Numerical stability of dynamic relaxation analysis of non‐linear structures

Cassell, A. C.; Hobbs, R.E.

doi:10.1002/nme.1620100620

Cited by 78 publications

(38 citation statements)

References 8 publications

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“…Thus, at the beginning of the dynamic relaxation process, displacement should be equal to (31). On the other hand, under these conditions, Eq.…”

Section: Rezaiee-pajand and Taghavian Hakkak Techniquementioning

confidence: 97%

“…Where the vector of the residual force r n i is evaluated in the position X n− 1 2 i calculated from (31). Then, the iterations of dynamic relaxation restart with these displacement and velocity vectors in order to maximize the kinetic energy again.…”

Section: Rezaiee-pajand and Taghavian Hakkak Techniquementioning

confidence: 99%

“…Bunce presented a method for calculating critical damping in the dynamic relaxation tactic using Rayleigh principle [30]. Cassel and Hobbs estimated the artificial mass by using Gershgorin's circle theorem to check the convergence and numerical stability of nonlinear analysis with the dynamic relaxation scheme [31]. Papadrakakis suggested an automatic technique for finding the fictitious parameters.…”

Section: Introductionmentioning

confidence: 99%

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

Rezaiee‐Pajand

Estiri²

2016

Period. Polytech. Civil Eng.

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“…Thus, at the beginning of the dynamic relaxation process, displacement should be equal to (31). On the other hand, under these conditions, Eq.…”

Section: Rezaiee-pajand and Taghavian Hakkak Techniquementioning

confidence: 97%

Section: Rezaiee-pajand and Taghavian Hakkak Techniquementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Rezaiee‐Pajand

Estiri²

2016

Period. Polytech. Civil Eng.

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“…This may be attributed to the type of mesh used in each analysis. A set of thin plate results comparisons presented here with Rushton [2] who employed the DR method coupled with finite olifferences. The present results for simply supported (SS4) square plates were computed for two thickness ratios using a…”

Section: Verification Of the Numerical Techniquementioning

confidence: 99%

“…The DR method was first proposed in 1960s and then passed through a series of studies to verify its validity by Turvey and Osman Refs. [4], [8] and [9] and Rushton [2], Cassel and Hobbs [10], and Day [11]. In this method, the equations of equilibrium are converted to dynamic equations by adding damping and inertia terms.…”

Section: Introductionmentioning

confidence: 99%

Deflection of Laminated Composite Plates Using Dynamic Relaxation Method

Suleiman

2017

ijpse

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First -order orthotropic shear deformation equations for the nonlinearly elastic bending response of rectangular plates are introduced. Their solution using a computer program based on finite differences implementation of the Dynamic Relaxation (DR) method is outlined. The convergence and accuracy of the DR solutions for elastic large deflection response of isotropic, orthotropic, and laminated plates are established by comparison with various exact and approximate solutions. The present Dynamic Relaxation method (DR) coupled with finite differences method shows a fairly good agreement with other analytical and numerical methods used in the verification scheme. It was found that: The convergence and accuracy of the DR solution are dependent on several factors including boundary conditions, mesh size and type, fictitious densities, damping coefficients, time increment and applied load. Also, the DR large deflection program using uniform finite differences meshes can be employed in the analysis of different thicknesses for isotropic, orthotropic or laminated plates under uniform loads. All the comparison results for simply supported (SS4) edge conditions showed that deflection is almost dependent on the direction of the applied load or the arrangement of the layers. Keywords DeflectionIn plane, out of plane and rotational fictitious densities.Curvature and twist components of plate mid -plane IntroductionComposites were first considered as structural materials a little more than half a century ago. From that time to now, they have received increasing attention in all aspects of material science, manufacturing technology, and theoretical analysis.The term composite could mean almost any thing if taken at face value, since all materials are composites of dissimilar subunits if examined at close enough details. But in modern engineering materials, the term usually refers to a matrix material that is reinforced with fibers. For instance, the term "FRP" which refers to Fiber Reinforced plastic, usually indicates a thermosetting polyester matrix containing glass fibers, and this particular composite has the lion's share of today commercial market.In the present work, a numerical method known as Dynamic Relaxation (DR) coupled with finite differences is used. The DR method was first proposed in 1960s and then passed through a series of studies to verify its validity by Turvey and Osman Refs. . In this method, the equations of equilibrium are converted to dynamic equations by adding damping and inertia terms. These are then expressed in finite difference form and the solution is obtained through iterations. The optimum damping coefficient and time increment used to stabilize the solution depend on a number of factors including the matrix properties of the structure, the applied load, the boundary conditions and the size of the mesh used.Numerical techniques other than the DR include finite element method, which widely used in the present studies i.e. of Damodar R. Ambur et al [12], Ying Qing Huang et al [...

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Criteria for static equilibrium in particulate mechanics computations

Andrade

2008

Numerical Meth Engineering

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SUMMARYThe underlying physics of granular matter can be clearly solved using particulate mechanics methods, e.g. the discrete element method (DEM) that is inherently discontinuous and heterogeneous. To solve static problems, explicit schemes using dynamic relaxation procedures have been widely employed, in which naturally dynamic material parameters are typically adapted into pure numerical artifacts with the sole purpose of attaining meaningful results. In discrete computations using these explicit schemes, algorithmic calibration is demanded under general conditions in order to achieve quasi-static states. Until now, procedures for algorithmic calibration have remained rather heuristic. This paper presents two criteria, using the concept of homogenized stresses, for evaluating equilibrium in quasi-static applications of particulate mechanics methods. It is shown, by way of numerical examples, that the criteria for static equilibrium can be applied successfully to obtain quasi-static solutions in explicit DEM codes through algorithmic calibrations. A general procedure is proposed herein for carrying out the algorithmic calibration effectively and efficiently.

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Numerical stability of dynamic relaxation analysis of non‐linear structures

Cited by 78 publications

References 8 publications

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

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

Deflection of Laminated Composite Plates Using Dynamic Relaxation Method

Criteria for static equilibrium in particulate mechanics computations

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