The purpose of this study is to propose generalised integral transform technique (GITT) to obtain the exact solutions for bending of clamped parallelogram plate resting on elastic foundation.
The GITT is used to solve the bending problem of the full clamped parallelogram plate under an elastic foundation. The auxiliary problem was developed and the corresponding eigenfunction and eigenvalue were calculated simultaneously. The original partial differential governed equation has been represented by the transformed ordinary differential equation system and solved by the subroutine DBVPFD from International Mathematics and Statistics Library.
The GITT has been proven to be an efficient approach to solve the bending problem of the plate with different loads, boundary conditions and elastic foundations. The parametric study indicates that the elastic foundation modulus has significant contribution in reducing the vertical deflections and moments for both rectangular and parallelogram plates. With the increasing of aspect ratio (a/b) and the elastic foundation modulus, the trends of the deflection and moment reduction decreased significantly.
The present hybrid analytical-numerical methodology was first used to solve the mechanics problem of the clamped parallelogram plate resting on elastic foundation. Excellent convergence and high accuracy was observed by comparing with the published results. It exhibits potential application to investigate the mechanics problem of the composite plate with different boundary conditions in the shipbuilding and civil engineering.
This work was supported by the National Natural Science Foundation of China [51709269, 51890914], Natural Science Foundation of Shandong [ZR2217BEE031, JQ201716]. Guangming Fu specially acknowledges the financial support from the Fundamental Research Funds for the Central Universities [17CX02013A], the Open Project Program of Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deepwater Oil and Gas Development [BIPT2018003] and the Scientific Research Common Program of Beijing Municipal Commission of Education [KM201610017002].
Fu, G., Peng, Y., Sun, B., An, C. and Su, J. (2019), "An exact GITT solution for static bending of clamped parallelogram plate resting on an elastic foundation", Engineering Computations, Vol. 36 No. 6, pp. 2034-2047. https://doi.org/10.1108/EC-12-2018-0582
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