On the use of bubble functions in the local buckling analysis of plate structures by the spline finite strip method

Azhari, Mojtaba; Hoshdar, Sina; Bradford, Mark A.

doi:10.1002/(sici)1097-0207(20000610)48:4<583::aid-nme898>3.0.co;2-a

Cited by 29 publications

(5 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The buckling loads for the square plate of thickness-to-length ratios h/b = 0.01 (moderate thick plate) and h/b = 0.01 (thin plate) with simply supported and clamped boundaries are computed and the results are given in Table III. The present results are again in close agreement with the available analytical [16,17] and numerical solutions [18]. The buckling loads of plate that is subjected to uniaxial in-plane loads are between those of the plate that is subjected to pure shear loads and biaxial in-plane loads.…”

Section: Buckling Of Rectangular Mindlin Plates Subjected To Uniform supporting

confidence: 90%

Mesh‐free radial point interpolation method for the buckling analysis of Mindlin plates subjected to in‐plane point loads

Liew¹,

Chen²

2004

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYIn this paper, a mesh-free approach is employed for buckling analysis of Mindlin plates that are subjected to in-plane point loads. The radial point interpolation method (RPIM) is used to approximate displacements based on nodes. Variational forms of the system equations are established. Two-step solution procedures are implemented. The non-uniform pre-stress distribution of plate is first obtained using the RPIM based on a two-dimensional (2D) elastic plane stress problem. This predetermined non-uniform pre-stress distribution is then used to compute buckling loads of plate using the RPIM based on Mindlin's plate assumption. The RPIM can easily handle any number and location of nodes in the plate domain for a desired computational accuracy without major difficulties in solving the initial stresses and buckling loads. Numerical examples considered here include circular and rectangular Mindlin plates that are subjected to in-plane uniform and point loads with different aspect ratios and boundary conditions. The present results are validated against the available analytical and numerical solutions.

show abstract

Section: Buckling Of Rectangular Mindlin Plates Subjected To Uniform supporting

confidence: 90%

Mesh‐free radial point interpolation method for the buckling analysis of Mindlin plates subjected to in‐plane point loads

Liew¹,

Chen²

2004

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…To this end, the same method but with the modifications needed for the buckling and free vibration analysis is used. The interpolation in the transverse direction is augmented utilizing the Legendre bubble functions, which has been shown to improve the convergence of the SFSM in terms of the strip subdivision and consequently faster eigenvalue extraction .…”

Section: Generalized Reproducing Kernel Particle Finite Strip Methodsmentioning

confidence: 99%

“…Azhari et al . augmented the conventional finite strip by adopting a new set of transverse functions, termed bubble functions, in addition to the usual cubic functions. These shape functions are

({, \begin{matrix} N_{1} = 1 - 3 {\overset{true¯}{y}}^{2} + 2 {\overset{true¯}{y}}^{3} \\ N_{2} = y (1 - 2 \overset{true¯}{y} + {\overset{true¯}{y}}^{2}) \\ N_{3} = (3 {\overset{true¯}{y}}^{2} - 2 {\overset{true¯}{y}}^{3}) \\ N_{4} = y ({\overset{true¯}{y}}^{2} - \overset{true¯}{y}) \\ N_{5} = \frac{A}{2^{2 n}} {\overset{true¯}{y}}^{n} {(1 - \overset{true¯}{y})}^{n} n = 2, 3, \dots, \end{matrix})

where

\overset{y}{false} = y / b

and in which b isthe width of the strip, and N 5 denotes the incorporated bubble functions.…”

Section: Generalized Reproducing Kernel Particle Finite Strip Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Application of RKP‐FSM in the buckling and free vibration analysis of thin plates with abrupt thickness changes and internal supports

Khezri

Bradford

Vrcelj

2015

Numerical Meth Engineering

View full text Add to dashboard Cite

A description is given of the development and use of the Reproducing Kernel Particle Finite Strip Method for the buckling and flexural vibration analysis of plates with intermediate supports and step thickness changes. The generalized 1-D shape functions of the Reproducing Kernel Particle Method replace the spline functions in the conventional spline finite strip method in the longitudinal direction. The structure of the generalized Reproducing Kernel Particle Method makes it a suitable tool for dealing with derivative-type essential boundary conditions, and its introduction in the finite strip method is beneficial for solving buckling and vibration problems for thin plates in which a number of the essential boundary conditions can include the first derivatives of the displacement function. Moreover, the modified corrected collocation method is further developed for the buckling and free vibration analysis of plates with abrupt thickness changes. This provides a versatile and powerful analysis capability which facilitates the analysis of problems including plate structures with abrupt thickness changes of its component plates. The application of the proposed technique for the treatment of discontinuities and the enforcement of the internal support conditions are illustrated with a series of numerical examples.

show abstract

“…Finite strip method is a modified finite element method introduced by Cheung and has been obtained by discretizing the plate into some finite strips [8]. Bradford and Azhari investigated the buckling of plates with different end conditions using the finite strip method [9].Azhari et al applied the spline finite strip method augmented by the bubble functions for elastic analysis of rectangular plates to show that efficiently improves the convergence of the spline finite strip method with respect to strip subdivision [10]. Lotfi et al studied the inelastic local buckling of skew thin thickness-tapered plates using Spline finite strip method [11].…”

Section: Introductionmentioning

confidence: 99%

Mechanical Buckling of Thick Composite Plates Reinforced with Randomly Oriented, Straight, Single-Walled Carbon Nanotubes Resting on an Elastic Foundation using the Finite Strip Method

Foroughi

Askariyeh

Azhari

2013

J. Nanomech. Micromech.

View full text Add to dashboard Cite

This paper is devoted to the buckling analysis of thin composite plates under straight single-walled carbon nanotubes reinforcement with uniform distribution and random orientations. In order to develop the fundamental equations, the B3-Spline finite strip method along with the classical plate theory (CPT) is employed and the total potential energy is minimized which leads to an eigenvalue problem. For deriving the effective modulus of thin composite plates reinforced with carbon nanotubes, the Mori-Tanaka method is used in which each straight carbon nanotube is modeled as a fiber with transversely isotropic elastic properties. The numerical results including the critical buckling loads for rectangular thin composite plates reinforced by carbon nanotubes with various boundary conditions and different volume fractions of nanotubes are provided and the positive effect of using carbon nanotubes reinforcement in buckling of thin plates is illustrated.

show abstract

On the use of bubble functions in the local buckling analysis of plate structures by the spline finite strip method

Cited by 29 publications

References 14 publications

Mesh‐free radial point interpolation method for the buckling analysis of Mindlin plates subjected to in‐plane point loads

Mesh‐free radial point interpolation method for the buckling analysis of Mindlin plates subjected to in‐plane point loads

Application of RKP‐FSM in the buckling and free vibration analysis of thin plates with abrupt thickness changes and internal supports

Mechanical Buckling of Thick Composite Plates Reinforced with Randomly Oriented, Straight, Single-Walled Carbon Nanotubes Resting on an Elastic Foundation using the Finite Strip Method

Contact Info

Product

Resources

About