On Surface Constraints in Plate Problems

1962 ◽  
Vol 29 (2) ◽  
pp. 340-344 ◽  
Author(s):  
F. Essenburg
Keyword(s):  
Shear Deformation ◽  
Circular Plate ◽  
General Problem ◽  
Transverse Shear ◽  
Plate Theory ◽  
Transverse Shear Deformation ◽  
Rigid Surface ◽  
Paraboloid Of Revolution ◽  
Surface Constraints ◽  
Theory Solution

The general problem of an axisymmetric circular plate, partially constrained from deflection by a smooth, rigid surface of revolution, is considered and the Reissner plate-theory solution is obtained. A specific example involving a clamped circular plate, concentrically loaded by a paraboloid of revolution, illustrates the importance of the inclusion of the effect of transverse shear deformation (even in the case of a thin plate).

On the Significance of the Inclusion of the Effect of Transverse Normal Strain in Problems Involving Beams With Surface Constraints

1975 ◽  
Vol 42 (1) ◽  
pp. 127-132 ◽  
Author(s):  
F. Essenburg
Keyword(s):  
Shear Deformation ◽  
General Problem ◽  
Transverse Shear ◽  
Beam Theory ◽  
Transverse Shear Deformation ◽  
Normal Strain ◽  
Rectangular Section ◽  
Surface Constraints ◽  
Transverse Normal Strain

The general problem of a beam of rectangular section with displacement components prescribed over portions of its top and bottom surfaces is considered. A beam theory which includes the effect of transverse normal strain (as well as the effect of transverse shear deformation) is developed and the advantages of applying this theory to the class of problems considered is examined by means of an example.

PLASTIC BUCKLING OF MODERATELY THICK ANNULAR PLATES

2005 ◽  
Vol 05 (03) ◽  
pp. 337-357 ◽  
Author(s):  
TUN MYINT AUNG ◽  
C. M. WANG ◽  
J. CHAKRABARTY
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Plate Theory ◽  
Outer Radius ◽  
Stress Factors ◽  
Mindlin Plate ◽  
Transverse Shear Deformation ◽  
Plastic Buckling ◽  
Annular Plates ◽  
Buckling Stress

This paper is concerned with the plastic buckling of moderately thick annular plates under a uniform compressive stress state. The analysis is based on the incremental theory of plasticity which employs the Prandtl–Reuss equations and the plate material is assumed to obey the Ramberg–Osgood stress–strain relation. The effect of transverse shear deformation is taken into consideration by adopting the Mindlin plate theory. The governing differential equations for the plastic buckling problem are solved analytically and the plastic buckling stress factors for annular plates with the allowance of transverse shear deformation are presented for the first time. The influences of the boundary conditions, thickness to outer radius ratios, and inner to outer radius ratios on the buckling stress factors are also examined.

Nonlinear Responses of Rectangular Magnetoelectroelastic Plates with Transverse Shear Deformation

2016 ◽  
Vol 689 ◽  
pp. 103-107 ◽  
Author(s):  
Yu Fang Zheng ◽  
Tao Chen ◽  
Feng Wang ◽  
Chang Ping Chen
Keyword(s):  
Differential Equations ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Plate Theory ◽  
Nonlinear Differential Equations ◽  
Shear Deformation Theory ◽  
Transverse Shear Deformation ◽  
Algebraic Equations ◽  
Nonlinear Load ◽  
Magnetic Potentials

With employing the transverse shear deformation theory and von Karman plate theory, the nonlinear static behavior of a simply supported rectangular magnetoelectroelastic plates is investigated. According to the Maxwell’s equations, when applying the magnetoelectric load on the plate’s surfaces and neglecting the in-plane electric and magnetic fields in thin plates, the electric and magnetic potentials varying along the thickness direction of the magnetoelectroelastic plates are determined. The nonlinear differential equations for magnetoelectroelastic plates are established based on the Hamilton’s principle. The Galerkin procedure furnishes an infinite system of differential equations into algebraic equations. In the numerical calculations, the effects of the nonlinearity and span-thickness ratio on the nonlinear load-deflection curves and electric/magnetic potentials for magnetoelectroelastic plates are discussed.

On the Sandwich Plate Twist Test for Shear Testing

2008 ◽  
Author(s):  
F. Avile´s ◽  
L. A. Carlsson
Keyword(s):  
Shear Deformation ◽  
Correction Factor ◽  
Transverse Shear ◽  
Plate Theory ◽  
Transverse Shear Deformation ◽  
Element Analysis ◽  
Shear Correction Factor ◽  
The Core ◽  
The Face ◽  
Data Reduction Method

This work examines the viability of the sandwich twist (anticlastic) test as a means to determine the in-plane and transverse shear properties of the face sheets and core in sandwich materials through analysis and testing. The contribution of core transverse shear to the total compliance of the specimen is quantified for different material systems and the adequacy of classical laminated plate theory (CLPT) as a data reduction method for such a test is examined. Parametric studies are conducted using finite element analysis (FEA) to examine the influence of transverse shear deformation on the plate compliance and propose some guidelines for specimen design. It is shown that CLPT greatly underestimates the plate compliance, except when very stiff cores and compliant face sheets are used, as a result of transverse core shear deformation. A shear correction factor is proposed to correct the CLPT compliance for transverse shear deformation of the core. For sandwich panels with compliant cores, the shear correction factor may be used to determine transverse shear modulus of the core.

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