Error estimates for a sixth-order theory of plate bending

1987 ◽  
Vol 21 (4) ◽  
pp. 263-270 ◽  
Author(s):  
Z. Rychter
Keyword(s):  
Error Estimates ◽  
Order Theory ◽  
Sixth Order ◽  
Plate Bending

A Sixth-Order Plate Theory—Derivation and Error Estimates

1987 ◽  
Vol 54 (2) ◽  
pp. 275-279 ◽  
Author(s):  
Z. Rychter
Keyword(s):  
Plate Theory ◽  
Three Dimensional ◽  
Composite Plates ◽  
Order Theory ◽  
Sixth Order ◽  
Plate Bending ◽  
Mean Square ◽  
Reissner’S Theory ◽  
Elasticity Solutions ◽  
Admissible Solutions

Two consistent variants of a sixth-order theory for elastic plate bending are developed together with corresponding three-dimensional statically and kinematically admissible solutions. The relative mean square error of these solutions as compared with exact elasticity solutions is found to be proportional to the thickness squared in analogy with previous estimates for Reissner’s theory, but the contribution to the error governed by transverse shear deformability is reduced and shown to be of the order of the thickness cubed, this contribution being decisive in composite plates.

A posteriori error estimates for the Morley plate bending element

2007 ◽  
Vol 106 (2) ◽  
pp. 165-179 ◽  
Author(s):  
L. Beirão da Veiga ◽  
J. Niiranen ◽  
R. Stenberg
Keyword(s):  
Error Estimates ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Plate Bending ◽  
A Posteriori ◽  
A Posteriori Error

The secular variations in the restricted problem's sixth-order theory and stability: An explicit numerical approach

1990 ◽  
Vol 167 (1) ◽  
pp. 139-158 ◽  
Author(s):  
Catherine J. Flogaitis ◽  
V. S. Geroyannis ◽  
G. A. Antonacopoulos
Keyword(s):  
Numerical Approach ◽  
Order Theory ◽  
Sixth Order ◽  
Secular Variations

A Sixth-Order Theory of Shear Deformable Beams With Variational Consistent Boundary Conditions

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
Guangyu Shi ◽  
George Z. Voyiadjis
Keyword(s):  
Boundary Conditions ◽  
Fourth Order ◽  
Cross Sections ◽  
Beam Theory ◽  
Order Theory ◽  
Sixth Order ◽  
Equilibrium Equations ◽  
Flexible Beams ◽  
Generalized Displacements ◽  
Shear Deformable

This paper presents the derivation of a new beam theory with the sixth-order differential equilibrium equations for the analysis of shear deformable beams. A sixth-order beam theory is desirable since the displacement constraints of some typical shear flexible beams clearly indicate that the boundary conditions corresponding to these constraints can be properly satisfied only by the boundary conditions associated with the sixth-order differential equilibrium equations as opposed to the fourth-order equilibrium equations in Timoshenko beam theory. The present beam theory is composed of three parts: the simple third-order kinematics of displacements reduced from the higher-order displacement field derived previously by the authors, a system of sixth-order differential equilibrium equations in terms of two generalized displacements w and ϕx of beam cross sections, and three boundary conditions at each end of shear deformable beams. A technique for the analytical solution of the new beam theory is also presented. To demonstrate the advantages and accuracy of the new sixth-order beam theory for the analysis of shear flexible beams, the proposed beam theory is applied to solve analytically three classical beam bending problems to which the fourth-order beam theory of Timoshenko has created some questions on the boundary conditions. The present solutions of these examples agree well with the elasticity solutions, and in particular they also show that the present sixth-order beam theory is capable of characterizing some boundary layer behavior near the beam ends or loading points.

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