A serendipity cubic-displacement hybrid-stress element for thin and moderately thick plates

1981 ◽  
Vol 13 (4) ◽  
pp. 244
Keyword(s):  
Thick Plates ◽  
Hybrid Stress Element ◽  
Moderately Thick Plates ◽  
Hybrid Stress

scholarly journals A Refined Higher-Order Hybrid Stress Quadrilateral Element for Free Vibration and Buckling Analyses of Reissner-Mindlin Plates

2017 ◽  
Vol 2017 ◽  
pp. 1-33 ◽  
Author(s):  
Tan Li ◽  
Xu Ma ◽  
Wanji Chen ◽  
Xili Jing
Keyword(s):  
Free Vibration ◽  
Plate Theory ◽  
Mass Matrix ◽  
Higher Order ◽  
Buckling Analysis ◽  
Hybrid Stress Element ◽  
Moderately Thick Plates ◽  
Plate Analysis ◽  
Natural Frequency Analysis ◽  
Hybrid Stress

This paper is devoted to develop a new 8-node higher-order hybrid stress element (QH8) for free vibration and buckling analysis based on the Mindlin/Reissner plate theory. In particular, a simple explicit expression of a refine method with an adjustable constant is introduced to improve the accuracy of the analysis. A combined mass matrix for natural frequency analysis and a combined geometric stiffness matrix for buckling analysis are obtained using the refined method. It is noted that numerical examples are presented to show the validity and efficiency of the present element for free vibration and buckling analysis of plates. Furthermore, satisfactory accuracy for thin and moderately thick plates is obtained and it is free from shear locking for thin plate analysis and can pass the nonzero shear stress patch test.

Sharp Corner Functions for Mindlin Plates

2005 ◽  
Vol 72 (1) ◽  
pp. 1-9 ◽  
Author(s):  
O. G. McGee ◽  
J. W. Kim ◽  
A. W. Leissa
Keyword(s):  
Plate Theory ◽  
Thin Plates ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Transverse Displacement ◽  
Thick Plates ◽  
Thin Plate Theory ◽  
Mindlin Plate Theory ◽  
Moderately Thick Plates ◽  
Sharp Corners

Transverse displacement and rotation eigenfunctions for the bending of moderately thick plates are derived for the Mindlin plate theory so as to satisfy exactly the differential equations of equilibrium and the boundary conditions along two intersecting straight edges. These eigenfunctions are in some ways similar to those derived by Max Williams for thin plates a half century ago. The eigenfunctions are called “corner functions,” for they represent the state of stress currently in sharp corners, demonstrating the singularities that arise there for larger angles. The corner functions, together with others, may be used with energy approaches to obtain accurate results for global behavior of moderately thick plates, such as static deflections, free vibration frequencies, buckling loads, and mode shapes. Comparisons of Mindlin corner functions with those of thin-plate theory are made in this work, and remarkable differences are found.

A 4-noded hybrid stress element with optimized stress for moderately thick and thin shallow shells

2004 ◽  
Vol 40 (7) ◽  
pp. 691-709 ◽  
Author(s):  
Chengyu Zhang ◽  
Nong Zhang ◽  
Qigen Song ◽  
Shenglin Di
Keyword(s):  
Shallow Shells ◽  
Hybrid Stress Element ◽  
Hybrid Stress

Nonlinear stability of shear deformable eccentrically stiffened functionally graded plates on elastic foundations with temperature-dependent properties

2017 ◽  
Vol 24 (3) ◽  
pp. 455-469 ◽  
Author(s):  
Pham Hong Cong ◽  
Pham Thi Ngoc An ◽  
Nguyen Dinh Duc
Keyword(s):  
Nonlinear Stability ◽  
Geometrical Nonlinearity ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Temperature Dependent ◽  
Thick Plates ◽  
Geometrical Properties ◽  
Elastic Foundations ◽  
Moderately Thick Plates ◽  
Temperature Dependent Properties

AbstractThis article investigates the nonlinear stability of eccentrically stiffened moderately thick plates made of functionally graded materials (FGM) subjected to in-plane compressive, thermo-mechanical loads. The equilibrium and compatibility equations for the moderately thick plates are derived by using the first-order shear deformation theory of plates, taking into account both the geometrical nonlinearity in the von Karman sense and initial geometrical imperfections, temperature-dependent properties with Pasternak type elastic foundations. By applying the Galerkin method and using a stress function, the effects of material and geometrical properties, temperature-dependent material properties, elastic foundations, boundary conditions, and eccentric stiffeners on the buckling and post-buckling loading capacity of the eccentrically stiffened moderately thick FGM plates in thermal environments are analyzed and discussed.

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