Mixing dynamic relaxation method with load factor and displacement increments

Finding equilibrium paths by minimizing external work in dynamic relaxation method

In this paper, various dynamic relaxation methods are investigated for geometric nonlinear analysis of bending plates. Sixteen wellknown algorithms are employed. Dynamic relaxation fictitious parameters are the mass matrix, the damping matrix and the time step. The difference between the mentioned tactics is how to implement these parameters. To compare the efficiency of these strategies, several bending plates’ problems with large deflections are solved. Based on the number of iterations and analysis time, the scores of the different schemes are calculated. These scores determine the ranking of each technique. The numerical results indicate the appropriate efficiency of Underwood and Rezaiee-Pajand & Alamatian processes for the nonlinear analysis of bending plates.

/pdf/a-comparison-of-large-deflection-analysis-of-bending-plates-3nrwc9n5ge.pdf

A Comparison of Large Deflection Analysis of Bending Plates by Dynamic Relaxation

In the last sixty years‎, ‎the Dynamic Relaxation methods have evolved significantly‎. ‎These explicit and iterative procedures are frequently used to solve the linear or nonlinear response of governing equations resulted from structural analyses‎. ‎In the first part of this study‎, ‎the common DR formulations are reviewed‎. ‎Mathematical bases and also physical concepts of these solvers are explained briefly‎. ‎All the DR parameters‎, ‎i.e‎. ‎fictitious mass‎, ‎fictitious damping‎, ‎fictitious time step and initial guess are described‎, ‎as well‎. ‎Furthermore‎, ‎solutions of structural problems along with kinetic and viscous damping formulations are discussed‎. ‎Analyses of the existing studies and suggestions for future research trends are presented‎. ‎In the second part‎, ‎the applications of Dynamic Relaxation method in engineering practices are reviewed.

https://ijnao.um.ac.ir/article_24586_0c73509c02360988751d269ab28e51fa.pdf

The state of the art in Dynamic Relaxation methods for structural mechanics Part 1: Formulations

Dynamic Relaxation Method (DRM) is an explicit approach for solving the simultaneous systems of equations. In this tactic, the fictitious mass and damping are added to the static governing equations, and an artificial dynamic system is constructed. By using DRM for nonlinear analysis, the structural static equilibrium path is obtained. This outcome is extremely valuable, since it leads to the behavior of structures. Among the finding related to the structural static path are the critical and buckling points for nonlinear structures. In this paper, a new way for calculating the load factor is proposed by setting the external work zero. Mixing the dynamic relaxation scheme with external work technique has not been formulated so far. In all incremental-iterative methods, the load factor increment sign should be determinated by extra calculations. This sign leads to increase or decrease of the load increment. It is worth emphasizing that sign of the load factor increment changes at the load limit points. Therefore, the sign determinations are required in the common work control methods. These disadvantages are eliminated in the proposed algorithm. In fact, the suggested load factor depends only on the Dynamic Relaxation (DR) fictitious parameters. Besides, all DR calculations are performed via vector operation. Moreover, the load factor is calculated only by one formula, and it has the same relation in the all solution processes. In contrast to the arc length techniques, which requires the sign determined, the proposed scheme does not need any sign finding. It is shown that author’s technique is quicker than the other dynamic relaxation strategies. To prove the capability and efficiency of the presented scheme, several numerical tests are performed. The results indicate that the suggested approach can trace the complex structural static paths, even in the snap-back and snap-through parts.

Finding buckling points for nonlinear structures by dynamic relaxation scheme

Problems involving beams or plates which deflect until contact is made with internal restraints are examined using a modified form of the dynamic relaxation method. Three particular problem...

Buckling of beams and plates onto an intermediate support studied by the dynamic relaxation method

The large deflections of rectangular plates and beams obeying a non-linear stress-strain law are examined. Solutions are obtained by use of dynamic relaxation, a numerical finite-difference technique. Comparisons are made with alternative solutions and experimental results. The effects of varying parameters in the non-linear expressions are considered.

http://sdj.sagepub.com/content/9/3/178.full.pdf

P M Hook

Papers

Buckling of beams and plates onto an intermediate support studied by the dynamic relaxation method

Large deflection of plates and beams obeying non-linear stress—strain laws