Dynamic Response of Timoshenko Beam Structures Solved by DQEM Using EDQ

2002 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Dynamic Response ◽  
Timoshenko Beam ◽  
Dynamic Equilibrium ◽  
Time Integration ◽  
Element Model ◽  
Equation System ◽  
Equilibrium Equations ◽  
Beam Structures ◽  
Integration Schemes ◽  
Time Element

The dynamic response of Timoshenko beam structures is solved by using the DQEM to the space discretization and EDQ to the time discretization. In the DQEM discretization, DQ is used to define the discrete element model. Discrete dynamic equilibrium equations defined at interior nodes in all elements, transition conditions defined on the inter-element boundary of two adjacent elements and boundary conditions at the structural boundary form a dynamic equation system at a specified time stage. The dynamic equilibrium equation system is solved by the direct time integration schemes of time-element by time-element method and stages by stages method which are developed by using EDQ and DQ. Numerical results obtained by the developed numerical algorithms are presented. They demonstrate the developed numerical solution procedure.

Dynamic Response of Composite Two-Dimensional Elasticity Problems Solved by DQEM and EDQ Based Time Integration Method

2004 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Dynamic Response ◽  
Dynamic Equilibrium ◽  
Time Integration ◽  
Element Model ◽  
Equation System ◽  
Two Dimensional ◽  
Equilibrium Equations ◽  
Integration Schemes ◽  
Time Element ◽  
Elasticity Problems

The dynamic response of composite two-dimensional elasticity problems is solved by using the DQEM to the spacial discretization and EDQ to the temporal discretization. In the DQEM discretization, DQ is used to define the discrete element model. Discrete dynamic equilibrium equations defined at interior nodes in all elements, transition conditions defined on the inter-element boundary of two adjacent elements and boundary conditions at the structural boundary form a dynamic equation system at a specified time stage. The dynamic equilibrium equation system can be solved by the direct time integration schemes of time-element by time-element method and stages by stages method which are developed by using EDQ and DQ. Numerical procedures and numerical results are presented.

Dynamic Responses of Frame Structures Solved Using DQEM and EDQ Based Time Integration Method

2004 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Dynamic Equilibrium ◽  
Time Integration ◽  
Element Model ◽  
Equation System ◽  
Dynamic Responses ◽  
Frame Structures ◽  
Equilibrium Equations ◽  
Integration Schemes ◽  
Time Element ◽  
Time Integration Schemes

The dynamic response of frame structures is solved by using the DQEM to the spacial discretization and EDQ to the temporal discretization. In the DQEM discretization, EDQ is also used to define the discrete element model. Discrete dynamic equilibrium equations defined at interior nodes in all elements, transition conditions defined on the inter-element boundary of two adjacent elements and boundary conditions at the structural boundary form a dynamic equation system at a specified time stage. The dynamic equilibrium equation system can be solved by the direct time integration schemes of time-element by time-element method and stages by stages method which are developed by using EDQ and DQ. Numerical procedures and numerical results are presented.

Dynamic Response of Shear-Deformable Axisymmetric Orthotropic Circular Plate Structures Solved by the DQEM and EDQ Based Time Integration Schemes

2003 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Dynamic Response ◽  
Dynamic Equilibrium ◽  
Time Integration ◽  
Equation System ◽  
Plate Structures ◽  
Integration Schemes ◽  
Time Element ◽  
Time Integration Schemes ◽  
Orthotropic Circular Plate ◽  
Shear Deformable

The dynamic response of shear-deformable axisymmetric orthotropic circular plate structures is solved by using the DQEM to the spacial discretization and EDQ to the temporal discretization. In the DQEM discretization, DQ is used to define the discrete element model. Discrete dynamic equilibrium equations defined at interior nodes in all elements, transition conditions defined on the inter-element boundary of two adjacent elements and boundary conditions at the structural boundary form a dynamic equation system at a specified time stage. The dynamic equilibrium equation system is solved by the direct time integration schemes of time-element by time-element method and stages by stages method which are developed by using EDQ and DQ. Numerical results obtained by the developed numerical algorithms are presented. They demonstrate the developed numerical solution procedure.

Transient Analysis of Heat Conduction in Orthotropic Medium by the DQEM and EDQ Based Time Integration Schemes

2003 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Heat Conduction ◽  
Time Integration ◽  
Numerical Algorithms ◽  
Transient Heat Conduction ◽  
Element Model ◽  
Equation System ◽  
Orthotropic Medium ◽  
Integration Schemes ◽  
Time Element ◽  
Time Integration Schemes

The transient heat conduction in orthotropic medium is solved by using the DQEM to the spacial discretization and EDQ to the temporal discretization. In the DQEM discretization, DQ is used to define the discrete element model. Discrete transient equations defined at interior nodes in all elements, transition conditions defined on the inter-element boundary of two adjacent elements and boundary conditions at the structural boundary form a transient equation system at a specified time stage. The transient equation system is solved by the direct time integration schemes of time-element by time-element method and stages by stages method which are developed by using EDQ and DQ. Numerical results obtained by the developed numerical algorithms are presented. They demonstrate the developed numerical solution procedure.

Comparison of Implicit Time Integration Schemes for Nonlinear Dynamic Problems

2010 ◽  
Author(s):  
Murat Demiral
Keyword(s):  
Dynamic Equilibrium ◽  
Time Integration ◽  
Nonlinear Problems ◽  
Implicit Time ◽  
Implicit Methods ◽  
Equilibrium Equations ◽  
Integration Schemes ◽  
Implicit Time Integration ◽  
Time Integration Schemes ◽  
The Stability

Implicit time integration schemes are used to obtain stable and accurate transient solutions of nonlinear problems. Methods that are unconditionally stable in linear analysis are sometimes observed to have convergence problems as in the case of solutions obtained with a trapezoidal method. On the other hand, a composite time integration method employing a trapezoidal rule and a three-point backward rule sequentially in two half steps can be used to obtain accurate results and enhance the stability of the system by means of a numerical damping introduced in the formulation. To have a better understanding of the differences in the numerical implementation of the algorithms of these two methods, a mathematical analysis of dynamic equilibrium equations is performed. Several practical problems are studied to compare the implicit methods.

Dynamic Response Analysis of Bridge Pier Subject to Earthquake and Ice Loads

2011 ◽  
Vol 250-253 ◽  
pp. 2211-2215
Author(s):  
Fu Qiang Qi
Keyword(s):  
Dynamic Response ◽  
Dynamic Equilibrium ◽  
Work Conditions ◽  
Bridge Pier ◽  
Dynamic Responses ◽  
Response Analysis ◽  
Analysis Method ◽  
Equilibrium Equations ◽  
Different Types ◽  
Ice Loads

In order to discuss the effect of earthquake and dynamic ice loads to a bridge pier, this paper considered the effect of added mass of dynamic water, and it deduced the dynamic equilibrium equations for a bridge pier subject to earthquake and dynamic ice loads on the basis of nonlinear Morision equation. Using numerical analysis method, it discussed the dynamic response of a bridge pier subject to different types of earthquake loads, forced ice loads, and both earthquake and forced ice loads. Through comparing the pier responses in different work conditions, it discovered that the dynamic responses of the bridge pier subject to forced dynamic ice loads rise and fall severely at the time of ice buckling broken periodic change. The coupling effects of forced dynamic ice loads and earthquake especially near-fault earthquake enhance the dynamic response of bridge pier significantly.

Extended GDQ and Related Discrete Element Analysis Methods for Transient Analyses of Continuum Mechanics Problems

2002 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Continuum Mechanics ◽  
Discrete System ◽  
Time Integration ◽  
Equation System ◽  
Element Analysis ◽  
Solution Algorithms ◽  
Time Element ◽  
Discretization Technique ◽  
Integration Algorithms ◽  
Transient System

The extended GDQ proposed by the author is used to develop solution algorithms for solving the discrete transient equation system of continuum mechanics problems. It is a direct integration approach. Two integration methods are developed. They are time-element by time-element method and stages by stages method. These two time integration algorithms can be used to solve generic discrete transient equation system of an originally discrete system or a discrete system resulting from the discretization of a transient system of continuum mechanics problems by using a certain discretization technique such as the DQEM, FEM, FDM,…, etc.

scholarly journals Modeling and Analysis of Progressive Ice Shedding along a Transmission Line during Thermal De-Icing

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Yunyun Xie ◽  
Linyan Huang ◽  
Da Wang ◽  
Huaiping Ding ◽  
Xiaochun Yin
Keyword(s):  
Dynamic Response ◽  
Transmission Line ◽  
Transmission Lines ◽  
Dynamic Equilibrium ◽  
Propagation Speed ◽  
Experimental Results ◽  
Small Scale ◽  
Equilibrium Equations ◽  
Modeling And Analysis ◽  
Ice Shedding

Progressive ice shedding (PIS) along transmission lines is a common type of ice shedding during thermal de-icing that requires investigation to ensure the security of transmission lines. In current research, PIS is commonly analyzed using a constant speed for ice detaching from the conductor, which is not accurate for PIS simulation. Therefore, a mechanical model of PIS is established in this study to analyze PIS during thermal de-icing. First, an ice detachment model during thermal de-icing is built to determine the detachment times of the initial ice and remaining ice. Then, a two-node isoparametric truss element is employed to derive the static and dynamic equilibrium equations of an iced conductor to simulate the dynamic response of PIS. Relative to commercial software, these equations can easily accommodate the changing mass of ice with the flow of melted water. The dynamic equilibrium equations are then solved using the ice detachment model to obtain the dynamic response of PIS. Finally, small-scale and full-scale experimental results are employed to verify the proposed method. The simulation results show that the results of the proposed method are more consistent with the experimental results than are the results of existing methods that assume a constant propagation speed. The proposed method can be further applied to optimize transmission line designs and evaluate the application of thermal de-icing devices.

scholarly journals Quasi-Static Analysis for Subsidence of Stacked B-25 Boxes

2005 ◽  
Author(s):  
Tsu-Te Wu ◽  
William E. Jones ◽  
Mark A. Phifer
Keyword(s):  
Time Integration ◽  
Structural Response ◽  
Element Model ◽  
Structural Deformation ◽  
Static Loads ◽  
Integration Schemes ◽  
Long Duration ◽  
Time Integration Schemes ◽  
Post Buckling ◽  
Structural Responses

This paper presents a quasi-static technique to evaluate the structural deformation of the four stacked B-25 boxes subjected to the static loads of overlaying soil and to determine the effect of corrosion on the deformation. Although the boxes are subjected to a static load, the structural responses of the boxes vary with time. The analytical results indeed show that the deflection, buckling and post buckling of the components of the stacked boxes occur in sequence rather than simultaneously. Therefore, it is more appropriate to treat the problems considered as quasistatic rather than static; namely, the structural response of the stacked boxes are dynamic but with very long duration. Furthermore, the finite-element model has complex contact and slide conditions between the interfaces of the adjoining components, and thus its numerical solution is more tractable by using explicit time integration schemes. The analysis covers the three corrosion scenarios following various time lengths of initial burial under an interim soil cover. The results qualitatively agree with expected differences in deformation for different degrees of corrosion subsidence potential reduction that can be achieved.

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