Nonlinear bending analysis of thin circular plates by differential quadrature

Striz, Alfred G.; Jang, S. K.; Bert, Charles W.

doi:10.1016/0263-8231(88)90025-0

Cited by 90 publications

(37 citation statements)

References 15 publications

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“…By assuming free vibration with frequency o for the curved panel and using equations (14), equations (12) are transformed to algebraic equations as…”

Section: Modified Relationshipsmentioning

confidence: 99%

“…The DQM first introduced by Bellman and Casti [10] is an efficient numerical method for rapid solutions of linear and non-linear partial differential equations. Bert et al [11][12][13] applied this method to structural problems involving fourth order partial differential equations. Since then, many researchers have applied this method in many engineering areas.…”

Section: Introductionmentioning

confidence: 98%

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Vibration Analysis of Non-Circular Curved Panels by the Differential Quadrature Method

Choi

Chou

2003

Journal of Sound and Vibration

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“…By assuming free vibration with frequency o for the curved panel and using equations (14), equations (12) are transformed to algebraic equations as…”

Section: Modified Relationshipsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Vibration Analysis of Non-Circular Curved Panels by the Differential Quadrature Method

Choi

Chou

2003

Journal of Sound and Vibration

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“…In addition the solutions are limited by the basic von Karman assumptions of small strains and rotations. A theory for axisymmetric deformation under arbitrarily large strains and rotations was developed by Brodland (1988) Striz, Jang and Bert (1988) who considered both uniform pressure and point loads on rigidly clamped and simply supported plates.…”

Section: Large Deflection Plate Solutionsmentioning

confidence: 99%

“…References for Table 3.1 1) Volmir (1962) 2) Banerjee (1983) 3) Ferriss (1991) 4) Bert and Martindale (1988), w/h=1 5) Way (1934), w/h=l1 6) Schmidt (1987), w/h=1 7) Dolovich, Brodland and Thornton-Trump (1988), w/h=1 8) Striz, Jang and Bert (1988), FEM-analysis, w/h=1 9) Eq. (3.76), Saibel and Tadjbaksh (1960) 10) Eq.…”

Section: D) Edges In Sliding Hingesmentioning

confidence: 99%

Simplified theory for contact indentation of sandwich panels

Olsson¹,

Manus²

1995

36th Structures, Structural Dynamics and Materials Conference

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Previous attempts to analyze indentation of sandwich panels have been based on small deflection theory and an assumed elastic core behaviour. The agreement with experiments was poor. The present work includes core crushing and large deflections of the face sheets in a simplified model of sandwich contact indentation. The model assumes transverse isotropy with respect to the load axis and is based on an infinite, elastic face sheet on a core bonded to a rigid foundation. The core is assumed to be elastic in tension and elastic-ideally plastic in compression. After initiation of core yielding the problem is separated in two regions. In the inner, plastic region, the core has yielded and exert a constant reactive pressure on the face sheet. In the outer region the core acts as an elastic foundation. The plastic radius is found by matching boundary conditions for the two regions.The outer region is modeled as a plate on an elastic foundation. The inner region is modeled using three different approaches. For small deflections classical plate theory with shear corrections is used. For intermediate deflections an upper limit of the contact force is given by first order large deflection plate theory and a lower limit by small deflection plate theory. The asymptotic behaviour at large deflections is given by an approximate solution based on membrane theory. The three solutions, which all require iteration, have been put in dimensionless form and tabulated. The approach due to Hertzian contact has been included in the plate solution. Bounds have been given for the residual indentation after unloading. Approximate expressions are given for analysis of orthotropic face sheets.Good agreement with experiments was found for sandwich panels of different materials and thickness. The often observed, approximately linear, load-indentation relation is found to be the combined effect of softening due to core crushing and stiffening due to face sheet membrane effects. A limited parametric study indicates a strong influence of the core yield stress and the face sheet properties, and a relatively weak influence of the thickness and elastic properties of the core. The local indentation model may be used in a global impact model to predict impact response of sandwich panels, or as a starting point for more detailed stress analyses for prediction of damage due to impact and contact loads.

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“…were the first to apply the DQ method to structural mechanics problems. Subsequently, a number of researchers utilized this method to solve a variety of structural problems relevant to thin plate theory [Striz et al 1988;Bert et al 1989;Sherbourne and Pandey 1991]. A bending analysis of thin/thick laminated plates with various boundary conditions based on first-order shear deformation theory was described in [Aghdam et al 2006].…”

Section: Introductionmentioning

confidence: 99%

Bending of laminated plates with mixed boundary conditions based on higher-order shear deformation theory

Yaghoubshahi

Rajaie

2010

JOMMS

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The bending of laminated plates is considered using higher-order transverse shear deformation theory. The principle of virtual work is used to derive a new set of seven governing equations and corresponding boundary conditions. These equations, combined with eighteen relationships between the resultant stress and displacement components, compose a system of first-order partial differential equations that is solved by the generalized differential quadrature method. Numerical results for laminated plates with a variety of mixed boundary conditions are calculated using the proposed method, and good agreement is found with the corresponding solutions obtained using ANSYS.

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Nonlinear bending analysis of thin circular plates by differential quadrature

Cited by 90 publications

References 15 publications

Vibration Analysis of Non-Circular Curved Panels by the Differential Quadrature Method

Vibration Analysis of Non-Circular Curved Panels by the Differential Quadrature Method

Simplified theory for contact indentation of sandwich panels

Bending of laminated plates with mixed boundary conditions based on higher-order shear deformation theory

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