Application of dynamic relaxation to the large deflection elasto-plastic analysis of plates

Frieze, P A; Hobbs, R.E.; Dowling, P J

doi:10.1016/0045-7949(78)90037-8

Cited by 34 publications

(8 citation statements)

References 8 publications

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“…In this study for the ultimate strength analysis of stiffened plates having initial shape and material imperfections, the dynamic relaxation (DR) technique (Day 1965;Frieze et al 1978) is adopted together with the finite element (FE) method as the basis of the developed analysis method. The procedure of the DR technique is straightforward and can also be employed in dynamic problems.…”

Section: Simplified Analysis Methodsmentioning

confidence: 99%

Ultimate strength formulation for stiffened plates subjected to combined axial compression, transverse compression, shear force and lateral pressure loadings

Cho

Kim

Doh

et al. 2013

Ships and Offshore Structures

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A robust ultimate strength formulation is proposed for stiffened plates subjected to combined axial compression, transverse compression, shear force and lateral pressure loadings. Before deriving the formulation, a simplified numerical method was developed to trace the structural behaviour of stiffened plates under combined loadings. A rigorous parametric study was then performed using the developed numerical method to predict the ultimate strength of various stiffened plates under various combinations of loadings. The formulation was derived by a regression study using the parametric study results. The accuracy and reliability of the proposed formulation were compared with those of commercial packages, such as ABAQUS and DNV PULS, and experimental results.

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Section: Simplified Analysis Methodsmentioning

confidence: 99%

Ultimate strength formulation for stiffened plates subjected to combined axial compression, transverse compression, shear force and lateral pressure loadings

Cho

Kim

Doh

et al. 2013

Ships and Offshore Structures

View full text Add to dashboard Cite

show abstract

“…e Dynamic Relaxation (DR) method is a way of finding the equilibrium solution for the static problem through the damping effect of the dynamic system. Since the method was proposed in the 1960s [1,2], it has been improved and applied in many fields [3][4][5], especially in structural mechanics such as plate analysis [6][7][8], frame and truss analysis [9], cable membrane structures [10][11][12], actively bent structures [13,14], and postbuckling analysis [15]. Recently, Rezaiee-Pajand et al [16] made a good summary in the structural applications of DR.…”

Section: Introductionmentioning

confidence: 99%

Implementation of Complex Position Constraints in the Kinetic Dynamic Relaxation Method

Liu

You

Han

2020

Mathematical Problems in Engineering

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The traditional Kinetic Dynamic Relaxation (KDR) method can only deal with simple constraints such as the fixed joints, which restricts its practical applications. This study has proposed a new algorithm to implement the complex position constraints in KDR. The proposed algorithm is developed by transforming the position constraints to the acceleration form through combining time differentiation and Taylor expansion with dimensional analysis, and then solving the governing equation of the constraint forces with the Newton’s 2nd law. For the nonlinear constraints, projection technique is applied to avoid the drift-off phenomenon. Several tests have been performed to verify the proposed algorithm. The numerical results show the algorithm is adaptive in both linear and nonlinear problems and works efficiently.

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“…For the solution of the governing equations of a structural system, several studies on nonlinear structural analysis have been done especially for large deflections of plates using the iterative Dynamic Relaxation (DR) method [11][12][13][14] with finite difference discritization. The second author has examined fiber reinforced laminated sector plates [15] with symmetric layer arrangements employing DR method.…”

mentioning

confidence: 99%

Nonlinear Viscoelastic Response of Unidirectional Polymeric Laminated Composite Plates Under Bending Loads

Falahatgar

Salehi

2011

Appl Compos Mater

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Nonlinear bending analysis of polymeric laminated composite plate is examined considering material nonlinearity for viscoelastic matrix material through a Micro-macro approach. The micromechanical Simplified Unit Cell Method (SUCM) in three-dimensional closed-form solution is used for the overall behavior of the unidirectional composite in any combination of loading conditions. The elastic fibers are transversely isotropic where Schapery single integral equation in multiaxial stress state describes the matrix material by recursive-iterative formulation. The finite difference Dynamic Relaxation (DR) method is utilized to study the bending behavior of Mindlin annular sector plate including geometric nonlinearity under uniform lateral pressure with clamped and hinged edge constraints. The unsymmetrical laminated plate deflection is predicted for different thicknesses and also various pressures in different time steps and they are compared with elastic finite element results. As a main objective, the deflection results of viscoelastic laminated sector plate are obtained for various fiber volume fractions in the composite system.

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Application of dynamic relaxation to the large deflection elasto-plastic analysis of plates

Cited by 34 publications

References 8 publications

Ultimate strength formulation for stiffened plates subjected to combined axial compression, transverse compression, shear force and lateral pressure loadings

Ultimate strength formulation for stiffened plates subjected to combined axial compression, transverse compression, shear force and lateral pressure loadings

Implementation of Complex Position Constraints in the Kinetic Dynamic Relaxation Method

Nonlinear Viscoelastic Response of Unidirectional Polymeric Laminated Composite Plates Under Bending Loads

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