Dynamic relaxation method (DRM)is one of the suitable numerical procedures for nonlinear structural analysis.Adding the fictitious inertia and damping forces to the static equation,and turning it to the dynamic system...Dynamic relaxation method (DRM)is one of the suitable numerical procedures for nonlinear structural analysis.Adding the fictitious inertia and damping forces to the static equation,and turning it to the dynamic system,are the basis of this technique.Proper selection of the DRM artificial factors leads to the better convergence rate and efficient solutions.This study aims to increase the numerical stability,and to decrease the analysis time.To fulfil this objective,the reduction rate of analysis error for consecutive iterations is minimized.Based on this formulation,a new time step is found for the viscous dynamic relaxation.After combining this novel relationship with the other DRM factors,various geometrical nonlinear structures,such as trusses,frames,and shells,are analyzed.The obtained results verify the efficiency of authors'scheme.展开更多
The analysis of cable structures is one of the most challenging problems for civil and mechanical engineers.Because they have highly nonlinear behavior,it is difficult to find solutions to these problems.Thus far,diff...The analysis of cable structures is one of the most challenging problems for civil and mechanical engineers.Because they have highly nonlinear behavior,it is difficult to find solutions to these problems.Thus far,different assumptions and methods have been proposed to solve such structures.The dynamic relaxation method(DRM)is an explicit procedure for analyzing these types of structures.To utilize this scheme,investigators have suggested various stiffness matrices for a cable element.In this study,the efficiency and suitability of six well-known proposed matrices are assessed using the DRM.To achieve this goal,16 numerical examples and two criteria,namely,the number of iterations and the analysis time,are employed.Based on a comprehensive comparison,the methods are ranked according to the two criteria.The numerical findings clearly reveal the best techniques.Moreover,a variety of benchmark problems are suggested by the authors for future studies of cable structures.展开更多
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 dyna...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.展开更多
文摘Dynamic relaxation method (DRM)is one of the suitable numerical procedures for nonlinear structural analysis.Adding the fictitious inertia and damping forces to the static equation,and turning it to the dynamic system,are the basis of this technique.Proper selection of the DRM artificial factors leads to the better convergence rate and efficient solutions.This study aims to increase the numerical stability,and to decrease the analysis time.To fulfil this objective,the reduction rate of analysis error for consecutive iterations is minimized.Based on this formulation,a new time step is found for the viscous dynamic relaxation.After combining this novel relationship with the other DRM factors,various geometrical nonlinear structures,such as trusses,frames,and shells,are analyzed.The obtained results verify the efficiency of authors'scheme.
文摘The analysis of cable structures is one of the most challenging problems for civil and mechanical engineers.Because they have highly nonlinear behavior,it is difficult to find solutions to these problems.Thus far,different assumptions and methods have been proposed to solve such structures.The dynamic relaxation method(DRM)is an explicit procedure for analyzing these types of structures.To utilize this scheme,investigators have suggested various stiffness matrices for a cable element.In this study,the efficiency and suitability of six well-known proposed matrices are assessed using the DRM.To achieve this goal,16 numerical examples and two criteria,namely,the number of iterations and the analysis time,are employed.Based on a comprehensive comparison,the methods are ranked according to the two criteria.The numerical findings clearly reveal the best techniques.Moreover,a variety of benchmark problems are suggested by the authors for future studies of cable structures.
文摘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.
