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.

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 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.

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.

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