Buckling Strength of Rectangular Plates with Elastically Restrained Edges Subjected to In-plane Impact Loading

2017 ◽  
pp. 233-240 ◽  
Author(s):  
B. Yang ◽  
D.Y. Wang
Keyword(s):  
Impact Loading ◽  
Rectangular Plates ◽  
Buckling Strength ◽  
Elastically Restrained Edges ◽  
Elastically Restrained

Buckling strength of rectangular plates with elastically restrained edges subjected to in-plane impact loading

2016 ◽  
Vol 231 (20) ◽  
pp. 3743-3752 ◽  
Author(s):  
Bin Yang ◽  
Deyu Wang
Keyword(s):  
Dynamic Response ◽  
Impact Loading ◽  
Time Integration ◽  
Double Fourier Series ◽  
Displacement Function ◽  
Dynamic Buckling ◽  
Rectangular Plates ◽  
Runge Kutta Method ◽  
Elastically Restrained Edges ◽  
Elastically Restrained

The dynamic buckling of rectangular plates with the elastically restrained edges subjected to in-plane impact loading is investigated. Budiansky–Hutchinson criterion is employed for calculation of dynamic buckling loads. The displacement function concluding the elastically restrained boundary condition is expressed as Navier’s double Fourier series. In order to solve the large deformation equations of plate, Galerkin method is applied. Also, the non-linear coupled time integration of the governing equation of plate is solved by using fourth-order Runge–Kutta method. The correctness of the method presented in the paper has been validated by comparing the results with the published literature. It is proved that the rotational restraint stiffness that is usually ignored by previous researchers plays an important role in dynamic response and dynamic buckling of the rectangular plates subjected to in-plane impact loading. Furthermore, the influence of the other parameters (initial imperfections, impact duration and geometric dimensions) on the dynamic response and dynamic buckling is studied in detail.

scholarly journals An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Xue Kai ◽  
Wang Jiufa ◽  
Li Qiuhong ◽  
Wang Weiyuan ◽  
Wang Ping
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Mindlin Plate ◽  
Rectangular Plates ◽  
Cross Sectional ◽  
Fourier Cosine ◽  
Cosine Series ◽  
The Matrix ◽  
Elastically Restrained Edges ◽  
Elastically Restrained

An analysis method is proposed for the vibration analysis of the Mindlin rectangular plates with general elastically restrained edges, in which the vibration displacements and the cross-sectional rotations of the mid-plane are expressed as the linear combination of a double Fourier cosine series and four one-dimensional Fourier series. The use of these supplementary functions is to solve the possible discontinuities with first derivatives at each edge. So this method can be applied to get the exact solution for vibration of plates with general elastic boundary conditions. The matrix eigenvalue equation which is equivalent to governing differential equations of the plate can be derived through using the boundary conditions and the governing equations based on Mindlin plate theory. The natural frequencies can be got through solving the matrix equation. Finally the numerical results are presented to validate the accuracy of the method.

An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges

2013 ◽  
Vol 572 ◽  
pp. 489-493 ◽  
Author(s):  
Kai Xue ◽  
Jiu Fa Wang ◽  
Qiu Hong Li ◽  
Wei Yuan Wang ◽  
Ping Wang
Keyword(s):  
Series Solution ◽  
Rectangular Plates ◽  
Analysis Method ◽  
Original Function ◽  
Cross Sectional ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Fourier Cosine Series ◽  
Elastically Restrained Edges ◽  
Elastically Restrained

An analysis method has been proposed for the vibration analysis of the Mindlin rectangular plates with general elastically boundary supports, in which the vibration displacements and the cross-sectional rotations of the mid-plane are sought as the linear combination of a double Fourier cosine series and auxiliary series functions. The use of these supplementary functions is to solve the potential discontinuity associated with the x-derivative and y-derivative of the original function along the four edges, so this method can be applied to get the exact solution. Finally the numerical results are presented to validate the correct of the method.

DSC ANALYSIS FOR BUCKLING AND VIBRATION OF RECTANGULAR PLATES WITH ELASTICALLY RESTRAINED EDGES AND LINEARLY VARYING IN-PLANE LOADING

2009 ◽  
Vol 09 (03) ◽  
pp. 511-531 ◽  
Author(s):  
S. K. LAI ◽  
Y. XIANG
Keyword(s):  
Numerical Stability ◽  
The Other ◽  
Rectangular Plates ◽  
Dsc Analysis ◽  
Vibration Problems ◽  
Discrete Singular Convolution ◽  
Dsc Method ◽  
Elastically Restrained Edges ◽  
Elastically Restrained ◽  
Two Sides

This paper presents the discrete singular convolution (DSC) method for solving buckling and vibration problems of rectangular plates with all edges transversely supported and restrained by uniform elastic rotational springs. The opposite plate edges are subjected to a linearly varying uni-axial in-plane loading. The rationale for using DSC method stems from its numerical stability and flexible implementation for structural analysis. To verify the present approach, convergence and comparison studies for rectangular plates with different combinations of elastically restrained and classical edges are carried out. Accurate buckling and vibration solutions of plates having two opposite edges elastically restrained and the other two sides clamped, or all edges elastically restrained are presented.

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