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.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
- 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 :
- 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 :
- 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 :
- 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
Woinowsky-Krieger, S., J. Appl. Mech. 21 (1954) 263.
Girkman, K., Flächentragwerke, p. 284, Springer, Vienna 1963.
Tolke, F., Ingenieur Archiv 5 (1934) 187.
Savin, G. N., Stress Concentration around Holes, Pergamon Press, Oxford 1961.
Muskhelishvili, N. I., Some basic problems of the mathematical theory of elasticity, Noordhoff, Groningen (Holland) 1963.
Sokolnikoff, I. S., Mathematical theory of elasticity, McGraw-Hill, New York 1956.
Gupta, K. K., Distribution of elastic moments in flat slabs with particular reference to Lift slab structures. Doctoral thesis, London University, London 1965.
Gupta, K. K. and R. C. Vaughan, J. Strain Anal. 2 (1967) 109.
Timoshenko, S. P. and S. Woinowsky-Krieger, Theory of Plates and Shells, Second Edition, p. 249, McGraw-Hill, New York 1959.
About this article
Cite this article
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
- Shear Force
- Variable Method
- Flat Plate
- Conformal Transformation
- Finite Dimension