Uniformly loaded, simply supported, antisymmetrically laminated, rectangular plate on a winkler-pasternak foundation

1977 ◽  
Vol 13 (5) ◽  
pp. 437-444 ◽  
Author(s):  
G.J. Turvey
Keyword(s):  
Rectangular Plate ◽  
Pasternak Foundation ◽  
Simply Supported

Large Deflection of a Rectangular Plate Resting on a Pasternak-Type Elastic Foundation

1977 ◽  
Vol 44 (3) ◽  
pp. 509-511 ◽  
Author(s):  
P. K. Ghosh
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Large Deflection ◽  
Lateral Load ◽  
Bending Moments ◽  
Shear Forces ◽  
Simply Supported ◽  
Base Parameters ◽  
Square Plate

The problem of large deflection of a rectangular plate resting on a Pasternak-type foundation and subjected to a uniform lateral load has been investigated by utilizing the linearized equation of plates due to H. M. Berger. The solutions derived and based on the effect of the two base parameters have been carried to practical conclusions by presenting graphs for bending moments and shear forces for a square plate with all edges simply supported.

A Quasi-Greens Function Method for the Bending Problem of Simply Supported Polygonal Shallow Spherical Shells on Pasternak Foundation

2013 ◽  
Vol 353-356 ◽  
pp. 3215-3219
Author(s):  
Shan Qing Li ◽  
Hong Yuan
Keyword(s):  
Function Method ◽  
Homogeneous Boundary Condition ◽  
Fredholm Integral Equations ◽  
Pasternak Foundation ◽  
Boundary Equation ◽  
Spherical Shells ◽  
Simply Supported ◽  
Suitable Form ◽  
Greens Function ◽  
Good Agreement

The quasi-Greens function method (QGFM) is applied to solve the bending problem of simply supported polygonal shallow spherical shells on Pasternak foundation. A quasi-Greens function is established by using the fundamental solution and the boundary equation of the problem. And the function satisfies the homogeneous boundary condition of the problem. Then the differential equation of the problem is reduced to two simultaneous Fredholm integral equations of the second kind by the Greens formula. The singularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The comparison with the ANSYS finite element solution shows a good agreement, and it demonstrates the feasibility and efficiency of the proposed method.

Analysis of a simply supported laminated anisotropic rectangular plate

AIAA Journal ◽  
1970 ◽  
Vol 8 (1) ◽  
pp. 28-33 ◽  
Author(s):  
J. M. WHITNEY ◽  
A. W. LEISSA
Keyword(s):  
Rectangular Plate ◽  
Simply Supported

Bending of a Uniformly Loaded Rectangular Plate With Two Adjacent Edges Clamped and the Others Either Simply Supported or Free

1952 ◽  
Vol 19 (4) ◽  
pp. 451-460
Author(s):  
M. K. Huang ◽  
H. D. Conway
Keyword(s):  
Rectangular Plate ◽  
Bending Moment ◽  
Simply Supported

Abstract The distribution of deflection and bending moment in a uniformly loaded rectangular plate having two adjacent edges clamped and the others either simply supported or free, are obtained by a method of superposition. Numerical values are given for square plates and, in one case, the results are compared with those obtained by another method.

A Levy-Type Solution for a Rectangular Plate of Variable Thickness

1958 ◽  
Vol 25 (2) ◽  
pp. 297-298
Author(s):  
H. D. Conway
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Variable Thickness ◽  
Thickness Variation ◽  
Type Solution ◽  
Arbitrary Boundary ◽  
Simply Supported ◽  
Arbitrary Boundary Conditions ◽  
Plate Of Variable Thickness

Abstract A solution is given for the bending of a uniformly loaded rectangular plate, simply supported on two opposite edges and having arbitrary boundary conditions on the others. The thickness variation is taken as exponential in order to make the solution tractable, and thus closely approximates to uniform taper if the latter is small.

Shear Buckling of Simply-Supported Rectangular Elastic Plate

1964 ◽  
Vol 68 (647) ◽  
pp. 773-773
Author(s):  
Bertrand T. Fang
Keyword(s):  
Rectangular Plate ◽  
Elastic Plate ◽  
Critical Loads ◽  
Nontrivial Solutions ◽  
Simply Supported ◽  
Shear Buckling ◽  
Rectangular Elastic Plate ◽  
Image Position

The equation for the buckling of a homogeneous elastic plate is well known For a simply-supported rectangular plate without shear (Nxy=0), the critical loads are usually found by substituting into equation (1) and determining the loads at which nontrivial solutions exist. In the presence of shear, however, the difficulty with the above approach is that the shear term would involve cosines instead of sines.

Three alternative versions of the theory for a Timoshenko–Ehrenfest beam on a Winkler–Pasternak foundation

2020 ◽  
pp. 108128652094777
Author(s):  
Giulio Maria Tonzani ◽  
Isaac Elishakoff
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Detailed Comparison ◽  
Vibration Frequencies ◽  
Pasternak Foundation ◽  
New Model ◽  
Simply Supported ◽  
Model Based

This paper analyzes the free vibration frequencies of a beam on a Winkler–Pasternak foundation via the original Timoshenko–Ehrenfest theory, a truncated version of the Timoshenko–Ehrenfest equation, and a new model based on slope inertia. We give a detailed comparison between the three models in the context of six different sets of boundary conditions. In particular, we analyze the most common combinations of boundary conditions deriving from three typical end constraints, namely the simply supported end, clamped end, and free end. An interesting intermingling phenomenon is presented for a simply-supported (S-S) beam together with proof of the ‘non-existence’ of zero frequencies for free-free (F-F) and simply supported-free (S-F) beams on a Winkler–Pasternak foundation.

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