aspects and the numerical calculation effort would be drastically decreased too. The complete procedure is mainly performed using the parametric design language assembled in the Finite Element Code Ansys. With the dynamic analysis of foundation and superstructure for a pile-supported 15-storey building, the influence of the participant effect on structural dynamic response will be depicted by various dynamic parameters of pile-soil-raft foundation in detail. Not only do the results have an agreement with some conclusions drawn by the general interaction theory, but also certain of phenomena which would be disagree with that by general analysis is involved. Even with the finite-element meshes for 68 piles, the time-history analysis procedure for PGSS (Pile-Group-Soil-Superstructure) system and the qualitative evaluation with various SSI parameters can be also fulfilled efficiently and rapidly by presented means. These results may be of help to the designers to quickly assess the significance of interaction effect for the high-rise buildings resting on any type or layout of pile-group foundation.

On the Equivalence of Acoustic Impedance and Squeeze Film Impedance in Micromechanical Resonators

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Charanjeet Kaur Malhi ◽  
Rudra Pratap
Keyword(s):  
Finite Element ◽  
Acoustic Impedance ◽  
Entire Range ◽  
Microelectromechanical Systems ◽  
Acoustic Analysis ◽  
Computational Cost ◽  
Squeeze Film ◽  
Frequency Range ◽  
Element Analysis ◽  
Structural Dynamic

In this work, we address the issue of modeling squeeze film damping in nontrivial geometries that are not amenable to analytical solutions. The design and analysis of microelectromechanical systems (MEMS) resonators, especially those that use platelike two-dimensional structures, require structural dynamic response over the entire range of frequencies of interest. This response calculation typically involves the analysis of squeeze film effects and acoustic radiation losses. The acoustic analysis of vibrating plates is a very well understood problem that is routinely carried out using the equivalent electrical circuits that employ lumped parameters (LP) for acoustic impedance. Here, we present a method to use the same circuit with the same elements to account for the squeeze film effects as well by establishing an equivalence between the parameters of the two domains through a rescaled equivalent relationship between the acoustic impedance and the squeeze film impedance. Our analysis is based on a simple observation that the squeeze film impedance rescaled by a factor of jω, where ω is the frequency of oscillation, qualitatively mimics the acoustic impedance over a large frequency range. We present a method to curvefit the numerically simulated stiffness and damping coefficients which are obtained using finite element analysis (FEA) analysis. A significant advantage of the proposed method is that it is applicable to any trivial/nontrivial geometry. It requires very limited finite element method (FEM) runs within the frequency range of interest, hence reducing the computational cost, yet modeling the behavior in the entire range accurately. We demonstrate the method using one trivial and one nontrivial geometry.

A Logarithmic Complexity Divide and Conquer Algorithm for Flexible Multibody Dynamics

2005 ◽  
Author(s):  
Rudranarayan Mukherjee ◽  
Kurt Anderson
Keyword(s):  
Elastic Deformation ◽  
Degrees Of Freedom ◽  
Parallel Implementation ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Flexible Multibody Dynamics ◽  
Divide And Conquer ◽  
Element Analysis ◽  
Large Rotations ◽  
Nonlinear Equations Of Motion

This paper presents an efficient algorithm for parallel implementation of multi-flexible-body dynamics systems simulation and analysis. The effective overall computational cost of the algorithm is logarithmic when implemented with a processor optimal O(n) processors. This algorithm formulates and solves the nonlinear equations of motion for mechanical systems with interconnected flexible bodies subject to small elastic deformation together with large rotations and translations. The large rotations or translations are modeled as rigid body degree of freedom associated with the interconnecting kinematic joint degrees of freedom. The elastic deformation of the component bodies is modeled through the use of admissible shape functions generated using standard finite element analysis software or otherwise. Apart from the approximation associated with the elastic deformations, this algorithm is exact, non-iterative and applicable to generalized multi-flexible chain and free topologies.

scholarly journals Explicit Dynamic Finite Element Method for Failure with Smooth Fracture Energy Dissipations

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Jeong-Hoon Song ◽  
Thomas Menouillard ◽  
Alireza Tabarraei
Keyword(s):  
Finite Element ◽  
Fracture Energy ◽  
Computational Cost ◽  
Quadrature Rule ◽  
Dynamic Failure ◽  
Structural Dynamic ◽  
Integration Schemes ◽  
Hourglass Control ◽  
Quadrilateral Finite Element ◽  
Explicit Dynamic

A numerical method for dynamic failure analysis through the phantom node method is further developed. A distinct feature of this method is the use of the phantom nodes with a newly developed correction force scheme. Through this improved approach, fracture energy can be smoothly dissipated during dynamic failure processes without emanating noisy artifact stress waves. This method is implemented to the standard 4-node quadrilateral finite element; a single quadrature rule is employed with an hourglass control scheme in order to decrease computational cost and circumvent difficulties associated with the subdomain integration schemes for cracked elements. The effectiveness and robustness of this method are demonstrated with several numerical examples. In these examples, we showed the effectiveness of the described correction force scheme along with the applicability of this method to an interesting class of structural dynamic failure problems.

Consistent Tangent Stiffness of a Three-Dimensional Wheel–Rail Interaction Element

2021 ◽  
Author(s):  
Quan Gu ◽  
Jinghao Pan ◽  
Yongdou Liu
Keyword(s):  
Finite Element ◽  
Quadratic Convergence ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Light Rail ◽  
Software Framework ◽  
Tangent Stiffness ◽  
Rail Vehicle ◽  
Interaction Element ◽  
Nonlinear Equations Of Motion

Consistent tangent stiffness plays a crucial role in delivering a quadratic rate of convergence when using Newton’s method in solving nonlinear equations of motion. In this paper, consistent tangent stiffness is derived for a three-dimensional (3D) wheel–rail interaction element (WRI element for short) originally developed by the authors and co-workers. The algorithm has been implemented in finite element (FE) software framework (OpenSees in this paper) and proven to be effective. Application examples of wheelset and light rail vehicle are provided to validate the consistent tangent stiffness. The quadratic convergence rate is verified. The speeds of calculation are compared between the use of consistent tangent stiffness and the tangent by perturbation method. The results demonstrate the improved computational efficiency of WRI element when consistent tangent stiffness is used.

Interval Finite Element Analysis of Structural Dynamic Problems

2015 ◽  
Vol 8 (2) ◽  
pp. 382-389 ◽  
Author(s):  
Naijia Xiao ◽  
Rafi L. Muhanna ◽  
Francesco Fedele ◽  
Robert L. Mullen
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Dynamic Problems ◽  
Element Analysis ◽  
Structural Dynamic

A Determination of Material Properties of Flexible Structures Using EMA and FEM Analysis

2014 ◽  
Vol 693 ◽  
pp. 293-298 ◽  
Author(s):  
Rastislav Duris
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Low Cost ◽  
Flexible Structures ◽  
Fem Analysis ◽  
Element Analysis ◽  
Structural Dynamic ◽  
Vibration Data ◽  
Complex Interactions ◽  
Applied Forces

Dynamic behavior of mechanical structures results from complex interactions between applied forces and the stiffness properties of the structure. Currently, many problems of structural dynamic analysis are solved using Finite Element Method (FEM). However, in recent years, the implementation of the Fast Fourier Transform (FFT) in low cost computer-based signal analyzers has provided a powerful tool for acquisition and analysis of vibration data. This article discusses combination of two approaches to structural dynamics testing; the experimental part which is referred to as Experimental Modal Analysis (EMA), respectively the analytical part, which is realized by Finite Element Analysis (FEA). Main goal of the paper is calculation of material properties from experimentally determined modal frequencies.

scholarly journals New Analytical Model Used in Finite Element Analysis of Solids Mechanics

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1401 ◽  
Author(s):  
Sorin Vlase ◽  
Adrian Eracle Nicolescu ◽  
Marin Marin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Elastic Solid ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Element Analysis ◽  
Elastic Multibody System

In classical mechanics, determining the governing equations of motion using finite element analysis (FEA) of an elastic multibody system (MBS) leads to a system of second order differential equations. To integrate this, it must be transformed into a system of first-order equations. However, this can also be achieved directly and naturally if Hamilton’s equations are used. The paper presents this useful alternative formalism used in conjunction with the finite element method for MBSs. The motion equations in the very general case of a three-dimensional motion of an elastic solid are obtained. To illustrate the method, two examples are presented. A comparison between the integration times in the two cases presents another possible advantage of applying this method.

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