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The bending of flat plate structures with rectangular symmetry

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A collocation technique is used in conjunction with complex variable methods and conformal transformation to determine the elastic bending moments and shear forces in a uniformly loaded infinite flat plate structure, supported at each node of a regular rectangular lattice by rigid rectangular columns of finite dimensions.

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A n :

coefficients in the series solution of the deflection function

a, b :

lengths of slab panel sides

C :

edge of column capital

c 1, c 2 :

column side dimensions

D :

plate rigidity

f 1, f 2 :

functions defining the boundary conditions of the problem

k x , k y , kα :

numerical factors for bending moments

k′ :

value characterizing the aspect ratio of the column sides

k n :

parameters associated with complex potentials

m, n :

coefficients defining the mapping function

M x , M y :

bending moments in x and y directions

M ρ, M α :

radial and tangential bending moments

Q x , Q y :

shear forces

q :

uniformly distributed load acting on plate surface

R :

constant of the mapping function

r, φ :

polar coordinate system

S :

plate region in the (x, y) plane

w :

deflection function in the plate region

α n , β n :

parameters associated with the deflection functions

γ :

unit circle

ζ :

complex mapping plane

ρ, θ :

curvilinear coordinate system

μ :

Poisson's ratio of the slab material

φ(ζ), x (ζ), ψ(ζ), Φ(ζ), Ψ(ζ) :

complex potentials defining the deflection functions

σ :

value of ζ on the unit circle


mapping function


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Gupta, K.K. The bending of flat plate structures with rectangular symmetry. Appl. Sci. Res. 20, 115–130 (1969). https://doi.org/10.1007/BF00382387

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  • Shear Force
  • Variable Method
  • Flat Plate
  • Conformal Transformation
  • Finite Dimension