9 research outputs found
A new fictitious time for the dynamic relaxation (DXDR) method
No full textThis paper addresses the development of the DXDR method by introducing a modified fictitious time (MFT) increment. The MFT is determined by minimizing the residual force after each iteration. The rank of the convergence rate shows the advantage of the new method. The results obtained from plate and truss analyses demonstrate the potential of the new method. It is shown that, compared with a unit fictitious time, the MFT is more efficient, especially during the initial iterations. Moreover, MFT does not impose any additional constraints on the DXDR method
A NEW FORMULATION FOR KINETIC DYNAMIC RELAXATION METHOD BASED ON LAGRANGIAN INTERPOLATION
No full textIn this paper, a new algorithm is presented for Dynamic Relaxation (DR) method
with kinetic damping. In the kinetic dynamic relaxation algorithm, some successive points with maximum kinetic energy are traced in the course of numerical fictitious time integration. In the absence of damping forces, the points with maximum kinetic energy are close to the static equilibrium position of structure. This paper deals with a new formulation for kinetic DR method. For this purpose, Lagrangian interpolation functions were utilized to derive iterative Dynamic Relaxation equations. In the Lagrangian interpolation functions, new estimation of structural displacement vector was obtained based on previous estimations of displacement vector. Therefore, this procedure leads to adopting a trial and error method. On the other hand, this procedure leads to a new formulation that, unlike the ubiquitous DR methods, does not require the calculation of nodal velocities, thereby marching forward only through successive nodal displacement. Elimination the nodal velocities from Dynamic Relaxation process increases the simplicity of DR algorithm. Moreover, the requirement analysis memory is reduced using the suggested technique so that velocity vectors would not be stored in the program memory. Also, the power iteration method was used to determine the optimal time step ratio. By utilizing this time step, the restarting analysis phase, considered as one of the drawbacks of the common kinetic DR strategies, is eliminated. To evaluate the performance and efficiency of the proposed method, several truss and frame structures were analyzed. These structures had geometrically nonlinear behavior (Large Deflection). Results of these analyses were also compared with those of other conventional Dynamic Relaxation methods. Numerical results showed that the convergence rate of the proposed kinetic DR technique was higher than that of common DR algorithms. In other words, the number of the required DR iterations for convergence was reduced using the proposed DR algorithm in comparison with other DR schemes. Moreover, the analysis time of the proposed method was shorter than that of other common techniques
Semi-explicit Unconditionally Stable Time Integration method based on Generalized-α technique
No full textIn structural dynamic analysis, various time integration techniques have been proposed. Generally, these algorithms discretize the time domain into a finite number of intervals and approximate the displacements, velocities, and accelerations via mathematical expressions at each time increment. Based on the structure of these approximations, time integration schemes are classified as explicit and implicit. Explicit schemes are much simpler and often march forward only through pure vector operations. On the other hand, implicit strategies require more computational efforts especially in nonlinear behaviors since they involve solving a system of simultaneous equations at each time step using iterative techniques. Although computationally more expensive, implicit schemes are unconditionally stable, meaning that the growth of solution errors at each time increment remains bounded. On the contrary, explicit techniques suffer from instabilities which manifest as unrealistic growth of amplitude of the responses. To overcome this issue, time step size should be chosen small enough to meet the stability criterion. In this paper, by gathering the advantages of both approach, a new semi-explicit unconditionally stable time integration method based on the well-known implicit Generalized-α (G-α) technique is proposed. To this end, first, the fundamental approximating relationships of the suggested method is introduced for a single degree of freedom system with the unknown integration parameters. Then, using the concept of amplification matrix, these unknown parameters are determined so that the method possesses the same characteristic equation as the G-α technique. This leads to a set of model-dependent integration parameters that are no longer scalar constants. Due to this kind of formulation, similar stability and accuracy behavior are observed when comparing the proposed method with the G-α technique, both analytically and numerically. After generalization of the proposed algorithm to the multi-degree of freedom systems, some numerical examples are solved and comparisons are also made with other similar time integration schemes. Findings reveal the merits of the proposed algorithm over the other well-known time stepping techniques
Numerical time integration for dynamic analysis using a new higher order predictor‐corrector method
No full textNonlinear bending analysis of variable cross-section laminated plates using the dynamic relaxation method
No full text
A DXDR large deflection analysis of uniformly loaded square, circular and elliptical orthotropic plates using non-uniform rectangular finite-differences
No full textA finite-difference analysis of the large deflection response of uniformly loaded square, circular and elliptical clamped and simply-supported orthotropic plates is presented. Several types of non-uniform (graded) mesh are investigated and a mesh suited to the curved boundary of the orthotropic circular and elliptical plate is identified. The DXDR method-a variant of the DR (dynamic relaxation) method-is used to solve the finite-difference forms of the governing orthotropic plate equations. The DXDR method and irregular rectilinear mesh are combined along with the Cartesian coordinates to treat all types of boundaries and to analyze the large deformation of non-isotropic circular/elliptical plates. The results obtained from plate analyses demonstrate the potential of the non-uniform meshes employed and it is shown that they are in good agreement with other results for square, circular and elliptical isotropic and orthotropic clamped and simply-supported plates in both fixed and movable cases subjected to transverse pressure loading
