Improving the convergence rate of kinetic dynamic relaxation method with new R-point

2021 ◽  
Author(s):  
Javad Alamatian
Keyword(s):  
Convergence Rate ◽  
Relaxation Method ◽  
Dynamic Relaxation ◽  
Dynamic Relaxation Method

NONLINEAR STRUCTURAL ANALYSIS USING DYNAMIC RELAXATION METHOD WITH IMPROVED CONVERGENCE RATE

2010 ◽  
Vol 07 (04) ◽  
pp. 627-654 ◽  
Author(s):  
M. REZAIEE-PAJAND ◽  
S. R. SARAFRAZI
Keyword(s):  
Structural Analysis ◽  
Convergence Rate ◽  
Relaxation Method ◽  
Optimal Time ◽  
Dynamic Relaxation ◽  
Time Step ◽  
Nonlinear Structural Analysis ◽  
Nonlinear Structural ◽  
Dynamic Relaxation Method ◽  
Critical Damping

This paper develops the optimal time-step ratio and the critical damping for nonlinear structural analysis, when using dynamic relaxation method (DRM). The convergence rate of the DRM depends on the value of the time step and the critical damping factor. In the present study, the effect of the time-step ratio is separated from the time-step value. Additionally, the effect of the eigenvalue on the error function is investigated. Using the eigenvalue definition, the critical damping is updated in each dynamic relaxation (DR) step to decrease the required computations. Moreover, the optimal time-step ratio is calculated. It is also shown that the value of the constant time step has no effect on the rate of convergence. The proposed procedure provides a simple and accelerated DRM, which can be used in the linear and nonlinear analyses of structures. The efficiency of the new method was verified by its application to a wide range of typical structures. The results show that the suggested scheme accelerates the convergence rate of the DR process.

Dynamic-relaxation solution for the large deflection of plates with specified boundary stresses

1969 ◽  
Vol 4 (2) ◽  
pp. 75-80 ◽  
Author(s):  
K R Rushton
Keyword(s):  
Large Deflection ◽  
Relaxation Method ◽  
Plane Boundary ◽  
Dynamic Relaxation ◽  
Simply Supported ◽  
Von Karman ◽  
Relaxation Solution ◽  
Von Kármán Equations ◽  
Mesh Spacing ◽  
Dynamic Relaxation Method

The von Kármán equations for the large deflection of plates are solved by the dynamic-relaxation method. Detailed results are presented for square plates having simply supported edges with zero in-plane boundary stresses. The results show that high stresses occur towards the corners of the plates. The mesh effect is investigated and recommendations are made for the optimum mesh spacing.

Form-finding of deployable mesh reflectors using dynamic relaxation method

2018 ◽  
Vol 151 ◽  
pp. 380-388 ◽  
Author(s):  
Xinyu Wang ◽  
Jianguo Cai ◽  
Ruiguo Yang ◽  
Jian Feng
Keyword(s):  
Relaxation Method ◽  
Dynamic Relaxation ◽  
Form Finding ◽  
Dynamic Relaxation Method

A Digital Computer Solution of the Laplace Equation Using the Dynamic Relaxation Method

1968 ◽  
Vol 19 (4) ◽  
pp. 375-387 ◽  
Author(s):  
K. R. Rushton ◽  
Lucy M. Laing
Keyword(s):  
Laplace Equation ◽  
Iterative Process ◽  
Basic Equation ◽  
Relaxation Method ◽  
Dynamic Relaxation ◽  
Computer Solution ◽  
Relaxation Solution ◽  
Simple Substitution ◽  
Dynamic Relaxation Method ◽  
Explicit Finite Difference

SummaryThe Dynamic Relaxation solution of the Laplace equation introduces dynamic terms into the basic equation. When this is written as an explicit finite difference formulation it can be solved by an iterative process which only requires a simple substitution routine. The method is easy to programme and requires small storage in the computer. By studying problems involving wind tunnel interference in steady flow, the potentialities of the method are demonstrated.

Cable-Membrane Structures - Numerical Analysis and Practical Application

2016 ◽  
Vol 837 ◽  
pp. 99-102
Author(s):  
Milos Huttner ◽  
Jiří Maca ◽  
Petr Fajman
Keyword(s):  
Numerical Analysis ◽  
Relaxation Method ◽  
Computation Method ◽  
Practical Application ◽  
Dynamic Relaxation ◽  
Membrane Structures ◽  
Form Finding ◽  
Correct Operation ◽  
Commercial Program ◽  
Dynamic Relaxation Method

This paper presents a practical application of form-finding process of cable-membrane structures. The dynamic relaxation method with kinetic damping is used as the computation method for numerical analysis. A brief description of the construction, a description of the models and the way of solving tasks will be introduced. The correct operation of the implemented algorithm will be compared with a commercial program.

Multidisciplinary collaborative optimization based on relaxation method for solving complex problems

2020 ◽  
Vol 28 (4) ◽  
pp. 280-289
Author(s):  
Hamda Chagraoui ◽  
Mohamed Soula
Keyword(s):  
Optimization Problems ◽  
Inequality Constraints ◽  
Relaxation Method ◽  
Multidisciplinary Optimization ◽  
Collaborative Optimization ◽  
System Level ◽  
Dynamic Relaxation ◽  
Dynamic Relaxation Method ◽  
Feasible Solutions ◽  
The Impact

The purpose of the present work is to improve the performance of the standard collaborative optimization (CO) approach based on an existing dynamic relaxation method. This approach may be weakened by starting design points. First, a New Relaxation (NR) method is proposed to solve the difficulties in convergence and low accuracy of CO. The new method is based on the existing dynamic relaxation method and it is achieved by changing the system-level consistency equality constraints into relaxation inequality constraints. Then, a Modified Collaborative Optimization (MCO) approach is proposed to eliminate the impact of the information inconsistency between the system-level and the discipline-level on the feasibility of optimal solutions. In the MCO approach, the impact of the inconsistency is treated by transforming the discipline-level constrained optimization problems into an unconstrained optimization problem using an exact penalty function. Based on the NR method, the performance of the MCO approach carried out by solving two multidisciplinary optimization problems. The obtained results show that the MCO approach has improved the convergence of CO significantly. These results prove that the present MCO succeeds in getting feasible solutions while the CO fails to provide feasible solutions with the used starting design points.

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