On the Bergan‐Wang approach for moderately thick plates

Abstract

SUMMARYThe Bergan-Wang approach for the transverse shear inclusion in thin and moderately thick plate deformation has led to an energy expression which is a function of the only lateral deflection. The corresponding Euler equation is an eighth-order partial differential equation. A variety of examples has been analysed. Analytical solutions have been presented for different thickness to span ratios under different boundary conditions. Results show very close resemblance to solutions based on Reissner plate theory.

Finite Elements for the One Variable Version of Mindlin-Reissner Plate

“…Finally, the strain energy expression per unit area, which is the sum of bending energy and shear energy according to Bergan and Wang approach [10,11], can be written as:…”

“…P.G. Bergan and X. Wang [10] H. Abdalla and K. Hassan [11] have employed an approximation that have led to general expressions of rotations of the normal as functions of displacement. Therefore, the strain energy is function of only one variable .…”

Bergan-Wang Solution of Clamped Moderately Thick Rectangular Plates

“…As a matter of fact, such a choice is a very severe clamping which cannot be realized in practice. Therefore, the boundary conditions were proposed to be; zero values for w , , and [10]. Such a choice has fortunately been fulfilled by the series given in…”

“…The difficulties of Bergan-Wang approach are the high order of the partial differential equation and the increased number of boundary conditions. A closed form solution for the case of simply supported square plate is given in [10] for different loadings. The clamped boundary conditions are more difficult [2].…”